source: anuga_core/documentation/user_manual/anuga_user_manual.tex @ 5672

Last change on this file since 5672 was 5672, checked in by ole, 16 years ago

Tested for bug where default_boundry was repeatedly added to by Field_boundary.
Fixed bug and updated manual accordingly.

This closes ticket:293

  • Property svn:keywords set to LastChangedDate LastChangedRevision LastChangedBy HeadURL Id
File size: 176.7 KB
Line 
1% Complete documentation on the extended LaTeX markup used for Python
2% documentation is available in ``Documenting Python'', which is part
3% of the standard documentation for Python.  It may be found online
4% at:
5%
6%     http://www.python.org/doc/current/doc/doc.html
7
8
9%labels
10%Sections and subsections \label{sec: }
11%Chapters \label{ch: }
12%Equations \label{eq: }
13%Figures \label{fig: }
14
15% Is latex failing with;
16% `modanuga_user_manual.ind' not found?
17% try this command-line
18%   makeindex modanuga_user_manual.idx
19% To produce the modanuga_user_manual.ind file.
20
21
22\documentclass{manual}
23
24\usepackage{graphicx}
25\usepackage{datetime}
26
27\input{definitions}
28
29\title{\anuga User Manual}
30\author{Geoscience Australia and the Australian National University}
31
32% Please at least include a long-lived email address;
33% the rest is at your discretion.
34\authoraddress{Geoscience Australia \\
35  Email: \email{ole.nielsen@ga.gov.au}
36}
37
38%Draft date
39
40% update before release!
41% Use an explicit date so that reformatting
42% doesn't cause a new date to be used.  Setting
43% the date to \today can be used during draft
44% stages to make it easier to handle versions.
45
46
47\longdate       % Make date format long using datetime.sty
48%\settimeformat{xxivtime} % 24 hour Format
49\settimeformat{oclock} % Verbose
50\date{\today, \ \currenttime}
51%\hyphenation{set\_datadir}
52
53\ifhtml
54\date{\today} % latex2html does not know about datetime
55\fi
56
57
58
59
60\input{version} % Get version info - this file may be modified by
61                % update_anuga_user_manual.py - if not a dummy
62                % will be used.
63               
64%\release{1.0}   % release version; this is used to define the
65%                % \version macro
66
67\makeindex          % tell \index to actually write the .idx file
68\makemodindex       % If this contains a lot of module sections.
69
70\setcounter{tocdepth}{3}
71\setcounter{secnumdepth}{3}
72
73
74\begin{document}
75\maketitle
76
77
78% This makes the contents more accessible from the front page of the HTML.
79\ifhtml
80\chapter*{Front Matter\label{front}}
81\fi
82
83%Subversion keywords:
84%
85%$LastChangedDate: 2008-08-21 06:32:14 +0000 (Thu, 21 Aug 2008) $
86%$LastChangedRevision: 5672 $
87%$LastChangedBy: ole $
88
89\input{copyright}
90
91
92\begin{abstract}
93\label{def:anuga}
94
95\noindent \anuga\index{\anuga} is a hydrodynamic modelling tool that
96allows users to model realistic flow problems in complex 2D geometries.
97Examples include dam breaks or the effects of natural hazards such
98as riverine flooding, storm surges and tsunami.
99
100The user must specify a study area represented by a mesh of triangular
101cells, the topography and bathymetry, frictional resistance, initial
102values for water level (called \emph{stage}\index{stage} within \anuga),
103boundary conditions and forces such as rainfall, stream flows, windstress or pressure gradients if applicable.
104
105\anuga tracks the evolution of water depth and horizontal momentum
106within each cell over time by solving the shallow water wave equation
107governing equation using a finite-volume method.
108
109\anuga also incorporates a mesh generator %, called \code{graphical
110                                %mesh generator},
111that
112allows the user to set up the geometry of the problem interactively as
113well as tools for interpolation and surface fitting, and a number of
114auxiliary tools for visualising and interrogating the model output.
115
116Most \anuga components are written in the object-oriented programming
117language Python and most users will interact with \anuga by writing
118small Python programs based on the \anuga library
119functions. Computationally intensive components are written for
120efficiency in C routines working directly with the Numerical Python
121structures.
122
123
124\end{abstract}
125
126\tableofcontents
127
128
129\chapter{Introduction}
130
131
132\section{Purpose}
133
134The purpose of this user manual is to introduce the new user to the
135inundation software, describe what it can do and give step-by-step
136instructions for setting up and running hydrodynamic simulations.
137
138\section{Scope}
139
140This manual covers only what is needed to operate the software after
141installation and configuration. It does not includes instructions
142for installing the software or detailed API documentation, both of
143which will be covered in separate publications and by documentation
144in the source code.
145
146\section{Audience}
147
148Readers are assumed to be familiar with the Python Programming language and
149its object oriented approach.
150Python tutorials include
151\url{http://docs.python.org/tut},
152\url{http://www.sthurlow.com/python}, and
153%\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}.
154\url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}.
155
156
157Readers also need to have a general understanding of scientific modelling,
158as well as
159enough programming experience to adapt the code to different
160requirements.
161
162
163
164\pagebreak
165\chapter{Background}
166
167
168Modelling the effects on the built environment of natural hazards such
169as riverine flooding, storm surges and tsunami is critical for
170understanding their economic and social impact on our urban
171communities.  Geoscience Australia and the Australian National
172University are developing a hydrodynamic inundation modelling tool
173called \anuga to help simulate the impact of these hazards.
174
175The core of \anuga is the fluid dynamics module, called \code{shallow\_water},
176which is based on a finite-volume method for solving the Shallow Water
177Wave Equation.  The study area is represented by a mesh of triangular
178cells.  By solving the governing equation within each cell, water
179depth and horizontal momentum are tracked over time.
180
181A major capability of \anuga is that it can model the process of
182wetting and drying as water enters and leaves an area.  This means
183that it is suitable for simulating water flow onto a beach or dry land
184and around structures such as buildings.  \anuga is also capable
185of modelling hydraulic jumps due to the ability of the finite-volume
186method to accommodate discontinuities in the solution.
187
188To set up a particular scenario the user specifies the geometry
189(bathymetry and topography), the initial water level (stage),
190boundary conditions such as tide, and any forcing terms that may
191drive the system such as rain_fall, abstraction of water, wind stress or atmospheric pressure
192gradients. Gravity and frictional resistance from the different
193terrains in the model are represented by predefined forcing terms.
194See section \ref{sec:forcing terms} for details on forcing terms available in ANUGA.
195
196The built-in mesh generator, called \code{graphical\_mesh\_generator},
197allows the user to set up the geometry
198of the problem interactively and to identify boundary segments and
199regions using symbolic tags.  These tags may then be used to set the
200actual boundary conditions and attributes for different regions
201(e.g.\ the Manning friction coefficient) for each simulation.
202
203Most \anuga components are written in the object-oriented programming
204language Python.  Software written in Python can be produced quickly
205and can be readily adapted to changing requirements throughout its
206lifetime.  Computationally intensive components are written for
207efficiency in C routines working directly with the Numerical Python
208structures.  The animation tool developed for \anuga is based on
209OpenSceneGraph, an Open Source Software (OSS) component allowing high
210level interaction with sophisticated graphics primitives.
211See \cite{nielsen2005} for more background on \anuga.
212
213\chapter{Restrictions and limitations on \anuga}
214\label{ch:limitations}
215
216Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a
217number of limitations that any potential user need to be aware of. They are
218
219\begin{itemize}
220  \item The mathematical model is the 2D shallow water wave equation.
221  As such it cannot resolve vertical convection and consequently not breaking
222  waves or 3D turbulence (e.g.\ vorticity).
223  %\item The surface is assumed to be open, e.g. \anuga cannot model
224  %flow under ceilings or in pipes
225  \item All spatial coordinates are assumed to be UTM (meters). As such,
226  ANUGA is unsuitable for modelling flows in areas larger than one UTM zone
227  (6 degrees wide).
228  \item Fluid is assumed to be inviscid - i.e.\ no kinematic viscosity included.
229  \item The finite volume is a very robust and flexible numerical technique,
230  but it is not the fastest method around. If the geometry is sufficiently
231  simple and if there is no need for wetting or drying, a finite-difference
232  method may be able to solve the problem faster than \anuga.
233  %\item Mesh resolutions near coastlines with steep gradients need to be...
234  \item Frictional resistance is implemented using Manning's formula, but
235  \anuga has not yet been fully validated in regard to bottom roughness
236  %\item ANUGA contains no tsunami-genic functionality relating to
237  %earthquakes.
238\end{itemize}
239
240
241
242\chapter{Getting Started}
243\label{ch:getstarted}
244
245This section is designed to assist the reader to get started with
246\anuga by working through some examples. Two examples are discussed;
247the first is a simple example to illustrate many of the concepts, and
248the second is a more realistic example.
249
250\section{A Simple Example}
251\label{sec:simpleexample}
252
253\subsection{Overview}
254
255What follows is a discussion of the structure and operation of a
256script called \file{runup.py}.
257
258This example carries out the solution of the shallow-water wave
259equation in the simple case of a configuration comprising a flat
260bed, sloping at a fixed angle in one direction and having a
261constant depth across each line in the perpendicular direction.
262
263The example demonstrates the basic ideas involved in setting up a
264complex scenario. In general the user specifies the geometry
265(bathymetry and topography), the initial water level, boundary
266conditions such as tide, and any forcing terms that may drive the
267system such as rain_fall, abstraction of water, wind stress or atmospheric pressure gradients.
268Frictional resistance from the different terrains in the model is
269represented by predefined forcing terms. In this example, the
270boundary is reflective on three sides and a time dependent wave on
271one side.
272
273The present example represents a simple scenario and does not
274include any forcing terms, nor is the data taken from a file as it
275would typically be.
276
277The conserved quantities involved in the
278problem are stage (absolute height of water surface),
279$x$-momentum and $y$-momentum. Other quantities
280involved in the computation are the friction and elevation.
281
282Water depth can be obtained through the equation
283
284\begin{tabular}{rcrcl}
285  \code{depth} &=& \code{stage} &$-$& \code{elevation}
286\end{tabular}
287
288
289\subsection{Outline of the Program}
290
291In outline, \file{runup.py} performs the following steps:
292
293\begin{enumerate}
294
295   \item Sets up a triangular mesh.
296
297   \item Sets certain parameters governing the mode of
298operation of the model-specifying, for instance, where to store the model output.
299
300   \item Inputs various quantities describing physical measurements, such
301as the elevation, to be specified at each mesh point (vertex).
302
303   \item Sets up the boundary conditions.
304
305   \item Carries out the evolution of the model through a series of time
306steps and outputs the results, providing a results file that can
307be visualised.
308
309\end{enumerate}
310
311\subsection{The Code}
312
313%FIXME: we are using the \code function here.
314%This should be used wherever possible
315For reference we include below the complete code listing for
316\file{runup.py}. Subsequent paragraphs provide a
317`commentary' that describes each step of the program and explains it
318significance.
319
320\verbatiminput{demos/runup.py}
321
322\subsection{Establishing the Mesh}\index{mesh, establishing}
323
324The first task is to set up the triangular mesh to be used for the
325scenario. This is carried out through the statement:
326
327{\small \begin{verbatim}
328    points, vertices, boundary = rectangular_cross(10, 10)
329\end{verbatim}}
330
331The function \function{rectangular_cross} is imported from a module
332\module{mesh\_factory} defined elsewhere. (\anuga also contains
333several other schemes that can be used for setting up meshes, but we
334shall not discuss these.) The above assignment sets up a $10 \times
33510$ rectangular mesh, triangulated in a regular way. The assignment
336
337{\small \begin{verbatim}
338    points, vertices, boundary = rectangular_cross(m, n)
339\end{verbatim}}
340
341returns:
342
343\begin{itemize}
344
345   \item a list \code{points} giving the coordinates of each mesh point,
346
347   \item a list \code{vertices} specifying the three vertices of each triangle, and
348
349   \item a dictionary \code{boundary} that stores the edges on
350   the boundary and associates each with one of the symbolic tags \code{`left'}, \code{`right'},
351   \code{`top'} or \code{`bottom'}.
352
353\end{itemize}
354
355(For more details on symbolic tags, see page
356\pageref{ref:tagdescription}.)
357
358An example of a general unstructured mesh and the associated data
359structures \code{points}, \code{vertices} and \code{boundary} is
360given in Section \ref{sec:meshexample}.
361
362
363
364
365\subsection{Initialising the Domain}
366
367These variables are then used to set up a data structure
368\code{domain}, through the assignment:
369
370{\small \begin{verbatim}
371    domain = Domain(points, vertices, boundary)
372\end{verbatim}}
373
374This creates an instance of the \class{Domain} class, which
375represents the domain of the simulation. Specific options are set at
376this point, including the basename for the output file and the
377directory to be used for data:
378
379{\small \begin{verbatim}
380    domain.set_name('runup')
381\end{verbatim}}
382
383{\small \begin{verbatim}
384    domain.set_datadir('.')
385\end{verbatim}}
386
387In addition, the following statement now specifies that the
388quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are
389to be stored:
390
391{\small \begin{verbatim}
392    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
393    'ymomentum'])
394\end{verbatim}}
395
396
397\subsection{Initial Conditions}
398
399The next task is to specify a number of quantities that we wish to
400set for each mesh point. The class \class{Domain} has a method
401\method{set\_quantity}, used to specify these quantities. It is a
402flexible method that allows the user to set quantities in a variety
403of ways---using constants, functions, numeric arrays, expressions
404involving other quantities, or arbitrary data points with associated
405values, all of which can be passed as arguments. All quantities can
406be initialised using \method{set\_quantity}. For a conserved
407quantity (such as \code{stage, xmomentum, ymomentum}) this is called
408an \emph{initial condition}. However, other quantities that aren't
409updated by the equation are also assigned values using the same
410interface. The code in the present example demonstrates a number of
411forms in which we can invoke \method{set\_quantity}.
412
413
414\subsubsection{Elevation}
415
416The elevation, or height of the bed, is set using a function,
417defined through the statements below, which is specific to this
418example and specifies a particularly simple initial configuration
419for demonstration purposes:
420
421{\small \begin{verbatim}
422    def f(x,y):
423        return -x/2
424\end{verbatim}}
425
426This simply associates an elevation with each point \code{(x, y)} of
427the plane.  It specifies that the bed slopes linearly in the
428\code{x} direction, with slope $-\frac{1}{2}$,  and is constant in
429the \code{y} direction.
430
431Once the function \function{f} is specified, the quantity
432\code{elevation} is assigned through the simple statement:
433
434{\small \begin{verbatim}
435    domain.set_quantity('elevation', f)
436\end{verbatim}}
437
438NOTE: If using function to set \code{elevation} it must be vector
439compatible. For example square root will not work.
440
441\subsubsection{Friction}
442
443The assignment of the friction quantity (a forcing term)
444demonstrates another way we can use \method{set\_quantity} to set
445quantities---namely, assign them to a constant numerical value:
446
447{\small \begin{verbatim}
448    domain.set_quantity('friction', 0.1)
449\end{verbatim}}
450
451This specifies that the Manning friction coefficient is set to 0.1
452at every mesh point.
453
454\subsubsection{Stage}
455
456The stage (the height of the water surface) is related to the
457elevation and the depth at any time by the equation
458
459{\small \begin{verbatim}
460    stage = elevation + depth
461\end{verbatim}}
462
463
464For this example, we simply assign a constant value to \code{stage},
465using the statement
466
467{\small \begin{verbatim}
468    domain.set_quantity('stage', -.4)
469\end{verbatim}}
470
471which specifies that the surface level is set to a height of $-0.4$,
472i.e. 0.4 units (m) below the zero level.
473
474Although it is not necessary for this example, it may be useful to
475digress here and mention a variant to this requirement, which allows
476us to illustrate another way to use \method{set\_quantity}---namely,
477incorporating an expression involving other quantities. Suppose,
478instead of setting a constant value for the stage, we wished to
479specify a constant value for the \emph{depth}. For such a case we
480need to specify that \code{stage} is everywhere obtained by adding
481that value to the value already specified for \code{elevation}. We
482would do this by means of the statements:
483
484{\small \begin{verbatim}
485    h = 0.05 # Constant depth
486    domain.set_quantity('stage', expression = 'elevation + %f' %h)
487\end{verbatim}}
488
489That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus
490the value of \code{elevation} already defined.
491
492The reader will probably appreciate that this capability to
493incorporate expressions into statements using \method{set\_quantity}
494greatly expands its power.) See Section \ref{sec:initial conditions} for more
495details.
496
497\subsection{Boundary Conditions}\index{boundary conditions}
498
499The boundary conditions are specified as follows:
500
501{\small \begin{verbatim}
502    Br = Reflective_boundary(domain)
503
504    Bt = Transmissive_boundary(domain)
505
506    Bd = Dirichlet_boundary([0.2,0.,0.])
507
508    Bw = Time_boundary(domain=domain,
509                f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
510\end{verbatim}}
511
512The effect of these statements is to set up a selection of different
513alternative boundary conditions and store them in variables that can be
514assigned as needed. Each boundary condition specifies the
515behaviour at a boundary in terms of the behaviour in neighbouring
516elements. The boundary conditions introduced here may be briefly described as
517follows:
518
519\begin{itemize}
520    \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as
521      as present in its neighbour volume but momentum vector
522      reversed 180 degrees (reflected).
523      Specific to the shallow water equation as it works with the
524      momentum quantities assumed to be the second and third conserved
525      quantities. A reflective boundary condition models a solid wall.
526    \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as
527      those present in its neighbour volume. This is one way of modelling
528      outflow from a domain, but it should be used with caution if flow is
529      not steady state as replication of momentum at the boundary
530      may cause occasional spurious effects. If this occurs,
531      consider using e.g. a Dirichlet boundary condition.
532    \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies
533      constant values for stage, $x$-momentum and $y$-momentum at the boundary.
534    \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet
535      boundary but with behaviour varying with time.
536\end{itemize}
537
538\label{ref:tagdescription}Before describing how these boundary
539conditions are assigned, we recall that a mesh is specified using
540three variables \code{points}, \code{vertices} and \code{boundary}.
541In the code we are discussing, these three variables are returned by
542the function \code{rectangular}; however, the example given in
543Section \ref{sec:realdataexample} illustrates another way of
544assigning the values, by means of the function
545\code{create\_mesh\_from\_regions}.
546
547These variables store the data determining the mesh as follows. (You
548may find that the example given in Section \ref{sec:meshexample}
549helps to clarify the following discussion, even though that example
550is a \emph{non-rectangular} mesh.)
551
552\begin{itemize}
553\item The variable \code{points} stores a list of 2-tuples giving the
554coordinates of the mesh points.
555
556\item The variable \code{vertices} stores a list of 3-tuples of
557numbers, representing vertices of triangles in the mesh. In this
558list, the triangle whose vertices are \code{points[i]},
559\code{points[j]}, \code{points[k]} is represented by the 3-tuple
560\code{(i, j, k)}.
561
562\item The variable \code{boundary} is a Python dictionary that
563not only stores the edges that make up the boundary but also assigns
564symbolic tags to these edges to distinguish different parts of the
565boundary. An edge with endpoints \code{points[i]} and
566\code{points[j]} is represented by the 2-tuple \code{(i, j)}. The
567keys for the dictionary are the 2-tuples \code{(i, j)} corresponding
568to boundary edges in the mesh, and the values are the tags are used
569to label them. In the present example, the value \code{boundary[(i,
570j)]} assigned to \code{(i, j)]} is one of the four tags
571\code{`left'}, \code{`right'}, \code{`top'} or \code{`bottom'},
572depending on whether the boundary edge represented by \code{(i, j)}
573occurs at the left, right, top or bottom of the rectangle bounding
574the mesh. The function \code{rectangular} automatically assigns
575these tags to the boundary edges when it generates the mesh.
576\end{itemize}
577
578The tags provide the means to assign different boundary conditions
579to an edge depending on which part of the boundary it belongs to.
580(In Section \ref{sec:realdataexample} we describe an example that
581uses different boundary tags --- in general, the possible tags are entirely selectable by the user when generating the mesh and not
582limited to `left', `right', `top' and `bottom' as in this example.)
583All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by ANUGA.
584
585
586Using the boundary objects described above, we assign a boundary
587condition to each part of the boundary by means of a statement like
588
589{\small \begin{verbatim}
590    domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br})
591\end{verbatim}}
592
593It is critical that all tags are assoctiated with a boundary conditing in this statement. If not the program will halt with a statement like
594
595\begin{verbatim}
596
597Traceback (most recent call last):
598  File "mesh_test.py", line 114, in ?
599    domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br})
600  File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary
601    raise msg
602ERROR (domain.py): Tag "exterior" has not been bound to a boundary object.
603All boundary tags defined in domain must appear in the supplied dictionary.
604The tags are: ['ocean', 'east', 'north', 'exterior', 'south']
605\end{verbatim}
606
607
608The command \code{set\_boundary} stipulates that, in the current example, the right
609boundary varies with time, as defined by the lambda function, while the other
610boundaries are all reflective.
611
612The reader may wish to experiment by varying the choice of boundary
613types for one or more of the boundaries. (In the case of \code{Bd}
614and \code{Bw}, the three arguments in each case represent the
615\code{stage}, $x$-momentum and $y$-momentum, respectively.)
616
617{\small \begin{verbatim}
618    Bw = Time_boundary(domain=domain,
619                       f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
620\end{verbatim}}
621
622
623
624\subsection{Evolution}\index{evolution}
625
626The final statement \nopagebreak[3]
627{\small \begin{verbatim}
628    for t in domain.evolve(yieldstep = 0.1, duration = 4.0):
629        print domain.timestepping_statistics()
630\end{verbatim}}
631
632causes the configuration of the domain to `evolve', over a series of
633steps indicated by the values of \code{yieldstep} and
634\code{duration}, which can be altered as required.  The value of
635\code{yieldstep} controls the time interval between successive model
636outputs.  Behind the scenes more time steps are generally taken.
637
638
639\subsection{Output}
640
641The output is a NetCDF file with the extension \code{.sww}. It
642contains stage and momentum information and can be used with the
643ANUGA viewer \code{animate} (see Section \ref{sec:animate})
644visualisation package
645to generate a visual display. See Section \ref{sec:file formats}
646(page \pageref{sec:file formats}) for more on NetCDF and other file
647formats.
648
649The following is a listing of the screen output seen by the user
650when this example is run:
651
652\verbatiminput{examples/runupoutput.txt}
653
654
655\section{How to Run the Code}
656
657The code can be run in various ways:
658
659\begin{itemize}
660  \item{from a Windows or Unix command line} as in\ \code{python runup.py}
661  \item{within the Python IDLE environment}
662  \item{within emacs}
663  \item{within Windows, by double-clicking the \code{runup.py}
664  file.}
665\end{itemize}
666
667
668\section{Exploring the Model Output}
669
670The following figures are screenshots from the \anuga visualisation
671tool \code{animate}. Figure \ref{fig:runupstart} shows the domain
672with water surface as specified by the initial condition, $t=0$.
673Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and
674$t=4$ where the system has been evolved and the wave is encroaching
675on the previously dry bed.  All figures are screenshots from an
676interactive animation tool called animate which is part of \anuga and
677distributed as in the package anuga\_viewer.
678Animate is described in more detail is Section \ref{sec:animate}.
679
680\begin{figure}[hbt]
681
682  \centerline{\includegraphics[width=75mm, height=75mm]
683    {graphics/bedslopestart.jpg}}
684
685  \caption{Runup example viewed with the ANUGA viewer}
686  \label{fig:runupstart}
687\end{figure}
688
689
690\begin{figure}[hbt]
691
692  \centerline{
693   \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg}
694    \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg}
695   }
696
697  \caption{Runup example viewed with ANGUA viewer}
698  \label{fig:runup2}
699\end{figure}
700
701
702
703\clearpage
704
705%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
706
707\section{A slightly more complex example}
708\label{sec:channelexample}
709
710\subsection{Overview}
711
712The next example is about waterflow in a channel with varying boundary conditions and
713more complex topograhies. These examples build on the
714concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
715The example will be built up through three progressively more complex scripts.
716
717\subsection{Overview}
718As in the case of \file{runup.py}, the actions carried
719out by the program can be organised according to this outline:
720
721\begin{enumerate}
722
723   \item Set up a triangular mesh.
724
725   \item Set certain parameters governing the mode of
726operation of the model---specifying, for instance, where to store the
727model output.
728
729   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
730
731   \item Set up the boundary conditions.
732
733   \item Carry out the evolution of the model through a series of time
734steps and output the results, providing a results file that can be
735visualised.
736
737\end{enumerate}
738
739
740\subsection{The Code}
741
742Here is the code for the first version of the channel flow \file{channel1.py}:
743
744\verbatiminput{demos/channel1.py}
745
746In discussing the details of this example, we follow the outline
747given above, discussing each major step of the code in turn.
748
749\subsection{Establishing the Mesh}\index{mesh, establishing}
750
751In this example we use a similar simple structured triangular mesh as in \code{runup.py}
752for simplicity, but this time we will use a symmetric one and also
753change the physical extent of the domain. The assignment
754
755{\small \begin{verbatim}
756    points, vertices, boundary = rectangular_cross(m, n,
757                                                   len1=length, len2=width)
758\end{verbatim}}
759returns a m x n mesh similar to the one used in the previous example, except that now the
760extent in the x and y directions are given by the value of \code{length} and \code{width}
761respectively.
762
763Defining m and n in terms of the extent as in this example provides a convenient way of
764controlling the resolution: By defining dx and dy to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows:
765
766{\small \begin{verbatim}
767length = 10.
768width = 5.
769dx = dy = 1           # Resolution: Length of subdivisions on both axes
770
771points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
772                                               len1=length, len2=width)
773\end{verbatim}}
774which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decrease the values of dx and dy.
775
776The rest of this script is as in the previous example.
777% except for an application of the 'expression' form of \code{set\_quantity} where we use the value of \code{elevation} to define the (dry) initial condition for \code{stage}:
778%{\small \begin{verbatim}
779%  domain.set_quantity('stage', expression='elevation')
780%\end{verbatim}}
781
782\section{Model Output}
783
784The following figure is a screenshot from the \anuga visualisation
785tool \code{animate} of output from this example.
786\begin{figure}[hbt]
787  \centerline{\includegraphics[height=75mm]
788    {graphics/channel1.png}}%
789
790  \caption{Simple channel example viewed with the ANUGA viewer.}
791  \label{fig:channel1}
792\end{figure}
793
794
795\subsection{Changing boundary conditions on the fly}
796\label{sec:change boundary}
797
798Here is the code for the second version of the channel flow \file{channel2.py}:
799\verbatiminput{demos/channel2.py}
800This example differs from the first version in that a constant outflow boundary condition has
801been defined
802{\small \begin{verbatim}
803    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
804\end{verbatim}}
805and that it is applied to the right hand side boundary when the water level there exceeds 0m.
806{\small \begin{verbatim}
807for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
808    domain.write_time()
809
810    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:
811        print 'Stage > 0: Changing to outflow boundary'
812        domain.set_boundary({'right': Bo})
813\end{verbatim}}
814\label{sec:change boundary code}
815
816The if statement in the timestepping loop (evolve) gets the quantity
817\code{stage} and obtain the interpolated value at the point (10m,
8182.5m) which is on the right boundary. If the stage exceeds 0m a
819message is printed and the old boundary condition at tag 'right' is
820replaced by the outflow boundary using the method
821{\small \begin{verbatim}
822    domain.set_boundary({'right': Bo})
823\end{verbatim}}
824This type of dynamically varying boundary could for example be
825used to model the
826breakdown of a sluice door when water exceeds a certain level.
827
828\subsection{Output}
829
830The text output from this example looks like this
831{\small \begin{verbatim}
832...
833Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
834Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
835Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
836Stage > 0: Changing to outflow boundary
837Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
838Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
839...
840\end{verbatim}}
841
842
843\subsection{Flow through more complex topograhies}
844
845Here is the code for the third version of the channel flow \file{channel3.py}:
846\verbatiminput{demos/channel3.py}
847
848This example differs from the first two versions in that the topography
849contains obstacles.
850
851This is accomplished here by defining the function \code{topography} as follows
852{\small \begin{verbatim}
853def topography(x,y):
854    """Complex topography defined by a function of vectors x and y
855    """
856
857    z = -x/10
858
859    N = len(x)
860    for i in range(N):
861
862        # Step
863        if 10 < x[i] < 12:
864            z[i] += 0.4 - 0.05*y[i]
865
866        # Constriction
867        if 27 < x[i] < 29 and y[i] > 3:
868            z[i] += 2
869
870        # Pole
871        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
872            z[i] += 2
873
874    return z
875\end{verbatim}}
876
877In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
878
879A screenshot of this model at time == 15s is
880\begin{figure}[hbt]
881
882  \centerline{\includegraphics[height=75mm]
883    {graphics/channel3.png}}
884
885  \caption{More complex flow in a channel}
886  \label{fig:channel3}
887\end{figure}
888
889
890
891
892\clearpage
893
894%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
895
896\section{An Example with Real Data}
897\label{sec:realdataexample} The following discussion builds on the
898concepts introduced through the \file{runup.py} example and
899introduces a second example, \file{runcairns.py}.  This refers to
900a {\bf hypothetical} scenario using real-life data,
901in which the domain of interest surrounds the
902Cairns region. Two scenarios are given; firstly, a
903hypothetical tsunami wave is generated by a submarine mass failure
904situated on the edge of the continental shelf, and secondly, a fixed wave
905of given amplitude and period is introduced through the boundary.
906
907{\bf
908Each scenario has been designed to generate a tsunami which will
909inundate the Cairns region. To achieve this, suitably large
910parameters were chosen and were not based on any known tsunami sources
911or realistic amplitudes.
912}
913
914\subsection{Overview}
915As in the case of \file{runup.py}, the actions carried
916out by the program can be organised according to this outline:
917
918\begin{enumerate}
919
920   \item Set up a triangular mesh.
921
922   \item Set certain parameters governing the mode of
923operation of the model---specifying, for instance, where to store the
924model output.
925
926   \item Input various quantities describing physical measurements, such
927as the elevation, to be specified at each mesh point (vertex).
928
929   \item Set up the boundary conditions.
930
931   \item Carry out the evolution of the model through a series of time
932steps and output the results, providing a results file that can be
933visualised.
934
935\end{enumerate}
936
937
938
939\subsection{The Code}
940
941Here is the code for \file{runcairns.py}:
942
943\verbatiminput{demos/cairns/runcairns.py}
944
945In discussing the details of this example, we follow the outline
946given above, discussing each major step of the code in turn.
947
948\subsection{Establishing the Mesh}\index{mesh, establishing}
949
950One obvious way that the present example differs from
951\file{runup.py} is in the use of a more complex method to
952create the mesh. Instead of imposing a mesh structure on a
953rectangular grid, the technique used for this example involves
954building mesh structures inside polygons specified by the user,
955using a mesh-generator.
956
957In its simplest form, the mesh-generator creates the mesh within a single
958polygon whose vertices are at geographical locations specified by
959the user. The user specifies the \emph{resolution}---that is, the
960maximal area of a triangle used for triangulation---and a triangular
961mesh is created inside the polygon using a mesh generation engine.
962On any given platform, the same mesh will be returned.
963%Figure
964%\ref{fig:pentagon} shows a simple example of this, in which the
965%triangulation is carried out within a pentagon.
966
967
968%\begin{figure}[hbt]
969
970%  \caption{Mesh points are created inside the polygon}
971  %\label{fig:pentagon}
972%\end{figure}
973
974Boundary tags are not restricted to \code{`left'}, \code{`bottom'},
975\code{`right'} and \code{`top'}, as in the case of
976\file{runup.py}. Instead the user specifies a list of
977tags appropriate to the configuration being modelled.
978
979In addition, the mesh-generator provides a way to adapt to geographic or
980other features in the landscape, whose presence may require an
981increase in resolution. This is done by allowing the user to specify
982a number of \emph{interior polygons}, each with a specified
983resolution. It is also
984possible to specify one or more `holes'---that is, areas bounded by
985polygons in which no triangulation is required.
986
987%\begin{figure}[hbt]
988%  \caption{Interior meshes with individual resolution}
989%  \label{fig:interior meshes}
990%\end{figure}
991
992In its general form, the mesh-generator takes for its input a bounding
993polygon and (optionally) a list of interior polygons. The user
994specifies resolutions, both for the bounding polygon and for each of
995the interior polygons. Given this data, the mesh-generator first creates a
996triangular mesh with varying resolution.
997
998The function used to implement this process is
999\function{create\_mesh\_from\_regions}. Its arguments include the
1000bounding polygon and its resolution, a list of boundary tags, and a
1001list of pairs \code{[polygon, resolution]}, specifying the interior
1002polygons and their resolutions.
1003
1004The resulting mesh is output to a \emph{mesh file}\index{mesh
1005file}\label{def:mesh file}. This term is used to describe a file of
1006a specific format used to store the data specifying a mesh. (There
1007are in fact two possible formats for such a file: it can either be a
1008binary file, with extension \code{.msh}, or an ASCII file, with
1009extension \code{.tsh}. In the present case, the binary file format
1010\code{.msh} is used. See Section \ref{sec:file formats} (page
1011\pageref{sec:file formats}) for more on file formats.)
1012
1013In practice, the details of the polygons used are read from a
1014separate file \file{project.py}. Here is a complete listing of
1015\file{project.py}:
1016
1017\verbatiminput{demos/cairns/project.py}
1018
1019Figure \ref{fig:cairns3d} illustrates the landscape of the region
1020for the Cairns example. Understanding the landscape is important in
1021determining the location and resolution of interior polygons. The
1022supporting data is found in the ASCII grid, \code{cairns.asc}, which
1023has been sourced from the publically available Australian Bathymetry
1024and Topography Grid 2005, \cite{grid250}. The required resolution
1025for inundation modelling will depend on the underlying topography and
1026bathymetry; as the terrain becomes more complex, the desired resolution
1027would decrease to the order of tens of metres.
1028
1029\begin{figure}[hbt]
1030\centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}}
1031\caption{Landscape of the Cairns scenario.}
1032\label{fig:cairns3d}
1033
1034\end{figure}
1035The following statements are used to read in the specific polygons
1036from \code{project.cairns} and assign a defined resolution to
1037each polygon.
1038
1039{\small \begin{verbatim}
1040    islands_res = 100000
1041    cairns_res = 100000
1042    shallow_res = 500000
1043    interior_regions = [[project.poly_cairns, cairns_res],
1044                        [project.poly_island0, islands_res],
1045                        [project.poly_island1, islands_res],
1046                        [project.poly_island2, islands_res],
1047                        [project.poly_island3, islands_res],
1048                        [project.poly_shallow, shallow_res]]
1049\end{verbatim}}
1050
1051Figure \ref{fig:cairnspolys}
1052illustrates the polygons used for the Cairns scenario.
1053
1054\begin{figure}[hbt]
1055
1056  \centerline{\includegraphics[scale=0.5]
1057      {graphics/cairnsmodel.jpg}}
1058  \caption{Interior and bounding polygons for the Cairns example.}
1059  \label{fig:cairnspolys}
1060\end{figure}
1061
1062The statement
1063
1064
1065{\small \begin{verbatim}
1066remainder_res = 10000000
1067create_mesh_from_regions(project.bounding_polygon,
1068                         boundary_tags={'top': [0],
1069                                        'ocean_east': [1],
1070                                        'bottom': [2],
1071                                        'onshore': [3]},
1072                         maximum_triangle_area=remainder_res,
1073                         filename=meshname,
1074                         interior_regions=interior_regions,
1075                         use_cache=True,
1076                         verbose=True)
1077\end{verbatim}}
1078is then used to create the mesh, taking the bounding polygon to be
1079the polygon \code{bounding\_polygon} specified in \file{project.py}.
1080The argument \code{boundary\_tags} assigns a dictionary, whose keys
1081are the names of the boundary tags used for the bounding
1082polygon---\code{`top'}, \code{`ocean\_east'}, \code{`bottom'}, and
1083\code{`onshore'}--- and whose values identify the indices of the
1084segments associated with each of these tags.
1085The polygon may be arranged either clock-wise or counter clock-wise and the
1086indices refer to edges in the order they appear: Edge 0 connects vertex 0 and vertex 1, edge 1 connects vertex 1 and 2; and so forth.
1087(Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges)
1088If polygons intersect, or edges coincide the resolution may be undefined in some regions.
1089Use the underlying mesh interface for such cases. See Section
1090\ref{sec:mesh interface}.
1091
1092Note that every point on each polygon defining the mesh will be used as vertices in triangles.
1093Consequently, polygons with points very close together will cause triangles with very small
1094areas to be generated irrespective of the requested resolution.
1095Make sure points on polygons are spaced to be no closer than the smallest resolution requested.
1096
1097
1098\subsection{Initialising the Domain}
1099
1100As with \file{runup.py}, once we have created the mesh, the next
1101step is to create the data structure \code{domain}. We did this for
1102\file{runup.py} by inputting lists of points and triangles and
1103specifying the boundary tags directly. However, in the present case,
1104we use a method that works directly with the mesh file
1105\code{meshname}, as follows:
1106
1107
1108{\small \begin{verbatim}
1109    domain = Domain(meshname, use_cache=True, verbose=True)
1110\end{verbatim}}
1111
1112Providing a filename instead of the lists used in \file{runup.py}
1113above causes \code{Domain} to convert a mesh file \code{meshname}
1114into an instance of \code{Domain}, allowing us to use methods like
1115\method{set\_quantity} to set quantities and to apply other
1116operations.
1117
1118%(In principle, the
1119%second argument of \function{pmesh\_to\_domain\_instance} can be any
1120%subclass of \class{Domain}, but for applications involving the
1121%shallow-water wave equation, the second argument of
1122%\function{pmesh\_to\_domain\_instance} can always be set simply to
1123%\class{Domain}.)
1124
1125The following statements specify a basename and data directory, and
1126identify quantities to be stored. For the first two, values are
1127taken from \file{project.py}.
1128
1129{\small \begin{verbatim}
1130    domain.set_name(project.basename)
1131    domain.set_datadir(project.outputdir)
1132    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
1133        'ymomentum'])
1134\end{verbatim}}
1135
1136
1137\subsection{Initial Conditions}
1138Quantities for \file{runcairns.py} are set
1139using similar methods to those in \file{runup.py}. However,
1140in this case, many of the values are read from the auxiliary file
1141\file{project.py} or, in the case of \code{elevation}, from an
1142ancillary points file.
1143
1144
1145
1146\subsubsection{Stage}
1147
1148For the scenario we are modelling in this case, we use a callable
1149object \code{tsunami\_source}, assigned by means of a function
1150\function{slide\_tsunami}. This is similar to how we set elevation in
1151\file{runup.py} using a function---however, in this case the
1152function is both more complex and more interesting.
1153
1154The function returns the water displacement for all \code{x} and
1155\code{y} in the domain. The water displacement is a double Gaussian
1156function that depends on the characteristics of the slide (length,
1157width, thickness, slope, etc), its location (origin) and the depth at that
1158location. For this example, we choose to apply the slide function
1159at a specified time into the simulation. {\bf Note, the parameters used
1160in this example have been deliberately chosen to generate a suitably
1161large amplitude tsunami which would inundate the Cairns region.}
1162
1163\subsubsection{Friction}
1164
1165We assign the friction exactly as we did for \file{runup.py}:
1166
1167{\small \begin{verbatim}
1168    domain.set_quantity('friction', 0.0)
1169\end{verbatim}}
1170
1171
1172\subsubsection{Elevation}
1173
1174The elevation is specified by reading data from a file:
1175
1176{\small \begin{verbatim}
1177    domain.set_quantity('elevation',
1178                        filename = project.dem_name + '.pts',
1179                        use_cache = True,
1180                        verbose = True)
1181\end{verbatim}}
1182
1183%However, before this step can be executed, some preliminary steps
1184%are needed to prepare the file from which the data is taken. Two
1185%source files are used for this data---their names are specified in
1186%the file \file{project.py}, in the variables \code{coarsedemname}
1187%and \code{finedemname}. They contain `coarse' and `fine' data,
1188%respectively---that is, data sampled at widely spaced points over a
1189%large region and data sampled at closely spaced points over a
1190%smaller subregion. The data in these files is combined through the
1191%statement
1192
1193%{\small \begin{verbatim}
1194%combine_rectangular_points_files(project.finedemname + '.pts',
1195%                                 project.coarsedemname + '.pts',
1196%                                 project.combineddemname + '.pts')
1197%\end{verbatim}}
1198%The effect of this is simply to combine the datasets by eliminating
1199%any coarse data associated with points inside the smaller region
1200%common to both datasets. The name to be assigned to the resulting
1201%dataset is also derived from the name stored in the variable
1202%\code{combinedname} in the file \file{project.py}.
1203
1204\subsection{Boundary Conditions}\index{boundary conditions}
1205
1206Setting boundaries follows a similar pattern to the one used for
1207\file{runup.py}, except that in this case we need to associate a
1208boundary type with each of the
1209boundary tag names introduced when we established the mesh. In place of the four
1210boundary types introduced for \file{runup.py}, we use the reflective
1211boundary for each of the
1212eight tagged segments defined by \code{create_mesh_from_regions}:
1213
1214{\small \begin{verbatim}
1215Bd = Dirichlet_boundary([0.0,0.0,0.0])
1216domain.set_boundary( {'ocean_east': Bd, 'bottom': Bd, 'onshore': Bd,
1217                          'top': Bd} )
1218\end{verbatim}}
1219
1220\subsection{Evolution}
1221
1222With the basics established, the running of the `evolve' step is
1223very similar to the corresponding step in \file{runup.py}. For the slide
1224scenario,
1225the simulation is run for 5000 seconds with the output stored every ten seconds.
1226For this example, we choose to apply the slide at 60 seconds into the simulation.
1227
1228{\small \begin{verbatim}
1229    import time t0 = time.time()
1230
1231
1232    for t in domain.evolve(yieldstep = 10, finaltime = 60):
1233            domain.write_time()
1234            domain.write_boundary_statistics(tags = 'ocean_east')
1235
1236        # add slide
1237        thisstagestep = domain.get_quantity('stage')
1238        if allclose(t, 60):
1239            slide = Quantity(domain)
1240            slide.set_values(tsunami_source)
1241            domain.set_quantity('stage', slide + thisstagestep)
1242
1243        for t in domain.evolve(yieldstep = 10, finaltime = 5000,
1244                               skip_initial_step = True):
1245            domain.write_time()
1246        domain.write_boundary_statistics(tags = 'ocean_east')
1247\end{verbatim}}
1248
1249For the fixed wave scenario, the simulation is run to 10000 seconds,
1250with the first half of the simulation stored at two minute intervals,
1251and the second half of the simulation stored at ten second intervals.
1252This functionality is especially convenient as it allows the detailed
1253parts of the simulation to be viewed at higher time resolution.
1254
1255
1256{\small \begin{verbatim}
1257
1258# save every two mins leading up to wave approaching land
1259    for t in domain.evolve(yieldstep = 120, finaltime = 5000):
1260        domain.write_time()
1261        domain.write_boundary_statistics(tags = 'ocean_east')
1262
1263    # save every 30 secs as wave starts inundating ashore
1264    for t in domain.evolve(yieldstep = 10, finaltime = 10000,
1265                           skip_initial_step = True):
1266        domain.write_time()
1267        domain.write_boundary_statistics(tags = 'ocean_east')
1268
1269\end{verbatim}}
1270
1271\section{Exploring the Model Output}
1272
1273Now that the scenario has been run, the user can view the output in a number of ways.
1274As described earlier, the user may run animate to view a three-dimensional representation
1275of the simulation.
1276
1277The user may also be interested in a maximum inundation map. This simply shows the
1278maximum water depth over the domain and is achieved with the function sww2dem (described in
1279Section \ref{sec:basicfileconversions}).
1280\file{ExportResults.py} demonstrates how this function can be used:
1281
1282\verbatiminput{demos/cairns/ExportResults.py}
1283
1284The script generates an maximum water depth ASCII grid at a defined
1285resolution (here 100 m$^2$) which can then be viewed in a GIS environment, for
1286example. The parameters used in the function are defined in \file{project.py}.
1287Figures \ref{fig:maxdepthcairnsslide} and \ref{fig:maxdepthcairnsfixedwave} show
1288the maximum water depth within the defined region for the slide and fixed wave scenario
1289respectively. {\bf Note, these inundation maps have been based on purely hypothetical
1290scenarios and were designed explicitly for demonstration purposes only.}
1291The user could develop a maximum absolute momentum or other expressions which can be
1292derived from the quantities.
1293It must be noted here that depth is more meaningful when the elevation is positive
1294(\code{depth} = \code{stage} $-$ \code{elevation}) as it describes the water height
1295above the available elevation. When the elevation is negative, depth is meauring the
1296water height from the sea floor. With this in mind, maximum inundation maps are
1297typically "clipped" to the coastline. However, the data input here did not contain a
1298coastline.
1299
1300\begin{figure}[hbt]
1301\centerline{\includegraphics[scale=0.5]{graphics/slidedepth.jpg}}
1302\caption{Maximum inundation map for the Cairns slide scenario. \bf Note, this
1303inundaiton map has been based on a purely hypothetical scenario which was
1304designed explictiy for demonstration purposes only.}
1305\label{fig:maxdepthcairnsslide}
1306\end{figure}
1307
1308\begin{figure}[hbt]
1309\centerline{\includegraphics[scale=0.5]{graphics/fixedwavedepth.jpg}}
1310\caption{Maximum inundation map for the Cairns fixed wave scenario.
1311\bf Note, this
1312inundaiton map has been based on a purely hypothetical scenario which was
1313designed explictiy for demonstration purposes only.}
1314\label{fig:maxdepthcairnsfixedwave}
1315\end{figure}
1316
1317The user may also be interested in interrogating the solution at a particular spatial
1318location to understand the behaviour of the system through time. To do this, the user
1319must first define the locations of interest. A number of locations have been
1320identified for the Cairns scenario, as shown in Figure \ref{fig:cairnsgauges}.
1321
1322\begin{figure}[hbt]
1323\centerline{\includegraphics[scale=0.5]{graphics/cairnsgauges.jpg}}
1324\caption{Point locations to show time series information for the Cairns scenario.}
1325\label{fig:cairnsgauges}
1326\end{figure}
1327
1328These locations
1329must be stored in either a .csv or .txt file. The corresponding .csv file for
1330the gauges shown in Figure \ref{fig:cairnsgauges} is \file{gauges.csv}
1331
1332\verbatiminput{demos/cairns/gauges.csv}
1333
1334Header information has been included to identify the location in terms of eastings and
1335northings, and each gauge is given a name. The elevation column can be zero here.
1336This information is then passed to the function \code{sww2csv_gauges} (shown in
1337\file{GetTimeseries.py} which generates the csv files for each point location. The csv files
1338can then be used in \code{csv2timeseries_graphs} to create the timeseries plot for each desired
1339quantity. \code{csv2timeseries_graphs} relies on \code{pylab} to be installed which is not part
1340of the standard \code{anuga} release, however it can be downloaded and installed from \code{http://matplotlib.sourceforge.net/}
1341
1342\verbatiminput{demos/cairns/GetTimeseries.py}
1343
1344Here, the time series for the quantities stage, depth and speed will be generated for
1345each gauge defined in the gauge file. As described earlier, depth is more meaningful
1346for onshore gauges, and stage is more appropriate for offshore gauges.
1347
1348As an example output,
1349Figure \ref{fig:reef} shows the time series for the quantity stage for the
1350Elford Reef location for each scenario (the elevation at this location is negative,
1351therefore stage is the more appropriate quantity to plot). Note the large negative stage value when the slide was
1352introduced. This is due to the double gaussian form of the initial surface
1353displacement of the slide. By contrast, the time series for depth is shown for the onshore location of the Cairns
1354Airport in Figure \ref{fig:airportboth}.
1355
1356\begin{figure}[hbt]
1357\centerline{\includegraphics[scale=0.5]{graphics/gaugeElfordReefstage.png}}
1358\caption{Time series information of the quantity stage for the Elford Reef location for the
1359fixed wave and slide scenario.}
1360\label{fig:reef}
1361\end{figure}
1362
1363\begin{figure}[hbt]
1364\centerline{\includegraphics[scale=0.5]{graphics/gaugeCairnsAirportdepth.png}}
1365\caption{Time series information of the quantity depth for the Cairns Airport
1366location for the slide and fixed wave scenario.}
1367\label{fig:airportboth}
1368\end{figure}
1369
1370
1371%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1372%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1373
1374\chapter{\anuga Public Interface}
1375\label{ch:interface}
1376
1377This chapter gives an overview of the features of \anuga available
1378to the user at the public interface. These are grouped under the
1379following headings, which correspond to the outline of the examples
1380described in Chapter \ref{ch:getstarted}:
1381
1382\begin{itemize}
1383    \item Establishing the Mesh: Section \ref{sec:establishing the mesh}
1384    \item Initialising the Domain: Section \ref{sec:initialising the domain}
1385    \item Specifying the Quantities: Section \ref{sec:quantitis}
1386    \item Initial Conditions: Section \ref{sec:initial conditions}
1387    \item Boundary Conditions: Section \ref{sec:boundary conditions}
1388    \item Forcing Terms: Section \ref{sec:forcing terms}
1389    \item Evolution: Section \ref{sec:evolution}
1390\end{itemize}
1391
1392The listings are intended merely to give the reader an idea of what
1393each feature is, where to find it and how it can be used---they do
1394not give full specifications; for these the reader
1395may consult the code. The code for every function or class contains
1396a documentation string, or `docstring', that specifies the precise
1397syntax for its use. This appears immediately after the line
1398introducing the code, between two sets of triple quotes.
1399
1400Each listing also describes the location of the module in which
1401the code for the feature being described can be found. All modules
1402are in the folder \file{inundation} or one of its subfolders, and the
1403location of each module is described relative to \file{inundation}. Rather
1404than using pathnames, whose syntax depends on the operating system,
1405we use the format adopted for importing the function or class for
1406use in Python code. For example, suppose we wish to specify that the
1407function \function{create\_mesh\_from\_regions} is in a module called
1408\module{mesh\_interface} in a subfolder of \module{inundation} called
1409\code{pmesh}. In Linux or Unix syntax, the pathname of the file
1410containing the function, relative to \file{inundation}, would be
1411
1412\begin{center}
1413%    \code{pmesh/mesh\_interface.py}
1414    \code{pmesh}$\slash$\code{mesh\_interface.py}
1415\end{center}
1416\label{sec:mesh interface}
1417
1418while in Windows syntax it would be
1419
1420\begin{center}
1421    \code{pmesh}$\backslash$\code{mesh\_interface.py}
1422\end{center}
1423
1424Rather than using either of these forms, in this chapter we specify
1425the location simply as \code{pmesh.mesh\_interface}, in keeping with
1426the usage in the Python statement for importing the function,
1427namely:
1428\begin{center}
1429    \code{from pmesh.mesh\_interface import create\_mesh\_from\_regions}
1430\end{center}
1431
1432Each listing details the full set of parameters for the class or
1433function; however, the description is generally limited to the most
1434important parameters and the reader is again referred to the code
1435for more details.
1436
1437The following parameters are common to many functions and classes
1438and are omitted from the descriptions given below:
1439
1440%\begin{center}
1441\begin{tabular}{ll}  %\hline
1442%\textbf{Name } & \textbf{Description}\\
1443%\hline
1444\emph{use\_cache} & Specifies whether caching is to be used for improved performance. See Section \ref{sec:caching} for details on the underlying caching functionality\\
1445\emph{verbose} & If \code{True}, provides detailed terminal output
1446to the user\\  % \hline
1447\end{tabular}
1448%\end{center}
1449
1450\section{Mesh Generation}\index{Mesh!generation}
1451\label{sec:establishing the mesh}
1452Before discussing the part of the interface relating to mesh
1453generation, we begin with a description of a simple example of a
1454mesh and use it to describe how mesh data is stored.
1455
1456\label{sec:meshexample} Figure \ref{fig:simplemesh} represents a
1457very simple mesh comprising just 11 points and 10 triangles.
1458
1459
1460\begin{figure}[h]
1461  \begin{center}
1462    \includegraphics[width=90mm, height=90mm]{triangularmesh.jpg}
1463  \end{center}
1464
1465  \caption{A simple mesh}
1466  \label{fig:simplemesh}
1467\end{figure}
1468
1469
1470The variables \code{points}, \code{vertices} and \code{boundary}
1471represent the data displayed in Figure \ref{fig:simplemesh} as
1472follows. The list \code{points} stores the coordinates of the
1473points, and may be displayed schematically as in Table
1474\ref{tab:points}.
1475
1476
1477\begin{table}
1478  \begin{center}
1479    \begin{tabular}[t]{|c|cc|} \hline
1480      index & \code{x} & \code{y}\\  \hline
1481      0 & 1 & 1\\
1482      1 & 4 & 2\\
1483      2 & 8 & 1\\
1484      3 & 1 & 3\\
1485      4 & 5 & 5\\
1486      5 & 8 & 6\\
1487      6 & 11 & 5\\
1488      7 & 3 & 6\\
1489      8 & 1 & 8\\
1490      9 & 4 & 9\\
1491      10 & 10 & 7\\  \hline
1492    \end{tabular}
1493  \end{center}
1494
1495  \caption{Point coordinates for mesh in
1496    Figure \protect \ref{fig:simplemesh}}
1497  \label{tab:points}
1498\end{table}
1499
1500The list \code{vertices} specifies the triangles that make up the
1501mesh. It does this by specifying, for each triangle, the indices
1502(the numbers shown in the first column above) that correspond to the
1503three points at its vertices, taken in an anti-clockwise order
1504around the triangle. Thus, in the example shown in Figure
1505\ref{fig:simplemesh}, the variable \code{vertices} contains the
1506entries shown in Table \ref{tab:vertices}. The starting point is
1507arbitrary so triangle $(0,1,3)$ is considered the same as $(1,3,0)$
1508and $(3,0,1)$.
1509
1510
1511\begin{table}
1512  \begin{center}
1513    \begin{tabular}{|c|ccc|} \hline
1514      index & \multicolumn{3}{c|}{\code{vertices}}\\ \hline
1515      0 & 0 & 1 & 3\\
1516      1 & 1 & 2 & 4\\
1517      2 & 2 & 5 & 4\\
1518      3 & 2 & 6 & 5\\
1519      4 & 4 & 5 & 9\\
1520      5 & 4 & 9 & 7\\
1521      6 & 3 & 4 & 7\\
1522      7 & 7 & 9 & 8\\
1523      8 & 1 & 4 & 3\\
1524      9 & 5 & 10 & 9\\  \hline
1525    \end{tabular}
1526  \end{center}
1527
1528  \caption{Vertices for mesh in Figure \protect \ref{fig:simplemesh}}
1529  \label{tab:vertices}
1530\end{table}
1531
1532Finally, the variable \code{boundary} identifies the boundary
1533triangles and associates a tag with each.
1534
1535\refmodindex[pmesh.meshinterface]{pmesh.mesh\_interface}\label{sec:meshgeneration}
1536
1537\begin{funcdesc}  {create\_mesh\_from\_regions}{bounding_polygon,
1538                             boundary_tags,
1539                             maximum_triangle_area,
1540                             filename=None,
1541                             interior_regions=None,
1542                             poly_geo_reference=None,
1543                             mesh_geo_reference=None,
1544                             minimum_triangle_angle=28.0}
1545Module: \module{pmesh.mesh\_interface}
1546
1547This function allows a user to initiate the automatic creation of a
1548mesh inside a specified polygon (input \code{bounding_polygon}).
1549Among the parameters that can be set are the \emph{resolution}
1550(maximal area for any triangle in the mesh) and the minimal angle
1551allowable in any triangle. The user can specify a number of internal
1552polygons within each of which the resolution of the mesh can be
1553specified. \code{interior_regions} is a paired list containing the
1554interior polygon and its resolution.  Additionally, the user specifies
1555a list of boundary tags, one for each edge of the bounding polygon.
1556
1557\textbf{WARNING}. Note that the dictionary structure used for the
1558parameter \code{boundary\_tags} is different from that used for the
1559variable \code{boundary} that occurs in the specification of a mesh.
1560In the case of \code{boundary}, the tags are the \emph{values} of
1561the dictionary, whereas in the case of \code{boundary_tags}, the
1562tags are the \emph{keys} and the \emph{value} corresponding to a
1563particular tag is a list of numbers identifying boundary edges
1564labelled with that tag. Because of this, it is theoretically
1565possible to assign the same edge to more than one tag. However, an
1566attempt to do this will cause an error.
1567
1568\textbf{WARNING}. Do not have polygon lines cross or be on-top of each
1569    other. This can result in regions of unspecified resolutions. Do
1570    not have polygon close to each other. This can result in the area
1571    between the polygons having small triangles.  For more control
1572    over the mesh outline use the methods described below.
1573
1574\end{funcdesc}
1575
1576
1577
1578\subsection{Advanced mesh generation}
1579
1580For more control over the creation of the mesh outline, use the
1581methods of the class \class{Mesh}.
1582
1583
1584\begin{classdesc}  {Mesh}{userSegments=None,
1585                 userVertices=None,
1586                 holes=None,
1587                 regions=None}
1588Module: \module{pmesh.mesh}
1589
1590A class used to build a mesh outline and generate a two-dimensional
1591triangular mesh. The mesh outline is used to describe features on the
1592mesh, such as the mesh boundary. Many of this classes methods are used
1593to build a mesh outline, such as \code{add\_vertices} and
1594\code{add\_region\_from\_polygon}.
1595
1596\end{classdesc}
1597
1598
1599\subsubsection{Key Methods of Class Mesh}
1600
1601
1602\begin{methoddesc} {add\_hole}{x,y}
1603Module: \module{pmesh.mesh},  Class: \class{Mesh}
1604
1605This method is used to build the mesh outline.  It defines a hole,
1606when the boundary of the hole has already been defined, by selecting a
1607point within the boundary.
1608
1609\end{methoddesc}
1610
1611
1612\begin{methoddesc}  {add\_hole\_from\_polygon}{self, polygon, tags=None}
1613Module: \module{pmesh.mesh},  Class: \class{Mesh}
1614
1615This method is used to add a `hole' within a region ---that is, to
1616define a interior region where the triangular mesh will not be
1617generated---to a \class{Mesh} instance. The region boundary is described by
1618the polygon passed in.  Additionally, the user specifies a list of
1619boundary tags, one for each edge of the bounding polygon.
1620\end{methoddesc}
1621
1622
1623\begin{methoddesc}  {add\_points_and_segments}{self, points, segments,
1624    segment\_tags=None}
1625Module: \module{pmesh.mesh},  Class: \class{Mesh}
1626
1627This method is used to build the mesh outline. It adds points and
1628segments connecting the points.  A tag for each segment can optionally
1629be added.
1630
1631\end{methoddesc}
1632
1633\begin{methoddesc} {add\_region}{x,y}
1634Module: \module{pmesh.mesh},  Class: \class{Mesh}
1635
1636This method is used to build the mesh outline.  It defines a region,
1637when the boundary of the region has already been defined, by selecting
1638a point within the boundary.  A region instance is returned.  This can
1639be used to set the resolution.
1640
1641\end{methoddesc}
1642
1643\begin{methoddesc}  {add\_region\_from\_polygon}{self, polygon,
1644segment_tags=None, region_tag=None
1645                                max_triangle_area=None}
1646Module: \module{pmesh.mesh},  Class: \class{Mesh}
1647
1648This method is used to build the mesh outline.  It adds a region to a
1649\class{Mesh} instance.  Regions are commonly used to describe an area
1650with an increased density of triangles, by setting
1651\code{max_triangle_area}.  The
1652region boundary is described by the input \code{polygon}.  Additionally, the
1653user specifies a list of segment tags, one for each edge of the
1654bounding polygon.  The regional tag is set using  \code{region}.
1655
1656\end{methoddesc}
1657
1658
1659
1660
1661
1662\begin{methoddesc} {add\_vertices}{point_data}
1663Module: \module{pmesh.mesh},  Class: \class{Mesh}
1664
1665Add user vertices. The point_data can be a list of (x,y) values, a numeric
1666array or a geospatial_data instance.
1667\end{methoddesc}
1668
1669\begin{methoddesc} {auto\_segment}{raw_boundary=raw_boundary,
1670                    remove_holes=remove_holes,
1671                    smooth_indents=smooth_indents,
1672                    expand_pinch=expand_pinch}
1673Module: \module{pmesh.mesh},  Class: \class{Mesh}
1674
1675Add segments between some of the user vertices to give the vertices an
1676outline.  The outline is an alpha shape. This method is
1677useful since a set of user vertices need to be outlined by segments
1678before generate_mesh is called.
1679
1680\end{methoddesc}
1681
1682\begin{methoddesc}  {export\_mesh_file}{self,ofile}
1683Module: \module{pmesh.mesh},  Class: \class{Mesh}
1684
1685This method is used to save the mesh to a file. \code{ofile} is the
1686name of the mesh file to be written, including the extension.  Use
1687the extension \code{.msh} for the file to be in NetCDF format and
1688\code{.tsh} for the file to be ASCII format.
1689\end{methoddesc}
1690
1691\begin{methoddesc}  {generate\_mesh}{self,
1692                      maximum_triangle_area=None,
1693                      minimum_triangle_angle=28.0,
1694                      verbose=False}
1695Module: \module{pmesh.mesh},  Class: \class{Mesh}
1696
1697This method is used to generate the triangular mesh.  The  maximal
1698area of any triangle in the mesh can be specified, which is used to
1699control the triangle density, along with the
1700minimum angle in any triangle.
1701\end{methoddesc}
1702
1703
1704
1705\begin{methoddesc}  {import_ungenerate_file}{self,ofile, tag=None,
1706region_tag=None}
1707Module: \module{pmesh.mesh},  Class: \class{Mesh}
1708
1709This method is used to import a polygon file in the ungenerate format,
1710which is used by arcGIS. The polygons from the file are converted to
1711vertices and segments. \code{ofile} is the name of the polygon file.
1712\code{tag} is the tag given to all the polygon's segments.
1713\code{region_tag} is the tag given to all the polygon's segments.  If
1714it is a string the one value will be assigned to all regions.  If it
1715is a list the first value in the list will be applied to the first
1716polygon etc.  If \code{tag} is not given a value it defaults to None,
1717which means the segement will not effect the water flow, it will only
1718effect the mesh generation.
1719
1720This function can be used to import building footprints.
1721\end{methoddesc}
1722
1723%%%%%%
1724\section{Initialising the Domain}\index{Initialising the Domain}
1725\label{sec:initialising the domain}
1726
1727%Include description of the class Domain and the module domain.
1728
1729%FIXME (Ole): This is also defined in a later chapter
1730%\declaremodule{standard}{...domain}
1731
1732\begin{classdesc} {Domain} {source=None,
1733                 triangles=None,
1734                 boundary=None,
1735                 conserved_quantities=None,
1736                 other_quantities=None,
1737                 tagged_elements=None,
1738                 use_inscribed_circle=False,
1739                 mesh_filename=None,
1740                 use_cache=False,
1741                 verbose=False,
1742                 full_send_dict=None,
1743                 ghost_recv_dict=None,
1744                 processor=0,
1745                 numproc=1}
1746Module: \refmodule{abstract_2d_finite_volumes.domain}
1747
1748This class is used to create an instance of a data structure used to
1749store and manipulate data associated with a mesh. The mesh is
1750specified either by assigning the name of a mesh file to
1751\code{source} or by specifying the points, triangle and boundary of the
1752mesh.
1753\end{classdesc}
1754
1755\subsection{Key Methods of Domain}
1756
1757\begin{methoddesc} {set\_name}{name}
1758    Module: \refmodule{abstract\_2d\_finite\_volumes.domain},
1759    page \pageref{mod:domain}
1760
1761    Assigns the name \code{name} to the domain.
1762\end{methoddesc}
1763
1764\begin{methoddesc} {get\_name}{}
1765    Module: \module{abstract\_2d\_finite\_volumes.domain}
1766
1767    Returns the name assigned to the domain by \code{set\_name}. If no name has been
1768    assigned, returns \code{`domain'}.
1769\end{methoddesc}
1770
1771\begin{methoddesc} {set\_datadir}{name}
1772    Module: \module{abstract\_2d\_finite\_volumes.domain}
1773
1774    Specifies the directory used for SWW files, assigning it to the
1775    pathname \code{name}. The default value, before
1776    \code{set\_datadir} has been run, is the value \code{default\_datadir}
1777    specified in \code{config.py}.
1778
1779    Since different operating systems use different formats for specifying pathnames,
1780    it is necessary to specify path separators using the Python code \code{os.sep}, rather than
1781    the operating-specific ones such as `$\slash$' or `$\backslash$'.
1782    For this to work you will need to include the statement \code{import os}
1783    in your code, before the first appearance of \code{set\_datadir}.
1784
1785    For example, to set the data directory to a subdirectory
1786    \code{data} of the directory \code{project}, you could use
1787    the statements:
1788
1789    {\small \begin{verbatim}
1790        import os
1791        domain.set_datadir{'project' + os.sep + 'data'}
1792    \end{verbatim}}
1793\end{methoddesc}
1794
1795\begin{methoddesc} {get\_datadir}{}
1796    Module: \module{abstract\_2d\_finite\_volumes.domain}
1797
1798    Returns the data directory set by \code{set\_datadir} or,
1799    if \code{set\_datadir} has not
1800    been run, returns the value \code{default\_datadir} specified in
1801    \code{config.py}.
1802\end{methoddesc}
1803
1804
1805\begin{methoddesc} {set\_minimum_allowed_height}{}
1806    Module: \module{shallow\_water.shallow\_water\_domain}
1807
1808    Set the minimum depth (in meters) that will be recognised in
1809    the numerical scheme (including limiters and flux computations)
1810
1811    Default value is $10^{-3}$ m, but by setting this to a greater value,
1812    e.g.\ for large scale simulations, the computation time can be
1813    significantly reduced.
1814\end{methoddesc}
1815
1816
1817\begin{methoddesc} {set\_minimum_storable_height}{}
1818    Module: \module{shallow\_water.shallow\_water\_domain}
1819
1820    Sets the minimum depth that will be recognised when writing
1821    to an sww file. This is useful for removing thin water layers
1822    that seems to be caused by friction creep.
1823\end{methoddesc}
1824
1825
1826\begin{methoddesc} {set\_maximum_allowed_speed}{}
1827    Module: \module{shallow\_water.shallow\_water\_domain}
1828
1829    Set the maximum particle speed that is allowed in water
1830    shallower than minimum_allowed_height. This is useful for
1831    controlling speeds in very thin layers of water and at the same time
1832    allow some movement avoiding pooling of water.
1833\end{methoddesc}
1834
1835
1836\begin{methoddesc} {set\_time}{time=0.0}
1837    Module: \module{abstract\_2d\_finite\_volumes.domain}
1838
1839    Sets the initial time, in seconds, for the simulation. The
1840    default is 0.0.
1841\end{methoddesc}
1842
1843\begin{methoddesc} {set\_default\_order}{n}
1844    Sets the default (spatial) order to the value specified by
1845    \code{n}, which must be either 1 or 2. (Assigning any other value
1846    to \code{n} will cause an error.)
1847\end{methoddesc}
1848
1849
1850\begin{methoddesc} {set\_store\_vertices\_uniquely}{flag}
1851Decide whether vertex values should be stored uniquely as
1852computed in the model or whether they should be reduced to one
1853value per vertex using averaging.
1854
1855Triangles stored in the sww file can be discontinuous reflecting
1856the internal representation of the finite-volume scheme
1857(this is a feature allowing for arbitrary steepness).
1858However, for visual purposes and also for use with \code{Field\_boundary}
1859(and \code{File\_boundary}) it is often desirable to store triangles
1860with values at each vertex point as the average of the potentially
1861discontinuous numbers found at vertices of different triangles sharing the
1862same vertex location.
1863
1864Storing one way or the other is controlled in ANUGA through the method
1865\code{domain.store\_vertices\_uniquely}. Options are
1866\begin{itemize}
1867  \item \code{domain.store\_vertices\_uniquely(True)}: Allow discontinuities in the sww file
1868  \item \code{domain.store\_vertices\_uniquely(False)}: (Default).
1869  Average values
1870  to ensure continuity in sww file. The latter also makes for smaller
1871  sww files.
1872\end{itemize}
1873
1874\end{methoddesc}
1875
1876
1877% Structural methods
1878\begin{methoddesc}{get\_nodes}{absolute=False}
1879    Return x,y coordinates of all nodes in mesh.
1880
1881    The nodes are ordered in an Nx2 array where N is the number of nodes.
1882    This is the same format they were provided in the constructor
1883    i.e. without any duplication.
1884
1885    Boolean keyword argument absolute determines whether coordinates
1886    are to be made absolute by taking georeference into account
1887    Default is False as many parts of ANUGA expects relative coordinates.
1888\end{methoddesc}
1889
1890
1891\begin{methoddesc}{get\_vertex_coordinates}{absolute=False}
1892
1893    Return vertex coordinates for all triangles.
1894
1895    Return all vertex coordinates for all triangles as a 3*M x 2 array
1896    where the jth vertex of the ith triangle is located in row 3*i+j and
1897    M the number of triangles in the mesh.
1898
1899    Boolean keyword argument absolute determines whether coordinates
1900    are to be made absolute by taking georeference into account
1901    Default is False as many parts of ANUGA expects relative coordinates.
1902\end{methoddesc}
1903
1904
1905\begin{methoddesc}{get\_triangles}{indices=None}
1906
1907        Return Mx3 integer array where M is the number of triangles.
1908        Each row corresponds to one triangle and the three entries are
1909        indices into the mesh nodes which can be obtained using the method
1910        get\_nodes()
1911
1912        Optional argument, indices is the set of triangle ids of interest.
1913\end{methoddesc}
1914
1915\begin{methoddesc}{get\_disconnected\_triangles}{}
1916
1917Get mesh based on nodes obtained from get_vertex_coordinates.
1918
1919        Return array Mx3 array of integers where each row corresponds to
1920        a triangle. A triangle is a triplet of indices into
1921        point coordinates obtained from get_vertex_coordinates and each
1922        index appears only once.\\
1923
1924        This provides a mesh where no triangles share nodes
1925        (hence the name disconnected triangles) and different
1926        nodes may have the same coordinates.\\
1927
1928        This version of the mesh is useful for storing meshes with
1929        discontinuities at each node and is e.g. used for storing
1930        data in sww files.\\
1931
1932        The triangles created will have the format
1933
1934    {\small \begin{verbatim}
1935        [[0,1,2],
1936         [3,4,5],
1937         [6,7,8],
1938         ...
1939         [3*M-3 3*M-2 3*M-1]]
1940     \end{verbatim}}
1941\end{methoddesc}
1942
1943
1944
1945%%%%%%
1946\section{Initial Conditions}\index{Initial Conditions}
1947\label{sec:initial conditions}
1948In standard usage of partial differential equations, initial conditions
1949refers to the values associated to the system variables (the conserved
1950quantities here) for \code{time = 0}. In setting up a scenario script
1951as described in Sections \ref{sec:simpleexample} and \ref{sec:realdataexample},
1952\code{set_quantity} is used to define the initial conditions of variables
1953other than the conserved quantities, such as friction. Here, we use the terminology
1954of initial conditions to refer to initial values for variables which need
1955prescription to solve the shallow water wave equation. Further, it must be noted
1956that \code{set_quantity} does not necessarily have to be used in the initial
1957condition setting; it can be used at any time throughout the simulation.
1958
1959\begin{methoddesc}{set\_quantity}{name,
1960    numeric = None,
1961    quantity = None,
1962    function = None,
1963    geospatial_data = None,
1964    filename = None,
1965    attribute_name = None,
1966    alpha = None,
1967    location = 'vertices',
1968    indices = None,
1969    verbose = False,
1970    use_cache = False}
1971  Module: \module{abstract\_2d\_finite\_volumes.domain}
1972  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
1973
1974This function is used to assign values to individual quantities for a
1975domain. It is very flexible and can be used with many data types: a
1976statement of the form \code{domain.set\_quantity(name, x)} can be used
1977to define a quantity having the name \code{name}, where the other
1978argument \code{x} can be any of the following:
1979
1980\begin{itemize}
1981\item a number, in which case all vertices in the mesh gets that for
1982the quantity in question.
1983\item a list of numbers or a Numeric array ordered the same way as the mesh vertices.
1984\item a function (e.g.\ see the samples introduced in Chapter 2)
1985\item an expression composed of other quantities and numbers, arrays, lists (for
1986example, a linear combination of quantities, such as
1987\code{domain.set\_quantity('stage','elevation'+x))}
1988\item the name of a file from which the data can be read. In this case, the optional argument attribute\_name will select which attribute to use from the file. If left out, set\_quantity will pick one. This is useful in cases where there is only one attribute.
1989\item a geospatial dataset (See Section \ref{sec:geospatial}).
1990Optional argument attribute\_name applies here as with files.
1991\end{itemize}
1992
1993
1994Exactly one of the arguments
1995  numeric, quantity, function, points, filename
1996must be present.
1997
1998
1999Set quantity will look at the type of the second argument (\code{numeric}) and
2000determine what action to take.
2001
2002Values can also be set using the appropriate keyword arguments.
2003If x is a function, for example, \code{domain.set\_quantity(name, x)}, \code{domain.set\_quantity(name, numeric=x)}, and \code{domain.set\_quantity(name, function=x)}
2004are all equivalent.
2005
2006
2007Other optional arguments are
2008\begin{itemize}
2009\item \code{indices} which is a list of ids of triangles to which set\_quantity should apply its assignment of values.
2010\item \code{location} determines which part of the triangles to assign
2011  to. Options are 'vertices' (default), 'edges', 'unique vertices', and 'centroids'.
2012\end{itemize}
2013
2014%%%
2015\anuga provides a number of predefined initial conditions to be used
2016with \code{set\_quantity}. See for example callable object
2017\code{slump\_tsunami} below.
2018
2019\end{methoddesc}
2020
2021
2022
2023
2024\begin{funcdesc}{set_region}{tag, quantity, X, location='vertices'}
2025  Module: \module{abstract\_2d\_finite\_volumes.domain}
2026
2027  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
2028
2029This function is used to assign values to individual quantities given
2030a regional tag.   It is similar to \code{set\_quantity}.
2031For example, if in the mesh-generator a regional tag of 'ditch' was
2032used, set\_region can be used to set elevation of this region to
2033-10m. X is the constant or function to be applied to the quantity,
2034over the tagged region.  Location describes how the values will be
2035applied.  Options are 'vertices' (default), 'edges', 'unique
2036vertices', and 'centroids'.
2037
2038This method can also be called with a list of region objects.  This is
2039useful for adding quantities in regions, and having one quantity
2040value based on another quantity. See  \module{abstract\_2d\_finite\_volumes.region} for
2041more details.
2042\end{funcdesc}
2043
2044
2045
2046
2047\begin{funcdesc}{slump_tsunami}{length, depth, slope, width=None, thickness=None,
2048                x0=0.0, y0=0.0, alpha=0.0,
2049                gravity=9.8, gamma=1.85,
2050                massco=1, dragco=1, frictionco=0, psi=0,
2051                dx=None, kappa=3.0, kappad=0.8, zsmall=0.01,
2052                domain=None,
2053                verbose=False}
2054Module: \module{shallow\_water.smf}
2055
2056This function returns a callable object representing an initial water
2057displacement generated by a submarine sediment failure. These failures can take the form of
2058a submarine slump or slide. In the case of a slide, use \code{slide_tsunami} instead.
2059
2060The arguments include as a minimum, the slump or slide length, the water depth to the centre of sediment
2061mass, and the bathymetric slope. Other slump or slide parameters can be included if they are known.
2062\end{funcdesc}
2063
2064
2065%%%
2066\begin{funcdesc}{file\_function}{filename,
2067    domain = None,
2068    quantities = None,
2069    interpolation_points = None,
2070    verbose = False,
2071    use_cache = False}
2072Module: \module{abstract\_2d\_finite\_volumes.util}
2073
2074Reads the time history of spatial data for
2075specified interpolation points from a NetCDF file (\code{filename})
2076and returns
2077a callable object. \code{filename} could be a \code{sww} or \code{sts} file.
2078Returns interpolated values based on the input
2079file using the underlying \code{interpolation\_function}.
2080
2081\code{quantities} is either the name of a single quantity to be
2082interpolated or a list of such quantity names. In the second case, the resulting
2083function will return a tuple of values---one for each quantity.
2084
2085\code{interpolation\_points} is a list of absolute coordinates or a
2086geospatial object
2087for points at which values are sought.
2088
2089\code{boundary_polygon} is a list of coordinates specifying the vertices of the boundary. This must be the same polygon as used when calling \code{create_mesh_from_regions}. This argument can only be used when reading boundary data from the STS format.
2090
2091The model time stored within the file function can be accessed using
2092the method \code{f.get\_time()}
2093
2094
2095The underlying algorithm used is as follows:\\
2096Given a time series (i.e.\ a series of values associated with
2097different times), whose values are either just numbers, a set of
2098 numbers defined at the vertices of a triangular mesh (such as those
2099 stored in SWW files) or a set of
2100 numbers defined at a number of points on the boundary (such as those
2101 stored in STS files), \code{Interpolation\_function} is used to
2102 create a callable object that interpolates a value for an arbitrary
2103 time \code{t} within the model limits and possibly a point \code{(x,
2104 y)} within a mesh region.
2105
2106 The actual time series at which data is available is specified by
2107 means of an array \code{time} of monotonically increasing times. The
2108 quantities containing the values to be interpolated are specified in
2109 an array---or dictionary of arrays (used in conjunction with the
2110 optional argument \code{quantity\_names}) --- called
2111 \code{quantities}. The optional arguments \code{vertex\_coordinates}
2112 and \code{triangles} represent the spatial mesh associated with the
2113 quantity arrays. If omitted the function must be created using an STS file
2114 or a TMS file.
2115
2116 Since, in practice, values need to be computed at specified points,
2117 the syntax allows the user to specify, once and for all, a list
2118 \code{interpolation\_points} of points at which values are required.
2119 In this case, the function may be called using the form \code{f(t,
2120 id)}, where \code{id} is an index for the list
2121 \code{interpolation\_points}.
2122
2123
2124\end{funcdesc}
2125
2126%%%
2127%% \begin{classdesc}{Interpolation\_function}{self,
2128%%     time,
2129%%     quantities,
2130%%     quantity_names = None,
2131%%     vertex_coordinates = None,
2132%%     triangles = None,
2133%%     interpolation_points = None,
2134%%     verbose = False}
2135%% Module: \module{abstract\_2d\_finite\_volumes.least\_squares}
2136
2137%% Given a time series (i.e.\ a series of values associated with
2138%% different times), whose values are either just numbers or a set of
2139%% numbers defined at the vertices of a triangular mesh (such as those
2140%% stored in SWW files), \code{Interpolation\_function} is used to
2141%% create a callable object that interpolates a value for an arbitrary
2142%% time \code{t} within the model limits and possibly a point \code{(x,
2143%% y)} within a mesh region.
2144
2145%% The actual time series at which data is available is specified by
2146%% means of an array \code{time} of monotonically increasing times. The
2147%% quantities containing the values to be interpolated are specified in
2148%% an array---or dictionary of arrays (used in conjunction with the
2149%% optional argument \code{quantity\_names}) --- called
2150%% \code{quantities}. The optional arguments \code{vertex\_coordinates}
2151%% and \code{triangles} represent the spatial mesh associated with the
2152%% quantity arrays. If omitted the function created by
2153%% \code{Interpolation\_function} will be a function of \code{t} only.
2154
2155%% Since, in practice, values need to be computed at specified points,
2156%% the syntax allows the user to specify, once and for all, a list
2157%% \code{interpolation\_points} of points at which values are required.
2158%% In this case, the function may be called using the form \code{f(t,
2159%% id)}, where \code{id} is an index for the list
2160%% \code{interpolation\_points}.
2161
2162%% \end{classdesc}
2163
2164%%%
2165%\begin{funcdesc}{set\_region}{functions}
2166%[Low priority. Will be merged into set\_quantity]
2167
2168%Module:\module{abstract\_2d\_finite\_volumes.domain}
2169%\end{funcdesc}
2170
2171
2172
2173%%%%%%
2174\section{Boundary Conditions}\index{boundary conditions}
2175\label{sec:boundary conditions}
2176
2177\anuga provides a large number of predefined boundary conditions,
2178represented by objects such as \code{Reflective\_boundary(domain)} and
2179\code{Dirichlet\_boundary([0.2, 0.0, 0.0])}, described in the examples
2180in Chapter 2. Alternatively, you may prefer to ``roll your own'',
2181following the method explained in Section \ref{sec:roll your own}.
2182
2183These boundary objects may be used with the function \code{set\_boundary} described below
2184to assign boundary conditions according to the tags used to label boundary segments.
2185
2186\begin{methoddesc}{set\_boundary}{boundary_map}
2187Module: \module{abstract\_2d\_finite\_volumes.domain}
2188
2189This function allows you to assign a boundary object (corresponding to a
2190pre-defined or user-specified boundary condition) to every boundary segment that
2191has been assigned a particular tag.
2192
2193This is done by specifying a dictionary \code{boundary\_map}, whose values are the boundary objects
2194and whose keys are the symbolic tags.
2195
2196\end{methoddesc}
2197
2198\begin{methoddesc} {get\_boundary\_tags}{}
2199Module: \module{abstract\_2d\_finite\_volumes.domain}
2200
2201Returns a list of the available boundary tags.
2202\end{methoddesc}
2203
2204%%%
2205\subsection{Predefined boundary conditions}
2206
2207\begin{classdesc}{Reflective\_boundary}{Boundary}
2208Module: \module{shallow\_water}
2209
2210Reflective boundary returns same conserved quantities as those present in
2211the neighbouring volume but reflected.
2212
2213This class is specific to the shallow water equation as it works with the
2214momentum quantities assumed to be the second and third conserved quantities.
2215\end{classdesc}
2216
2217%%%
2218\begin{classdesc}{Transmissive\_boundary}{domain = None}
2219Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2220
2221A transmissive boundary returns the same conserved quantities as
2222those present in the neighbouring volume.
2223
2224The underlying domain must be specified when the boundary is instantiated.
2225\end{classdesc}
2226
2227%%%
2228\begin{classdesc}{Dirichlet\_boundary}{conserved_quantities=None}
2229Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2230
2231A Dirichlet boundary returns constant values for each of conserved
2232quantities. In the example of \code{Dirichlet\_boundary([0.2, 0.0, 0.0])},
2233the \code{stage} value at the boundary is 0.2 and the \code{xmomentum} and
2234\code{ymomentum} at the boundary are set to 0.0. The list must contain
2235a value for each conserved quantity.
2236\end{classdesc}
2237
2238%%%
2239\begin{classdesc}{Time\_boundary}{domain = None, f = None}
2240Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2241
2242A time-dependent boundary returns values for the conserved
2243quantities as a function \code{f(t)} of time. The user must specify
2244the domain to get access to the model time.
2245\end{classdesc}
2246
2247%%%
2248\begin{classdesc}{File\_boundary}{Boundary}
2249Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2250
2251This method may be used if the user wishes to apply a SWW file, STS file or
2252a time series file (TMS) to a boundary segment or segments.
2253The boundary values are obtained from a file and interpolated to the
2254appropriate segments for each conserved quantity.
2255
2256Optional argument \code{default\_boundary} can be used to specify another boundary object to be used in case model time exceeds the time availabel in the file used by \code{File\_boundary}.
2257The \code{default\_boundary} could be a simple Dirichlet condition or
2258even another \code{File\_boundary} 
2259typically using data pertaining to another time interval. 
2260\end{classdesc}
2261
2262\begin{classdesc}{Field\_boundary}{Boundary}
2263Module: \module{shallow\_water.shallow\_water\_domain}
2264
2265This method works in the same way as \code{File\_boundary} except that it
2266allows for the value of stage to be offset by a constant specified in the
2267keyword argument \code{mean\_stage}.
2268
2269This functionality allows for models to be run for a range of tides using
2270the same boundary information (from .sts, .sww or .tms files). The tidal value
2271for each run would then be specified in the keyword argument
2272\code{mean\_stage}.
2273If \code{mean\_stage} = 0.0, \code{Field\_boundary} and \code{File\_boundary} 
2274behave identically.
2275
2276
2277Note that if the optional argument \code{default\_boundary} is specified
2278it's stage value will be adjusted by \code{mean\_stage} just like the values
2279obtained from the file.
2280
2281See \code{File\_boundary} for further details.
2282\end{classdesc}
2283
2284%%%
2285\begin{classdesc}{Transmissive\_Momentum\_Set\_Stage\_boundary}{Boundary}
2286Module: \module{shallow\_water}
2287
2288This boundary returns same momentum conserved quantities as
2289those present in its neighbour volume but sets stage as in a Time\_boundary.
2290The underlying domain must be specified when boundary is instantiated
2291
2292This type of boundary is useful when stage is known at the boundary as a
2293function of time, but momenta (or speeds) aren't.
2294
2295This class is specific to the shallow water equation as it works with the
2296momentum quantities assumed to be the second and third conserved quantities.
2297\end{classdesc}
2298
2299
2300\begin{classdesc}{Dirichlet\_Discharge\_boundary}{Boundary}
2301Module: \module{shallow\_water}
2302
2303Sets stage (stage0)
2304Sets momentum (wh0) in the inward normal direction.
2305\end{classdesc}
2306
2307
2308
2309\subsection{User-defined boundary conditions}
2310\label{sec:roll your own}
2311
2312All boundary classes must inherit from the generic boundary class
2313\code{Boundary} and have a method called \code{evaluate} which must
2314take as inputs \code{self, vol\_id, edge\_id} where self refers to the
2315object itself and vol\_id and edge\_id are integers referring to
2316particular edges. The method must return a list of three floating point
2317numbers representing values for \code{stage},
2318\code{xmomentum} and \code{ymomentum}, respectively.
2319
2320The constructor of a particular boundary class may be used to specify
2321particular values or flags to be used by the \code{evaluate} method.
2322Please refer to the source code for the existing boundary conditions
2323for examples of how to implement boundary conditions.
2324
2325
2326
2327\section{Forcing Terms}\index{Forcing terms}
2328\label{sec:forcing terms}
2329
2330\anuga provides a number of predefined forcing functions to be used with simulations.
2331Gravity and friction are always calculated using the elevation and friction quantities, but the user may additionally add forcing terms to the list
2332\code{domain.forcing\_terms} and have them affect the model.
2333 
2334Currently, predefined forcing terms are
2335
2336\begin{funcdesc}{General\_forcing}{}
2337  Module: \module{shallow\_water.shallow\_water\_domain}
2338
2339  This is a general class to modify any quantity according to a given rate of change.
2340  Other specific forcing terms are based on this class but it can be used by itself as well (e.g.\ to modify momentum).
2341 
2342  The General\_forcing class takes as input:
2343  \begin{itemize} 
2344    \item \code{domain}: a reference to the domain being evolved
2345    \item \code{quantity\_name}: The name of the quantity that will be affected by this forcing term
2346    \item \code{rate}: The rate at which the quantity should change. The parameter \code{rate} can be eithe a constant or a
2347                function of time. Positive values indicate increases,
2348                negative values indicate decreases.
2349                The parametr \code{rate} can be \code{None} at initialisation but must be specified
2350                before forcing term is applied (i.e. simulation has started).
2351                The default value is 0.0 - i.e.\ no forcing.
2352    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2353    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2354  \end{itemize}
2355  Note specifying both center, radius and polygon will cause an exception to be thrown.
2356  Moreover, if the specified polygon or circle does not lie fully within the mesh boundary an Exception will be thrown.
2357
2358  \bigskip 
2359  Example:
2360  {\scriptsize \begin{verbatim} 
2361    P = [[x0, y0], [x1, y0], [x1, y1], [x0, y1]] # Square polygon
2362 
2363    xmom = General_forcing(domain, 'xmomentum', polygon=P)
2364    ymom = General_forcing(domain, 'ymomentum', polygon=P)
2365
2366    xmom.rate = f
2367    ymom.rate = g
2368 
2369    domain.forcing_terms.append(xmom)
2370    domain.forcing_terms.append(ymom)   
2371  \end{verbatim}}
2372  Here, \code{f}, \code{g} are assumed to be defined as functions of time providing a time dependent rate of change for xmomentum and ymomentum respectively.
2373  P is assumed to be polygon, specified as a list of points.
2374 
2375\end{funcdesc} 
2376
2377
2378\begin{funcdesc}{Inflow}{}
2379  Module: \module{shallow\_water.shallow\_water\_domain}
2380
2381  This is a general class for inflow and abstraction of water according to a given rate of change.
2382  This class will always modify the \code{stage} quantity.
2383 
2384  Inflow is based on the General_forcing class so the functionality is similar.
2385 
2386  The Inflow class takes as input:
2387  \begin{itemize} 
2388    \item \code{domain}: a reference to the domain being evolved
2389    \item \code{rate}: The flow rate in $m^3/s$ at which the stage should change. The parameter \code{rate} can be eithe a constant or a
2390                function of time. Positive values indicate inflow,
2391                negative values indicate outflow.
2392               
2393                Note: The specified flow will be divided by the area of
2394                the inflow region and then applied to update the
2395                stage quantity.     
2396    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2397    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2398  \end{itemize}
2399
2400  \bigskip     
2401  Example:
2402  {\scriptsize \begin{verbatim} 
2403    hydrograph = Inflow(center=(320, 300), radius=10,
2404                        rate=file_function('QPMF_Rot_Sub13.tms'))
2405
2406    domain.forcing_terms.append(hydrograph)
2407  \end{verbatim}}
2408  Here, \code{'QPMF_Rot_Sub13.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for a hydrograph.
2409\end{funcdesc} 
2410
2411
2412\begin{funcdesc}{Rainfall}{}
2413  Module: \module{shallow\_water.shallow\_water\_domain}
2414
2415  This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon.
2416  This class will always modify the \code{stage} quantity.
2417 
2418  Rainfall is based on the General_forcing class so the functionality is similar.
2419 
2420  The Rainfall class takes as input:
2421  \begin{itemize} 
2422    \item \code{domain}: a reference to the domain being evolved
2423    \item \code{rate}: Total rain rate over the specified domain. 
2424                  Note: Raingauge Data needs to reflect the time step.
2425                  For example: if rain gauge is mm read every \code{dt} seconds, then the input
2426                  here is as \code{mm/dt} so 10 mm in 5 minutes becomes
2427                  10/(5x60) = 0.0333mm/s.
2428       
2429                  This parameter can be either a constant or a
2430                  function of time. Positive values indicate rain being added (or be used for general infiltration),
2431                  negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction).
2432    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2433    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2434  \end{itemize}
2435 
2436  \bigskip   
2437  Example:
2438  {\scriptsize \begin{verbatim} 
2439 
2440    catchmentrainfall = Rainfall(rain=file_function('Q100_2hr_Rain.tms')) 
2441    domain.forcing_terms.append(catchmentrainfall)
2442
2443  \end{verbatim}}
2444  Here, \code{'Q100_2hr_Rain.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for the rainfall.
2445\end{funcdesc} 
2446
2447
2448
2449\begin{funcdesc}{Culvert\_flow}{}
2450  Module: \module{culver\_flows.culvert\_class}
2451
2452  This is a general class for implementing flow through a culvert.
2453  This class modifies the quantities \code{stage, xmomentum, ymomentum} in areas at both ends of the culvert.
2454 
2455  The Culvert\_flow forcing term uses \code{Inflow} and {General\_forcing} to update the quantities. The flow drection is determined on-the-fly so
2456  openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow and Outflow.
2457 
2458  The Culvert\_flow class takes as input:
2459  \begin{itemize} 
2460    \item \code{domain}: a reference to the domain being evolved
2461    \item \code{label}: Short text naming the culvert
2462    \item \code{description}: Text describing it
2463    \item \code{end_point0}: Coordinates of one opening
2464    \item \code{end_point1}: Coordinates of other opening
2465    \item \code{width}:
2466    \item \code{height}:
2467    \item \code{diameter}:
2468    \item \code{manning}: Mannings Roughness for Culvert
2469    \item \code{invert_level0}: Invert level if not the same as the Elevation on the Domain
2470    \item \code{invert_level1}: Invert level if not the same as the Elevation on the Domain
2471    \item \code{culvert_routine}: Function specifying the calculation of flow based on energy difference between the two openings (see below)
2472  \end{itemize}
2473
2474  The user can specify different culvert routines. Hower ANUGA currently provides only one, namely the \code{boyd\_generalised\_culvert\_model} as used in the example below.
2475     
2476  \bigskip       
2477  Example:
2478  {\scriptsize \begin{verbatim} 
2479    from anuga.culvert_flows.culvert_class import Culvert_flow
2480    from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model 
2481
2482    culvert1 = Culvert_flow(domain,
2483                           label='Culvert No. 1',
2484                           description='This culvert is a test unit 1.2m Wide by 0.75m High',   
2485                           end_point0=[9.0, 2.5],
2486                           end_point1=[13.0, 2.5],
2487                           width=1.20,height=0.75,
2488                           culvert_routine=boyd_generalised_culvert_model,       
2489                           verbose=True)
2490
2491    culvert2 = Culvert_flow(domain,
2492                           label='Culvert No. 2',
2493                           description='This culvert is a circular test with d=1.2m',   
2494                           end_point0=[9.0, 1.5],
2495                           end_point1=[30.0, 3.5],
2496                           diameter=1.20,
2497                           invert_level0=7,
2498                           culvert_routine=boyd_generalised_culvert_model,       
2499                           verbose=True)
2500                           
2501    domain.forcing_terms.append(culvert1)
2502    domain.forcing_terms.append(culvert2)
2503
2504   
2505  \end{verbatim}}
2506\end{funcdesc} 
2507
2508
2509
2510
2511
2512
2513\section{Evolution}\index{evolution}
2514\label{sec:evolution}
2515
2516  \begin{methoddesc}{evolve}{yieldstep = None, finaltime = None, duration = None, skip_initial_step = False}
2517
2518  Module: \module{abstract\_2d\_finite\_volumes.domain}
2519
2520  This function (a method of \class{domain}) is invoked once all the
2521  preliminaries have been completed, and causes the model to progress
2522  through successive steps in its evolution, storing results and
2523  outputting statistics whenever a user-specified period
2524  \code{yieldstep} is completed (generally during this period the
2525  model will evolve through several steps internally
2526  as the method forces the water speed to be calculated
2527  on successive new cells). The user
2528  specifies the total time period over which the evolution is to take
2529  place, by specifying values (in seconds) for either \code{duration}
2530  or \code{finaltime}, as well as the interval in seconds after which
2531  results are to be stored and statistics output.
2532
2533  You can include \method{evolve} in a statement of the type:
2534
2535  {\small \begin{verbatim}
2536      for t in domain.evolve(yieldstep, finaltime):
2537          <Do something with domain and t>
2538  \end{verbatim}}
2539
2540  \end{methoddesc}
2541
2542
2543
2544\subsection{Diagnostics}
2545\label{sec:diagnostics}
2546
2547
2548  \begin{funcdesc}{statistics}{}
2549  Module: \module{abstract\_2d\_finite\_volumes.domain}
2550
2551  \end{funcdesc}
2552
2553  \begin{funcdesc}{timestepping\_statistics}{}
2554  Module: \module{abstract\_2d\_finite\_volumes.domain}
2555
2556  Returns a string of the following type for each
2557  timestep:
2558
2559  \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12
2560  (12)}
2561
2562  Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and
2563  the number of first-order steps, respectively.\\
2564
2565  The optional keyword argument \code{track_speeds=True} will
2566  generate a histogram of speeds generated by each triangle. The
2567  speeds relate to the size of the timesteps used by ANUGA and
2568  this diagnostics may help pinpoint problem areas where excessive speeds
2569  are generated.
2570
2571  \end{funcdesc}
2572
2573
2574  \begin{funcdesc}{boundary\_statistics}{quantities = None, tags = None}
2575  Module: \module{abstract\_2d\_finite\_volumes.domain}
2576
2577  Returns a string of the following type when \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']}:
2578
2579  {\small \begin{verbatim}
2580 Boundary values at time 0.5000:
2581    top:
2582        stage in [ -0.25821218,  -0.02499998]
2583    bottom:
2584        stage in [ -0.27098821,  -0.02499974]
2585  \end{verbatim}}
2586
2587  \end{funcdesc}
2588
2589
2590  \begin{funcdesc}{get\_quantity}{name, location='vertices', indices = None}
2591  Module: \module{abstract\_2d\_finite\_volumes.domain}
2592
2593  Allow access to individual quantities and their methods
2594
2595  \end{funcdesc}
2596
2597
2598  \begin{funcdesc}{set\_quantities\_to\_be\_monitored}{}
2599  Module: \module{abstract\_2d\_finite\_volumes.domain}
2600
2601  Selects quantities and derived quantities for which extrema attained at internal timesteps
2602  will be collected.
2603
2604  Information can be tracked in the evolve loop by printing \code{quantity\_statistics} and
2605  collected data will be stored in the sww file.
2606
2607  Optional parameters \code{polygon} and \code{time\_interval} may be specified to restrict the
2608  extremum computation.
2609  \end{funcdesc}
2610
2611  \begin{funcdesc}{quantity\_statistics}{}
2612  Module: \module{abstract\_2d\_finite\_volumes.domain}
2613
2614  Reports on extrema attained by selected quantities.
2615
2616  Returns a string of the following type for each
2617  timestep:
2618
2619  \begin{verbatim}
2620  Monitored quantities at time 1.0000:
2621    stage-elevation:
2622      values since time = 0.00 in [0.00000000, 0.30000000]
2623      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2624      maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667)
2625    ymomentum:
2626      values since time = 0.00 in [0.00000000, 0.06241221]
2627      minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667)
2628      maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667)
2629    xmomentum:
2630      values since time = 0.00 in [-0.06062178, 0.47886313]
2631      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2632      maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667)
2633  \end{verbatim}
2634
2635  The quantities (and derived quantities) listed here must be selected at model
2636  initialisation using the method \code{domain.set_quantities_to_be_monitored}.\\
2637
2638  The optional keyword argument \code{precision='\%.4f'} will
2639  determine the precision used for floating point values in the output.
2640  This diagnostics helps track extrema attained by the selected quantities
2641  at every internal timestep.
2642
2643  These values are also stored in the sww file for post processing.
2644
2645  \end{funcdesc}
2646
2647
2648
2649  \begin{funcdesc}{get\_values}{location='vertices', indices = None}
2650  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2651
2652  Extract values for quantity as an array
2653
2654  \end{funcdesc}
2655
2656
2657  \begin{funcdesc}{get\_integral}{}
2658  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2659
2660  Return computed integral over entire domain for this quantity
2661
2662  \end{funcdesc}
2663
2664
2665
2666
2667  \begin{funcdesc}{get\_maximum\_value}{indices = None}
2668  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2669
2670  Return maximum value of quantity (on centroids)
2671
2672  Optional argument indices is the set of element ids that
2673  the operation applies to. If omitted all elements are considered.
2674
2675  We do not seek the maximum at vertices as each vertex can
2676  have multiple values - one for each triangle sharing it.
2677  \end{funcdesc}
2678
2679
2680
2681  \begin{funcdesc}{get\_maximum\_location}{indices = None}
2682  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2683
2684  Return location of maximum value of quantity (on centroids)
2685
2686  Optional argument indices is the set of element ids that
2687  the operation applies to.
2688
2689  We do not seek the maximum at vertices as each vertex can
2690  have multiple values - one for each triangle sharing it.
2691
2692  If there are multiple cells with same maximum value, the
2693  first cell encountered in the triangle array is returned.
2694  \end{funcdesc}
2695
2696
2697
2698  \begin{funcdesc}{get\_wet\_elements}{indices=None}
2699  Module: \module{shallow\_water.shallow\_water\_domain}
2700
2701  Return indices for elements where h $>$ minimum_allowed_height
2702  Optional argument indices is the set of element ids that the operation applies to.
2703  \end{funcdesc}
2704
2705
2706  \begin{funcdesc}{get\_maximum\_inundation\_elevation}{indices=None}
2707  Module: \module{shallow\_water.shallow\_water\_domain}
2708
2709  Return highest elevation where h $>$ 0.\\
2710  Optional argument indices is the set of element ids that the operation applies to.\\
2711
2712  Example to find maximum runup elevation:\\
2713     z = domain.get_maximum_inundation_elevation()
2714  \end{funcdesc}
2715
2716
2717  \begin{funcdesc}{get\_maximum\_inundation\_location}{indices=None}
2718  Module: \module{shallow\_water.shallow\_water\_domain}
2719
2720  Return location (x,y) of highest elevation where h $>$ 0.\\
2721  Optional argument indices is the set of element ids that the operation applies to.\\
2722
2723  Example to find maximum runup location:\\
2724     x, y = domain.get_maximum_inundation_location()
2725  \end{funcdesc}
2726
2727
2728\section{Queries of SWW model output files}
2729After a model has been run, it is often useful to extract various information from the sww
2730output file (see Section \ref{sec:sww format}). This is typically more convenient than using the
2731diagnostics described in Section \ref{sec:diagnostics} which rely on the model running - something
2732that can be very time consuming. The sww files are easy and quick to read and offer much information
2733about the model results such as runup heights, time histories of selected quantities,
2734flow through cross sections and much more.
2735
2736\begin{funcdesc}{get\_maximum\_inundation\_elevation}{filename, polygon=None,
2737    time_interval=None, verbose=False}
2738  Module: \module{shallow\_water.data\_manager}
2739
2740  Return highest elevation where depth is positive ($h > 0$)
2741
2742  Example to find maximum runup elevation:\\
2743  max_runup = get_maximum_inundation_elevation(filename,
2744  polygon=None,
2745  time_interval=None,
2746  verbose=False)
2747
2748
2749  filename is a NetCDF sww file containing ANUGA model output.
2750  Optional arguments polygon and time_interval restricts the maximum runup calculation
2751  to a points that lie within the specified polygon and time interval.
2752
2753  If no inundation is found within polygon and time_interval the return value
2754  is None signifying "No Runup" or "Everything is dry".
2755
2756  See doc string for general function get_maximum_inundation_data for details.
2757\end{funcdesc}
2758
2759
2760\begin{funcdesc}{get\_maximum\_inundation\_location}{filename, polygon=None,
2761    time_interval=None, verbose=False}
2762  Module: \module{shallow\_water.data\_manager}
2763
2764  Return location (x,y) of highest elevation where depth is positive ($h > 0$)
2765
2766  Example to find maximum runup location:\\
2767  max_runup_location = get_maximum_inundation_location(filename,
2768  polygon=None,
2769  time_interval=None,
2770  verbose=False)
2771
2772
2773  filename is a NetCDF sww file containing ANUGA model output.
2774  Optional arguments polygon and time_interval restricts the maximum runup calculation
2775  to a points that lie within the specified polygon and time interval.
2776
2777  If no inundation is found within polygon and time_interval the return value
2778  is None signifying "No Runup" or "Everything is dry".
2779
2780  See doc string for general function get_maximum_inundation_data for details.
2781\end{funcdesc}
2782
2783
2784\begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report = None, reportname = None,
2785plot_quantity = None, generate_fig = False, surface = None, time_min = None, time_max = None, time_thinning = 1,
2786time_unit = None, title_on = None, use_cache = False, verbose = False}
2787
2788  Module: \module{anuga.abstract\_2d\_finite\_volumes.util}
2789
2790  Return csv files for the location in the \code{gauge_filename} and can also return plots of them
2791
2792  See doc string for general function sww2timeseries for details.
2793
2794\end{funcdesc}
2795
2796
2797\begin{funcdesc}{get\_flow\_through\_cross\_section}{filename, cross\_section, verbose=False}
2798  Module: \module{shallow\_water.data\_manager}
2799
2800  Obtain flow $[m^3/s]$ perpendicular to specified cross section.
2801
2802  Inputs:
2803  \begin{itemize} 
2804        \item filename: Name of sww file containing ANUGA model output.
2805        \item polyline: Representation of desired cross section - it may contain multiple
2806          sections allowing for complex shapes. Assume absolute UTM coordinates.
2807  \end{itemize} 
2808
2809  Output:
2810  \begin{itemize}
2811    \item time: All stored times in sww file
2812    \item Q: Hydrograph of total flow across given segments for all stored times.
2813  \end{itemize} 
2814 
2815  The normal flow is computed for each triangle intersected by the polyline and
2816  added up.  Multiple segments at different angles are specified the normal flows
2817  may partially cancel each other.
2818 
2819  Example to find flow through cross section:
2820 
2821  \begin{verbatim} 
2822  cross_section = [[x, 0], [x, width]]
2823  time, Q = get_flow_through_cross_section(filename,
2824                                           cross_section,
2825                                           verbose=False)
2826  \end{verbatim} 
2827
2828
2829  See doc string for general function get_maximum_inundation_data for details.
2830 
2831\end{funcdesc}
2832
2833
2834
2835\section{Other}
2836
2837  \begin{funcdesc}{domain.create\_quantity\_from\_expression}{string}
2838
2839  Handy for creating derived quantities on-the-fly as for example
2840  \begin{verbatim}
2841  Depth = domain.create_quantity_from_expression('stage-elevation')
2842
2843  exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5')
2844  Absolute_momentum = domain.create_quantity_from_expression(exp)
2845  \end{verbatim}
2846
2847  %See also \file{Analytical\_solution\_circular\_hydraulic\_jump.py} for an example of use.
2848  \end{funcdesc}
2849
2850
2851
2852
2853
2854%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2855%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2856
2857\chapter{\anuga System Architecture}
2858
2859
2860\section{File Formats}
2861\label{sec:file formats}
2862
2863\anuga makes use of a number of different file formats. The
2864following table lists all these formats, which are described in more
2865detail in the paragraphs below.
2866
2867\bigskip
2868
2869\begin{center}
2870
2871\begin{tabular}{|ll|}  \hline
2872
2873\textbf{Extension} & \textbf{Description} \\
2874\hline\hline
2875
2876\code{.sww} & NetCDF format for storing model output with mesh information
2877\code{f(t,x,y)}\\
2878
2879\code{.sts} & NetCDF format for storing model ouput \code{f(t,x,y)} without any mesh information\\
2880
2881\code{.tms} & NetCDF format for storing time series \code{f(t)}\\
2882
2883\code{.csv/.txt} & ASCII format called points csv for storing
2884arbitrary points and associated attributes\\
2885
2886\code{.pts} & NetCDF format for storing arbitrary points and
2887associated attributes\\
2888
2889\code{.asc} & ASCII format of regular DEMs as output from ArcView\\
2890
2891\code{.prj} & Associated ArcView file giving more metadata for
2892\code{.asc} format\\
2893
2894\code{.ers} & ERMapper header format of regular DEMs for ArcView\\
2895
2896\code{.dem} & NetCDF representation of regular DEM data\\
2897
2898\code{.tsh} & ASCII format for storing meshes and associated
2899boundary and region info\\
2900
2901\code{.msh} & NetCDF format for storing meshes and associated
2902boundary and region info\\
2903
2904\code{.nc} & Native ferret NetCDF format\\
2905
2906\code{.geo} & Houdinis ASCII geometry format (?) \\  \par \hline
2907%\caption{File formats used by \anuga}
2908\end{tabular}
2909
2910
2911\end{center}
2912
2913The above table shows the file extensions used to identify the
2914formats of files. However, typically, in referring to a format we
2915capitalise the extension and omit the initial full stop---thus, we
2916refer, for example, to `SWW files' or `PRJ files'.
2917
2918\bigskip
2919
2920A typical dataflow can be described as follows:
2921
2922\subsection{Manually Created Files}
2923
2924\begin{tabular}{ll}
2925ASC, PRJ & Digital elevation models (gridded)\\
2926NC & Model outputs for use as boundary conditions (e.g. from MOST)
2927\end{tabular}
2928
2929\subsection{Automatically Created Files}
2930
2931\begin{tabular}{ll}
2932ASC, PRJ  $\rightarrow$  DEM  $\rightarrow$  PTS & Convert
2933DEMs to native \code{.pts} file\\
2934
2935NC $\rightarrow$ SWW & Convert MOST boundary files to
2936boundary \code{.sww}\\
2937
2938PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\
2939
2940TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using
2941\code{animate}\\
2942
2943TSH + Boundary SWW $\rightarrow$ SWW & Simulation using
2944\code{\anuga}\\
2945
2946Polygonal mesh outline $\rightarrow$ & TSH or MSH
2947\end{tabular}
2948
2949
2950
2951
2952\bigskip
2953
2954\subsection{SWW, STS and TMS Formats}
2955\label{sec:sww format}
2956
2957The SWW, STS and TMS formats are all NetCDF formats, and are of key
2958importance for \anuga.
2959
2960An SWW file is used for storing \anuga output and therefore pertains
2961to a set of points and a set of times at which a model is evaluated.
2962It contains, in addition to dimension information, the following
2963variables:
2964
2965\begin{itemize}
2966    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2967    \item \code{elevation}, a Numeric array storing bed-elevations
2968    \item \code{volumes}, a list specifying the points at the vertices of each of the
2969    triangles
2970    % Refer here to the example to be provided in describing the simple example
2971    \item \code{time}, a Numeric array containing times for model
2972    evaluation
2973\end{itemize}
2974
2975
2976The contents of an SWW file may be viewed using the anuga viewer
2977\code{animate}, which creates an on-screen geometric
2978representation. See section \ref{sec:animate} (page
2979\pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more
2980on \code{animate}.
2981
2982Alternatively, there are tools, such as \code{ncdump}, that allow
2983you to convert an NetCDF file into a readable format such as the
2984Class Definition Language (CDL). The following is an excerpt from a
2985CDL representation of the output file \file{runup.sww} generated
2986from running the simple example \file{runup.py} of
2987Chapter \ref{ch:getstarted}:
2988
2989\verbatiminput{examples/bedslopeexcerpt.cdl}
2990
2991The SWW format is used not only for output but also serves as input
2992for functions such as \function{file\_boundary} and
2993\function{file\_function}, described in Chapter \ref{ch:interface}.
2994
2995An STS file is used for storing a set of points and and associated set of times.
2996It contains, in addition to dimension information, the following
2997variables:
2998\begin{itemize}
2999    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
3000    \item \code{elevation}, a Numeric array storing bed-elevations
3001    % Refer here to the example to be provided in describing the simple example
3002    \item \code{time}, a Numeric array containing times for model
3003    evaluation
3004\end{itemize}
3005The only difference between the STS format and the SWW format is the former does not contain a list specifying the points at the vertices of each of the triangles (\code{volumes}). Consequenlty information (arrays) stored within an STS file such as \code{elevation} can be accessed in exactly the same way as it would be extraced from an SWW file.
3006
3007A TMS file is used to store time series data that is independent of
3008position.
3009
3010
3011\subsection{Mesh File Formats}
3012
3013A mesh file is a file that has a specific format suited to
3014triangular meshes and their outlines. A mesh file can have one of
3015two formats: it can be either a TSH file, which is an ASCII file, or
3016an MSH file, which is a NetCDF file. A mesh file can be generated
3017from the function \function{create\_mesh\_from\_regions} (see
3018Section \ref{sec:meshgeneration}) and used to initialise a domain.
3019
3020A mesh file can define the outline of the mesh---the vertices and
3021line segments that enclose the region in which the mesh is
3022created---and the triangular mesh itself, which is specified by
3023listing the triangles and their vertices, and the segments, which
3024are those sides of the triangles that are associated with boundary
3025conditions.
3026
3027In addition, a mesh file may contain `holes' and/or `regions'. A
3028hole represents an area where no mesh is to be created, while a
3029region is a labelled area used for defining properties of a mesh,
3030such as friction values.  A hole or region is specified by a point
3031and bounded by a number of segments that enclose that point.
3032
3033A mesh file can also contain a georeference, which describes an
3034offset to be applied to $x$ and $y$ values---eg to the vertices.
3035
3036
3037\subsection{Formats for Storing Arbitrary Points and Attributes}
3038
3039
3040A CSV/TXT file is used to store data representing
3041arbitrary numerical attributes associated with a set of points.
3042
3043The format for an CSV/TXT file is:\\
3044%\begin{verbatim}
3045
3046            first line:     \code{[column names]}\\
3047            other lines:  \code{[x value], [y value], [attributes]}\\
3048
3049            for example:\\
3050            \code{x, y, elevation, friction}\\
3051            \code{0.6, 0.7, 4.9, 0.3}\\
3052            \code{1.9, 2.8, 5, 0.3}\\
3053            \code{2.7, 2.4, 5.2, 0.3}
3054
3055        The delimiter is a comma. The first two columns are assumed to
3056        be x, y coordinates.
3057       
3058
3059A PTS file is a NetCDF representation of the data held in an points CSV
3060file. If the data is associated with a set of $N$ points, then the
3061data is stored using an $N \times 2$ Numeric array of float
3062variables for the points and an $N \times 1$ Numeric array for each
3063attribute.
3064
3065%\end{verbatim}
3066
3067\subsection{ArcView Formats}
3068
3069Files of the three formats ASC, PRJ and ERS are all associated with
3070data from ArcView.
3071
3072An ASC file is an ASCII representation of DEM output from ArcView.
3073It contains a header with the following format:
3074
3075\begin{tabular}{l l}
3076\code{ncols}      &   \code{753}\\
3077\code{nrows}      &   \code{766}\\
3078\code{xllcorner}  &   \code{314036.58727982}\\
3079\code{yllcorner}  & \code{6224951.2960092}\\
3080\code{cellsize}   & \code{100}\\
3081\code{NODATA_value} & \code{-9999}
3082\end{tabular}
3083
3084The remainder of the file contains the elevation data for each grid point
3085in the grid defined by the above information.
3086
3087A PRJ file is an ArcView file used in conjunction with an ASC file
3088to represent metadata for a DEM.
3089
3090
3091\subsection{DEM Format}
3092
3093A DEM file in \anuga is a NetCDF representation of regular DEM data.
3094
3095
3096\subsection{Other Formats}
3097
3098
3099
3100
3101\subsection{Basic File Conversions}
3102\label{sec:basicfileconversions}
3103
3104  \begin{funcdesc}{sww2dem}{basename_in, basename_out = None,
3105            quantity = None,
3106            timestep = None,
3107            reduction = None,
3108            cellsize = 10,
3109            number_of_decimal_places = None,
3110            NODATA_value = -9999,
3111            easting_min = None,
3112            easting_max = None,
3113            northing_min = None,
3114            northing_max = None,
3115            expand_search = False,
3116            verbose = False,
3117            origin = None,
3118            datum = 'WGS84',
3119            format = 'ers'}
3120  Module: \module{shallow\_water.data\_manager}
3121
3122  Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or
3123  ERS) of a desired grid size \code{cellsize} in metres. The user can select how
3124  many the decimal places the output data can be written to using \code{number_of_decimal_places},
3125  with the default being 3.
3126  The easting and northing values are used if the user wished to determine the output
3127  within a specified rectangular area. The \code{reduction} input refers to a function
3128  to reduce the quantities over all time step of the SWW file, example, maximum.
3129  \end{funcdesc}
3130
3131
3132  \begin{funcdesc}{dem2pts}{basename_in, basename_out=None,
3133            easting_min=None, easting_max=None,
3134            northing_min=None, northing_max=None,
3135            use_cache=False, verbose=False}
3136  Module: \module{shallow\_water.data\_manager}
3137
3138  Takes DEM data (a NetCDF file representation of data from a regular Digital
3139  Elevation Model) and converts it to PTS format.
3140  \end{funcdesc}
3141
3142  \begin{funcdesc}{urs2sts}{basename_in, basename_out=None,
3143            weights=None, verbose=False,
3144            origin=None,mean_stage=0.0,
3145            zscale=1.0, ordering_filename=None}
3146  Module: \module{shallow\_water.data\_manager}
3147
3148  Takes urs data in (timeseries data in mux2 format) and converts it to STS format.
3149  \end{funcdesc}
3150
3151
3152
3153%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3154%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3155
3156\chapter{\anuga mathematical background}
3157\label{cd:mathematical background}
3158
3159\section{Introduction}
3160
3161This chapter outlines the mathematics underpinning \anuga.
3162
3163
3164
3165\section{Model}
3166\label{sec:model}
3167
3168The shallow water wave equations are a system of differential
3169conservation equations which describe the flow of a thin layer of
3170fluid over terrain. The form of the equations are:
3171\[
3172\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
3173x}+\frac{\partial \GG}{\partial y}=\SSS
3174\]
3175where $\UU=\left[ {{\begin{array}{*{20}c}
3176 h & {uh} & {vh} \\
3177\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
3178$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
3179entering the system are bed elevation $z$ and stage (absolute water
3180level) $w$, where the relation $w = z + h$ holds true at all times.
3181The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
3182by
3183\[
3184\EE=\left[ {{\begin{array}{*{20}c}
3185 {uh} \hfill \\
3186 {u^2h+gh^2/2} \hfill \\
3187 {uvh} \hfill \\
3188\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
3189 {vh} \hfill \\
3190 {vuh} \hfill \\
3191 {v^2h+gh^2/2} \hfill \\
3192\end{array} }} \right]
3193\]
3194and the source term (which includes gravity and friction) is given
3195by
3196\[
3197\SSS=\left[ {{\begin{array}{*{20}c}
3198 0 \hfill \\
3199 -{gh(z_{x} + S_{fx} )} \hfill \\
3200 -{gh(z_{y} + S_{fy} )} \hfill \\
3201\end{array} }} \right]
3202\]
3203where $S_f$ is the bed friction. The friction term is modelled using
3204Manning's resistance law
3205\[
3206S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
3207=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
3208\]
3209in which $\eta$ is the Manning resistance coefficient.
3210The model does not currently include consideration of kinematic viscosity.
3211
3212As demonstrated in our papers, \cite{ZR1999,nielsen2005} these
3213equations and their implementation in \anuga provide a reliable
3214model of general flows associated with inundation such as dam breaks
3215and tsunamis.
3216
3217\section{Finite Volume Method}
3218\label{sec:fvm}
3219
3220We use a finite-volume method for solving the shallow water wave
3221equations \cite{ZR1999}. The study area is represented by a mesh of
3222triangular cells as in Figure~\ref{fig:mesh} in which the conserved
3223quantities of  water depth $h$, and horizontal momentum $(uh, vh)$,
3224in each volume are to be determined. The size of the triangles may
3225be varied within the mesh to allow greater resolution in regions of
3226particular interest.
3227
3228\begin{figure}
3229\begin{center}
3230\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five}
3231\caption{Triangular mesh used in our finite volume method. Conserved
3232quantities $h$, $uh$ and $vh$ are associated with the centroid of
3233each triangular cell.} \label{fig:mesh}
3234\end{center}
3235\end{figure}
3236
3237The equations constituting the finite-volume method are obtained by
3238integrating the differential conservation equations over each
3239triangular cell of the mesh. Introducing some notation we use $i$ to
3240refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the
3241set of indices referring to the cells neighbouring the $i$th cell.
3242Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is
3243the length of the edge between the $i$th and $j$th cells.
3244
3245By applying the divergence theorem we obtain for each volume an
3246equation which describes the rate of change of the average of the
3247conserved quantities within each cell, in terms of the fluxes across
3248the edges of the cells and the effect of the source terms. In
3249particular, rate equations associated with each cell have the form
3250$$
3251 \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i
3252$$
3253where
3254\begin{itemize}
3255\item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell,
3256\item $\SSS_i$ is the source term associated with the $i$th cell,
3257and
3258\item $\HH_{ij}$ is the outward normal flux of
3259material across the \textit{ij}th edge.
3260\end{itemize}
3261
3262
3263%\item $l_{ij}$ is the length of the edge between the $i$th and $j$th
3264%cells
3265%\item $m_{ij}$ is the midpoint of
3266%the \textit{ij}th edge,
3267%\item
3268%$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing
3269%normal along the \textit{ij}th edge, and The
3270
3271The flux $\HH_{ij}$ is evaluated using a numerical flux function
3272$\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow
3273water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$
3274$$
3275H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 .
3276$$
3277
3278Then
3279$$
3280\HH_{ij}  = \HH(\UU_i(m_{ij}),
3281\UU_j(m_{ij}); \mathbf{n}_{ij})
3282$$
3283where $m_{ij}$ is the midpoint of the \textit{ij}th edge and
3284$\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the
3285\textit{ij}th edge. The function $\UU_i(x)$ for $x \in
3286T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and
3287neighbouring  cells.
3288
3289We use a second order reconstruction to produce a piece-wise linear
3290function construction of the conserved quantities for  all $x \in
3291T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This
3292function is allowed to be discontinuous across the edges of the
3293cells, but the slope of this function is limited to avoid
3294artificially introduced oscillations.
3295
3296Godunov's method (see \cite{Toro1992}) involves calculating the
3297numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly
3298solving the corresponding one dimensional Riemann problem normal to
3299the edge. We use the central-upwind scheme of \cite{KurNP2001} to
3300calculate an approximation of the flux across each edge.
3301
3302\begin{figure}
3303\begin{center}
3304\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct}
3305\caption{From the values of the conserved quantities at the centroid
3306of the cell and its neighbouring cells, a discontinuous piecewise
3307linear reconstruction of the conserved quantities is obtained.}
3308\label{fig:mesh:reconstruct}
3309\end{center}
3310\end{figure}
3311
3312In the computations presented in this paper we use an explicit Euler
3313time stepping method with variable timestepping adapted to the
3314observed CFL condition:
3315
3316\begin{equation} 
3317  \Delta t = \min_{k,i=[0,1,2]}  \min \left( \frac{r_k}{v_{k,i}}, \frac{r_{n_{k,i}}}{v_{k,i}} \right )
3318  \label{eq:CFL condition}
3319\end{equation} 
3320where $r_k$ is the radius of the $k$'th triangle and $v_{k,i}$ is the maximal velocity across
3321edge joining triangle $k$ and it's $i$'th neighbour, triangle $n_{k,i}$, as calculated by the
3322numerical flux function
3323using the central upwind scheme of \cite{KurNP2001}. The symbol $r_{n_{k,i}}$  denotes the radius
3324of the $i$'th neighbour of triangle $k$. The radii are calculated as radii of the inscribed circles
3325of each triangle.
3326
3327\section{Flux limiting}
3328
3329The shallow water equations are solved numerically using a
3330finite volume method on unstructured triangular grid.
3331The upwind central scheme due to Kurganov and Petrova is used as an
3332approximate Riemann solver for the computation of inviscid flux functions.
3333This makes it possible to handle discontinuous solutions.
3334
3335To alleviate the problems associated with numerical instabilities due to
3336small water depths near a wet/dry boundary we employ a new flux limiter that
3337ensures that unphysical fluxes are never encounted.
3338
3339
3340Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction,
3341$w$ the absolute water level (stage) and
3342$z$ the bed elevation. The latter are assumed to be relative to the
3343same height datum.
3344The conserved quantities tracked by ANUGA are momentum in the
3345$x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$)
3346and depth ($h = w-z$).
3347
3348The flux calculation requires access to the velocity vector $(u, v)$
3349where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively.
3350In the presence of very small water depths, these calculations become
3351numerically unreliable and will typically cause unphysical speeds.
3352
3353We have employed a flux limiter which replaces the calculations above with
3354the limited approximations.
3355\begin{equation}
3356  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
3357\end{equation}
3358where $h_0$ is a regularisation parameter that controls the minimal
3359magnitude of the denominator. Taking the limits we have for $\hat{u}$
3360\[
3361  \lim_{h \rightarrow 0} \hat{u} =
3362  \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0
3363\]
3364and
3365\[
3366  \lim_{h \rightarrow \infty} \hat{u} =
3367  \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u
3368\]
3369with similar results for $\hat{v}$.
3370
3371The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator)
3372\[
3373  1 - h_0/h^2 = 0
3374\]
3375or
3376\[
3377  h_0 = h^2
3378\]
3379
3380
3381ANUGA has a global parameter $H_0$ that controls the minimal depth which
3382is considered in the various equations. This parameter is typically set to
3383$10^{-3}$. Setting
3384\[
3385  h_0 = H_0^2
3386\]
3387provides a reasonable balance between accurracy and stability. In fact,
3388setting $h=H_0$ will scale the predicted speed by a factor of $0.5$:
3389\[
3390  \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \frac{\mu}{2 H_0}
3391\]
3392In general, for multiples of the minimal depth $N H_0$ one obtains
3393\[
3394  \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
3395  \frac{\mu}{H_0 (1 + 1/N^2)}
3396\]
3397which converges quadratically to the true value with the multiple N.
3398
3399
3400%The developed numerical model has been applied to several test cases as well as to real flows. Numerical tests prove the robustness and accuracy of the model.
3401
3402
3403
3404
3405
3406\section{Slope limiting}
3407A multidimensional slope-limiting technique is employed to achieve second-order spatial accuracy and to prevent spurious oscillations. This is using the MinMod limiter and is documented elsewhere.
3408
3409However close to the bed, the limiter must ensure that no negative depths occur. On the other hand, in deep water, the bed topography should be ignored for the purpose of the limiter.
3410
3411
3412Let $w, z, h$  be the stage, bed elevation and depth at the centroid and
3413let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$.
3414Define the minimal depth across all vertices as $\hmin$ as
3415\[
3416  \hmin = \min_i h_i
3417\]
3418
3419Let $\tilde{w_i}$ be the stage obtained from a gradient limiter
3420limiting on stage only. The corresponding depth is then defined as
3421\[
3422  \tilde{h_i} = \tilde{w_i} - z_i
3423\]
3424We would use this limiter in deep water which we will define (somewhat boldly)
3425as
3426\[
3427  \hmin \ge \epsilon
3428\]
3429
3430
3431Similarly, let $\bar{w_i}$ be the stage obtained from a gradient
3432limiter limiting on depth respecting the bed slope.
3433The corresponding depth is defined as
3434\[
3435  \bar{h_i} = \bar{w_i} - z_i
3436\]
3437
3438
3439We introduce the concept of a balanced stage $w_i$ which is obtained as
3440the linear combination
3441
3442\[
3443  w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i}
3444\]
3445or
3446\[
3447  w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i}
3448\]
3449where $\alpha \in [0, 1]$.
3450
3451Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope
3452is ignored we have immediately that
3453\[
3454  \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0
3455\]
3456%where the maximal bed elevation range $dz$ is defined as
3457%\[
3458%  dz = \max_i |z_i - z|
3459%\]
3460
3461If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that
3462no negative depths occur. Formally, we will require that
3463\[
3464  \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i
3465\]
3466or
3467\begin{equation}
3468  \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i
3469  \label{eq:limiter bound}
3470\end{equation}
3471
3472There are two cases:
3473\begin{enumerate}
3474  \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage)
3475  vertex is at least as far away from the bed than the shallow water
3476  (limited using depth). In this case we won't need any contribution from
3477  $\bar{h_i}$ and can accept any $\alpha$.
3478
3479  E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to
3480  \[
3481    \tilde{h_i} > \epsilon
3482  \]
3483  whereas $\alpha=0$ yields
3484  \[
3485    \bar{h_i} > \epsilon
3486  \]
3487  all well and good.
3488  \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is
3489  closer to the bed than the shallow water vertex or even below the bed.
3490  In this case we need to find an $\alpha$ that will ensure a positive depth.
3491  Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one
3492  obtains the bound
3493  \[
3494    \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i
3495  \]
3496\end{enumerate}
3497
3498Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one
3499arrives at the definition
3500\[
3501  \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}}
3502\]
3503which will guarantee that no vertex 'cuts' through the bed. Finally, should
3504$\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting
3505$\alpha=0$ and similarly capping $\alpha$ at 1 just in case.
3506
3507%Furthermore,
3508%dropping the $\epsilon$ ensures that alpha is always positive and also
3509%provides a numerical safety {??)
3510
3511
3512
3513
3514
3515%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3516%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3517
3518\chapter{Basic \anuga Assumptions}
3519
3520
3521Physical model time cannot be earlier than 1 Jan 1970 00:00:00.
3522If one wished to recreate scenarios prior to that date it must be done
3523using some relative time (e.g. 0).
3524
3525
3526All spatial data relates to the WGS84 datum (or GDA94) and has been
3527projected into UTM with false easting of 500000 and false northing of
35281000000 on the southern hemisphere (0 on the northern).
3529
3530It is assumed that all computations take place within one UTM zone and
3531all locations must consequently be specified in Cartesian coordinates
3532(eastings, northings) or (x,y) where the unit is metres.
3533
3534DEMs, meshes and boundary conditions can have different origins within
3535one UTM zone. However, the computation will use that of the mesh for
3536numerical stability.
3537
3538When generating a mesh it is assumed that polygons do not cross.
3539Having polygons tht cross can cause the mesh generation to fail or bad
3540meshes being produced.
3541
3542
3543%OLD
3544%The dataflow is: (See data_manager.py and from scenarios)
3545%
3546%
3547%Simulation scenarios
3548%--------------------%
3549%%
3550%
3551%Sub directories contain scrips and derived files for each simulation.
3552%The directory ../source_data contains large source files such as
3553%DEMs provided externally as well as MOST tsunami simulations to be used
3554%as boundary conditions.
3555%
3556%Manual steps are:
3557%  Creation of DEMs from argcview (.asc + .prj)
3558%  Creation of mesh from pmesh (.tsh)
3559%  Creation of tsunami simulations from MOST (.nc)
3560%%
3561%
3562%Typical scripted steps are%
3563%
3564%  prepare_dem.py:  Convert asc and prj files supplied by arcview to
3565%                   native dem and pts formats%
3566%
3567%  prepare_pts.py: Convert netcdf output from MOST to an sww file suitable
3568%                  as boundary condition%
3569%
3570%  prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares
3571%                   smoothing. The outputs are tsh files with elevation data.%
3572%
3573%  run_simulation.py: Use the above together with various parameters to
3574%                     run inundation simulation.
3575
3576
3577%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3578%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3579
3580\appendix
3581
3582\chapter{Supporting Tools}
3583\label{ch:supportingtools}
3584
3585This section describes a number of supporting tools, supplied with \anuga, that offer a
3586variety of types of functionality and enhance the basic capabilities of \anuga.
3587
3588\section{caching}
3589\label{sec:caching}
3590
3591The \code{cache} function is used to provide supervised caching of function
3592results. A Python function call of the form
3593
3594      {\small \begin{verbatim}
3595      result = func(arg1,...,argn)
3596      \end{verbatim}}
3597
3598  can be replaced by
3599
3600      {\small \begin{verbatim}
3601      from caching import cache
3602      result = cache(func,(arg1,...,argn))
3603      \end{verbatim}}
3604
3605  which returns the same output but reuses cached
3606  results if the function has been computed previously in the same context.
3607  \code{result} and the arguments can be simple types, tuples, list, dictionaries or
3608  objects, but not unhashable types such as functions or open file objects.
3609  The function \code{func} may be a member function of an object or a module.
3610
3611  This type of caching is particularly useful for computationally intensive
3612  functions with few frequently used combinations of input arguments. Note that
3613  if the inputs or output are very large caching may not save time because
3614  disc access may dominate the execution time.
3615
3616  If the function definition changes after a result has been cached, this will be
3617  detected by examining the functions \code{bytecode (co\_code, co\_consts,
3618  func\_defaults, co\_argcount)} and the function will be recomputed.
3619  However, caching will not detect changes in modules used by \code{func}.
3620  In this case cache must be cleared manually.
3621
3622  Options are set by means of the function \code{set\_option(key, value)},
3623  where \code{key} is a key associated with a
3624  Python dictionary \code{options}. This dictionary stores settings such as the name of
3625  the directory used, the maximum
3626  number of cached files allowed, and so on.
3627
3628  The \code{cache} function allows the user also to specify a list of dependent files. If any of these
3629  have been changed, the function is recomputed and the results stored again.
3630
3631  %Other features include support for compression and a capability to \ldots
3632
3633
3634   \textbf{USAGE:} \nopagebreak
3635
3636    {\small \begin{verbatim}
3637    result = cache(func, args, kwargs, dependencies, cachedir, verbose,
3638                   compression, evaluate, test, return_filename)
3639    \end{verbatim}}
3640
3641
3642\section{ANUGA viewer - animate}
3643\label{sec:animate}
3644 The output generated by \anuga may be viewed by
3645means of the visualisation tool \code{animate}, which takes the
3646\code{SWW} file output by \anuga and creates a visual representation
3647of the data. Examples may be seen in Figures \ref{fig:runupstart}
3648and \ref{fig:runup2}. To view an \code{SWW} file with
3649\code{animate} in the Windows environment, you can simply drag the
3650icon representing the file over an icon on the desktop for the
3651\code{animate} executable file (or a shortcut to it), or set up a
3652file association to make files with the extension \code{.sww} open
3653with \code{animate}. Alternatively, you can operate \code{animate}
3654from the command line, in both Windows and Linux environments.
3655
3656On successful operation, you will see an interactive moving-picture
3657display. You can use keys and the mouse to slow down, speed up or
3658stop the display, change the viewing position or carry out a number
3659of other simple operations. Help is also displayed when you press
3660the \code{h} key.
3661
3662The main keys operating the interactive screen are:\\
3663
3664\begin{center}
3665\begin{tabular}{|ll|}   \hline
3666
3667\code{w} & toggle wireframe \\
3668
3669space bar & start/stop\\
3670
3671up/down arrows & increase/decrease speed\\
3672
3673left/right arrows & direction in time \emph{(when running)}\\
3674& step through simulation \emph{(when stopped)}\\
3675
3676left mouse button & rotate\\
3677
3678middle mouse button & pan\\
3679
3680right mouse button & zoom\\  \hline
3681
3682\end{tabular}
3683\end{center}
3684
3685\vfill
3686
3687The following table describes how to operate animate from the command line:
3688
3689Usage: \code{animate [options] swwfile \ldots}\\  \nopagebreak
3690Options:\\  \nopagebreak
3691\begin{tabular}{ll}
3692  \code{--display <type>} & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\
3693                                    & \code{HEAD\_MOUNTED\_DISPLAY}\\
3694  \code{--rgba} & Request a RGBA colour buffer visual\\
3695  \code{--stencil} & Request a stencil buffer visual\\
3696  \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\
3697                                    & overridden by environmental variable\\
3698  \code{--stereo <mode>} & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\
3699                                    & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\
3700                                     & \code{ON | OFF} \\
3701  \code{-alphamax <float 0-1>} & Maximum transparency clamp value\\
3702  \code{-alphamin <float 0-1>} & Transparency value at \code{hmin}\\
3703\end{tabular}
3704
3705\begin{tabular}{ll}
3706  \code{-cullangle <float angle 0-90>} & Cull triangles steeper than this value\\
3707  \code{-help} & Display this information\\
3708  \code{-hmax <float>} & Height above which transparency is set to
3709                                     \code{alphamax}\\
3710\end{tabular}
3711
3712\begin{tabular}{ll}
3713
3714  \code{-hmin <float>} & Height below which transparency is set to
3715                                     zero\\
3716\end{tabular}
3717
3718\begin{tabular}{ll}
3719  \code{-lightpos <float>,<float>,<float>} & $x,y,z$ of bedslope directional light ($z$ is
3720                                     up, default is overhead)\\
3721\end{tabular}
3722
3723\begin{tabular}{ll}
3724  \code{-loop}  & Repeated (looped) playback of \code{.swm} files\\
3725
3726\end{tabular}
3727
3728\begin{tabular}{ll}
3729  \code{-movie <dirname>} & Save numbered images to named directory and
3730                                     quit\\
3731
3732  \code{-nosky} & Omit background sky\\
3733
3734
3735  \code{-scale <float>} & Vertical scale factor\\
3736  \code{-texture <file>} & Image to use for bedslope topography\\
3737  \code{-tps <rate>} & Timesteps per second\\
3738  \code{-version} & Revision number and creation (not compile)
3739                                     date\\
3740\end{tabular}
3741
3742\section{utilities/polygons}
3743
3744  \declaremodule{standard}{utilities.polygon}
3745  \refmodindex{utilities.polygon}
3746
3747  \begin{classdesc}{Polygon\_function}{regions, default=0.0, geo_reference=None}
3748  Module: \code{utilities.polygon}
3749
3750  Creates a callable object that returns one of a specified list of values when
3751  evaluated at a point \code{x, y}, depending on which polygon, from a specified list of polygons, the
3752  point belongs to. The parameter \code{regions} is a list of pairs
3753  \code{(P, v)}, where each \code{P} is a polygon and each \code{v}
3754  is either a constant value or a function of coordinates \code{x}
3755  and \code{y}, specifying the return value for a point inside \code{P}. The
3756  optional parameter \code{default} may be used to specify a value
3757  (or a function)
3758  for a point not lying inside any of the specified polygons. When a
3759  point lies in more than one polygon, the return value is taken to
3760  be the value for whichever of these polygon appears later in the
3761  list.
3762  %FIXME (Howard): CAN x, y BE VECTORS?
3763  The optional parameter geo\_reference refers to the status of points
3764  that are passed into the function. Typically they will be relative to
3765  some origin. In ANUGA, a typical call will take the form:
3766  {\small \begin{verbatim}
3767     set_quantity('elevation',
3768                  Polygon_function([(P1, v1), (P2, v2)],
3769                                   default=v3,
3770                                   geo_reference=domain.geo_reference))
3771  \end{verbatim}}
3772 
3773
3774  \end{classdesc}
3775
3776  \begin{funcdesc}{read\_polygon}{filename}
3777  Module: \code{utilities.polygon}
3778
3779  Reads the specified file and returns a polygon. Each
3780  line of the file must contain exactly two numbers, separated by a comma, which are interpreted
3781  as coordinates of one vertex of the polygon.
3782  \end{funcdesc}
3783
3784  \begin{funcdesc}{populate\_polygon}{polygon, number_of_points, seed = None, exclude = None}
3785  Module: \code{utilities.polygon}
3786
3787  Populates the interior of the specified polygon with the specified number of points,
3788  selected by means of a uniform distribution function.
3789  \end{funcdesc}
3790
3791  \begin{funcdesc}{point\_in\_polygon}{polygon, delta=1e-8}
3792  Module: \code{utilities.polygon}
3793
3794  Returns a point inside the specified polygon and close to the edge. The distance between
3795  the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the
3796  second argument \code{delta}, which is taken as $10^{-8}$ by default.
3797  \end{funcdesc}
3798
3799  \begin{funcdesc}{inside\_polygon}{points, polygon, closed = True, verbose = False}
3800  Module: \code{utilities.polygon}
3801
3802  Used to test whether the members of a list of points
3803  are inside the specified polygon. Returns a Numeric
3804  array comprising the indices of the points in the list that lie inside the polygon.
3805  (If none of the points are inside, returns \code{zeros((0,), 'l')}.)
3806  Points on the edges of the polygon are regarded as inside if
3807  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3808  \end{funcdesc}
3809
3810  \begin{funcdesc}{outside\_polygon}{points, polygon, closed = True, verbose = False}
3811  Module: \code{utilities.polygon}
3812
3813  Exactly like \code{inside\_polygon}, but with the words `inside' and `outside' interchanged.
3814  \end{funcdesc}
3815
3816  \begin{funcdesc}{is\_inside\_polygon}{point, polygon, closed=True, verbose=False}
3817  Module: \code{utilities.polygon}
3818
3819  Returns \code{True} if \code{point} is inside \code{polygon} or
3820  \code{False} otherwise. Points on the edges of the polygon are regarded as inside if
3821  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3822  \end{funcdesc}
3823
3824  \begin{funcdesc}{is\_outside\_polygon}{point, polygon, closed=True, verbose=False}
3825  Module: \code{utilities.polygon}
3826
3827  Exactly like \code{is\_outside\_polygon}, but with the words `inside' and `outside' interchanged.
3828  \end{funcdesc}
3829
3830  \begin{funcdesc}{point\_on\_line}{x, y, x0, y0, x1, y1}
3831  Module: \code{utilities.polygon}
3832
3833  Returns \code{True} or \code{False}, depending on whether the point with coordinates
3834  \code{x, y} is on the line passing through the points with coordinates \code{x0, y0}
3835  and \code{x1, y1} (extended if necessary at either end).
3836  \end{funcdesc}
3837
3838  \begin{funcdesc}{separate\_points\_by\_polygon}{points, polygon, closed = True, verbose = False}
3839    \indexedcode{separate\_points\_by\_polygon}
3840  Module: \code{utilities.polygon}
3841
3842  \end{funcdesc}
3843
3844  \begin{funcdesc}{polygon\_area}{polygon}
3845  Module: \code{utilities.polygon}
3846
3847  Returns area of arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html)
3848  \end{funcdesc}
3849
3850  \begin{funcdesc}{plot\_polygons}{polygons, style, figname, verbose = False}
3851    Module: \code{utilities.polygon}
3852 
3853    Plots each polygon contained in input polygon list, e.g.
3854   \code{polygons = [poly1, poly2, poly3]} where \code{poly1 = [[x11,y11],[x12,y12],[x13,y13]]}
3855   etc.  Each polygon can be closed for plotting purposes by assigning the style type to each
3856   polygon in the list, e.g. \code{style = ['line','line','line']}. The default will be a line
3857   type when \code{style = None}.
3858   The subsequent plot will be saved to \code{figname} or defaulted to \code{test_image.png}.
3859    The function returns a list containing the minimum and maximum of \code{x} and \code{y},
3860    i.e. \code{[x_{min}, x_{max}, y_{min}, y_{max}]}.
3861  \end{funcdesc}
3862
3863\section{coordinate\_transforms}
3864
3865\section{geospatial\_data}
3866\label{sec:geospatial}
3867
3868This describes a class that represents arbitrary point data in UTM
3869coordinates along with named attribute values.
3870
3871%FIXME (Ole): This gives a LaTeX error
3872%\declaremodule{standard}{geospatial_data}
3873%\refmodindex{geospatial_data}
3874
3875
3876
3877\begin{classdesc}{Geospatial\_data}
3878  {data_points = None,
3879    attributes = None,
3880    geo_reference = None,
3881    default_attribute_name = None,
3882    file_name = None}
3883Module: \code{geospatial\_data}
3884
3885This class is used to store a set of data points and associated
3886attributes, allowing these to be manipulated by methods defined for
3887the class.
3888
3889The data points are specified either by reading them from a NetCDF
3890or CSV file, identified through the parameter \code{file\_name}, or
3891by providing their \code{x}- and \code{y}-coordinates in metres,
3892either as a sequence of 2-tuples of floats or as an $M \times 2$
3893Numeric array of floats, where $M$ is the number of points.
3894Coordinates are interpreted relative to the origin specified by the
3895object \code{geo\_reference}, which contains data indicating the UTM
3896zone, easting and northing. If \code{geo\_reference} is not
3897specified, a default is used.
3898
3899Attributes are specified through the parameter \code{attributes},
3900set either to a list or array of length $M$ or to a dictionary whose
3901keys are the attribute names and whose values are lists or arrays of
3902length $M$. One of the attributes may be specified as the default
3903attribute, by assigning its name to \code{default\_attribute\_name}.
3904If no value is specified, the default attribute is taken to be the
3905first one.
3906
3907Note that the Geospatial\_data object currently reads entire datasets
3908into memory i.e.\ no memomry blocking takes place. 
3909For this we refer to the set\_quantity method which will read .pts and .csv files into \anuga using memory blocking allowing large files to be used.
3910\end{classdesc}
3911
3912
3913\begin{methoddesc}{import\_points\_file}{delimiter = None, verbose = False}
3914
3915\end{methoddesc}
3916
3917
3918\begin{methoddesc}{export\_points\_file}{ofile, absolute=False}
3919
3920\end{methoddesc}
3921
3922
3923\begin{methoddesc}{get\_data\_points}{absolute = True, as\_lat\_long =
3924    False}
3925    If \code{as\_lat\_long} is\code{True} the point information
3926    returned will be in Latitudes and Longitudes.
3927
3928\end{methoddesc}
3929
3930
3931\begin{methoddesc}{set\_attributes}{attributes}
3932
3933\end{methoddesc}
3934
3935
3936\begin{methoddesc}{get\_attributes}{attribute_name = None}
3937
3938\end{methoddesc}
3939
3940
3941\begin{methoddesc}{get\_all\_attributes}{}
3942
3943\end{methoddesc}
3944
3945
3946\begin{methoddesc}{set\_default\_attribute\_name}{default_attribute_name}
3947
3948\end{methoddesc}
3949
3950
3951\begin{methoddesc}{set\_geo\_reference}{geo_reference}
3952
3953\end{methoddesc}
3954
3955
3956\begin{methoddesc}{add}{}
3957
3958\end{methoddesc}
3959
3960
3961\begin{methoddesc}{clip}{}
3962Clip geospatial data by a polygon
3963
3964Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3965a Geospatial data object and \code{closed}(optional) which determines
3966whether points on boundary should be regarded as belonging to the polygon
3967(\code{closed=True}) or not (\code{closed=False}).
3968Default is \code{closed=True}.
3969
3970Returns new Geospatial data object representing points
3971inside specified polygon.
3972\end{methoddesc}
3973
3974
3975\begin{methoddesc}{clip_outside}{}
3976Clip geospatial data by a polygon
3977
3978Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3979a Geospatial data object and \code{closed}(optional) which determines
3980whether points on boundary should be regarded as belonging to the polygon
3981(\code{closed=True}) or not (\code{closed=False}).
3982Default is \code{closed=True}.
3983
3984Returns new Geospatial data object representing points
3985\emph{out}side specified polygon.
3986\end{methoddesc}
3987
3988\begin{methoddesc}{split}{factor=0.5, seed_num=None, verbose=False}
3989Returns two geospatial_data object, first is the size of the 'factor'
3990smaller the original and the second is the remainder. The two
3991new object are disjoin set of each other.
3992       
3993Points of the two new geospatial_data object are selected RANDOMLY.
3994       
3995Input - the (\code{factor}) which to split the object, if 0.1 then 10% of the
3996together object will be returned
3997       
3998Output - two geospatial_data objects that are disjoint sets of the original
3999\end{methoddesc}
4000
4001\begin{methoddesc}{find_optimal_smoothing_parameter}{data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000,
4002north_boundary=None, south_boundary=None, east_boundary=None, west_boundary=None, plot_name='all_alphas', split_factor=0.1, seed_num=None, cache=False, verbose=False}
4003
4004Removes a small random sample of points from 'data_file'. Creates
4005models from resulting points in 'data_file' with different alpha values from 'alpha_list' and cross validates
4006the predicted value to the previously removed point data. Returns the
4007alpha value which has the smallest covariance.
4008
4009data_file: must not contain points outside the boundaries defined
4010and it either a pts, txt or csv file.
4011   
4012alpha_list: the alpha values to test in a single list
4013   
4014mesh_file: name of the created mesh file or if passed in will read it.
4015NOTE, if there is a mesh file mesh_resolution, north_boundary, south... etc will be ignored.
4016   
4017mesh_resolution: the maximum area size for a triangle
4018   
4019north_boundary... west_boundary: the value of the boundary
4020   
4021plot_name: the name for the plot contain the results
4022   
4023seed_num: the seed to the random number generator
4024   
4025USAGE:
4026convariance_value, alpha = find_optimal_smoothing_parameter(data_file=fileName,
4027                                             alpha_list=[0.0001, 0.01, 1],
4028                                             mesh_file=None,
4029                                             mesh_resolution=3,
4030                                             north_boundary=5,
4031                                             south_boundary=-5,
4032                                             east_boundary=5,
4033                                             west_boundary=-5,
4034                                             plot_name='all_alphas',
4035                                             seed_num=100000,
4036                                             verbose=False)
4037   
4038OUTPUT: returns the minumum normalised covalance calculate AND the
4039alpha that created it. PLUS writes a plot of the results
4040           
4041NOTE: code will not work if the data_file extent is greater than the
4042boundary_polygon or any of the boundaries, eg north_boundary...west_boundary
4043\end{methoddesc}
4044
4045
4046
4047\section{Graphical Mesh Generator GUI}
4048The program \code{graphical\_mesh\_generator.py} in the pmesh module
4049allows the user to set up the mesh of the problem interactively.
4050It can be used to build the outline of a mesh or to visualise a mesh
4051automatically generated.
4052
4053Graphical Mesh Generator will let the user select various modes. The
4054current allowable modes are vertex, segment, hole or region.  The mode
4055describes what sort of object is added or selected in response to
4056mouse clicks.  When changing modes any prior selected objects become
4057deselected.
4058
4059In general the left mouse button will add an object and the right
4060mouse button will select an object.  A selected object can de deleted
4061by pressing the the middle mouse button (scroll bar).
4062
4063\section{alpha\_shape}
4064\emph{Alpha shapes} are used to generate close-fitting boundaries
4065around sets of points. The alpha shape algorithm produces a shape
4066that approximates to the `shape formed by the points'---or the shape
4067that would be seen by viewing the points from a coarse enough
4068resolution. For the simplest types of point sets, the alpha shape
4069reduces to the more precise notion of the convex hull. However, for
4070many sets of points the convex hull does not provide a close fit and
4071the alpha shape usually fits more closely to the original point set,
4072offering a better approximation to the shape being sought.
4073
4074In \anuga, an alpha shape is used to generate a polygonal boundary
4075around a set of points before mesh generation. The algorithm uses a
4076parameter $\alpha$ that can be adjusted to make the resultant shape
4077resemble the shape suggested by intuition more closely. An alpha
4078shape can serve as an initial boundary approximation that the user
4079can adjust as needed.
4080
4081The following paragraphs describe the class used to model an alpha
4082shape and some of the important methods and attributes associated
4083with instances of this class.
4084
4085\begin{classdesc}{Alpha\_Shape}{points, alpha = None}
4086Module: \code{alpha\_shape}
4087
4088To instantiate this class the user supplies the points from which
4089the alpha shape is to be created (in the form of a list of 2-tuples
4090\code{[[x1, y1],[x2, y2]}\ldots\code{]}, assigned to the parameter
4091\code{points}) and, optionally, a value for the parameter
4092\code{alpha}. The alpha shape is then computed and the user can then
4093retrieve details of the boundary through the attributes defined for
4094the class.
4095\end{classdesc}
4096
4097
4098\begin{funcdesc}{alpha\_shape\_via\_files}{point_file, boundary_file, alpha= None}
4099Module: \code{alpha\_shape}
4100
4101This function reads points from the specified point file
4102\code{point\_file}, computes the associated alpha shape (either
4103using the specified value for \code{alpha} or, if no value is
4104specified, automatically setting it to an optimal value) and outputs
4105the boundary to a file named \code{boundary\_file}. This output file
4106lists the coordinates \code{x, y} of each point in the boundary,
4107using one line per point.
4108\end{funcdesc}
4109
4110
4111\begin{methoddesc}{set\_boundary\_type}{self,raw_boundary=True,
4112                          remove_holes=False,
4113                          smooth_indents=False,
4114                          expand_pinch=False,
4115                          boundary_points_fraction=0.2}
4116Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4117
4118This function sets flags that govern the operation of the algorithm
4119that computes the boundary, as follows:
4120
4121\code{raw\_boundary = True} returns raw boundary, i.e. the regular edges of the
4122                alpha shape.\\
4123\code{remove\_holes = True} removes small holes (`small' is defined by
4124\code{boundary\_points\_fraction})\\
4125\code{smooth\_indents = True} removes sharp triangular indents in
4126boundary\\
4127\code{expand\_pinch = True} tests for pinch-off and
4128corrects---preventing a boundary vertex from having more than two edges.
4129\end{methoddesc}
4130
4131
4132\begin{methoddesc}{get\_boundary}{}
4133Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4134
4135Returns a list of tuples representing the boundary of the alpha
4136shape. Each tuple represents a segment in the boundary by providing
4137the indices of its two endpoints.
4138\end{methoddesc}
4139
4140
4141\begin{methoddesc}{write\_boundary}{file_name}
4142Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4143
4144Writes the list of 2-tuples returned by \code{get\_boundary} to the
4145file \code{file\_name}, using one line per tuple.
4146\end{methoddesc}
4147
4148\section{Numerical Tools}
4149
4150The following table describes some useful numerical functions that
4151may be found in the module \module{utilities.numerical\_tools}:
4152
4153\begin{tabular}{|p{8cm} p{8cm}|}  \hline
4154\code{angle(v1, v2=None)} & Angle between two-dimensional vectors
4155\code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if
4156\code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\
4157
4158\code{normal\_vector(v)} & Normal vector to \code{v}.\\
4159
4160\code{mean(x)} & Mean value of a vector \code{x}.\\
4161
4162\code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}.
4163If \code{y} is \code{None}, returns \code{cov(x, x)}.\\
4164
4165\code{err(x, y=0, n=2, relative=True)} & Relative error of
4166$\parallel$\code{x}$-$\code{y}$\parallel$ to
4167$\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm
4168if \code{n} = \code{None}). If denominator evaluates to zero or if
4169\code{y}
4170is omitted or if \code{relative = False}, absolute error is returned.\\
4171
4172\code{norm(x)} & 2-norm of \code{x}.\\
4173
4174\code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If
4175\code{y} is \code{None} returns autocorrelation of \code{x}.\\
4176
4177\code{ensure\_numeric(A, typecode = None)} & Returns a Numeric array
4178for any sequence \code{A}. If \code{A} is already a Numeric array it
4179will be returned unaltered. Otherwise, an attempt is made to convert
4180it to a Numeric array. (Needed because \code{array(A)} can
4181cause memory overflow.)\\
4182
4183\code{histogram(a, bins, relative=False)} & Standard histogram. If
4184\code{relative} is \code{True}, values will be normalised against
4185the total and thus represent frequencies rather than counts.\\
4186
4187\code{create\_bins(data, number\_of\_bins = None)} & Safely create
4188bins for use with histogram. If \code{data} contains only one point
4189or is constant, one bin will be created. If \code{number\_of\_bins}
4190is omitted, 10 bins will be created.\\  \hline
4191
4192\section{Finding the Optimal Alpha Value}
4193
4194The function ????
4195more to come very soon
4196
4197\end{tabular}
4198
4199
4200\chapter{Modules available in \anuga}
4201
4202
4203\section{\module{abstract\_2d\_finite\_volumes.general\_mesh} }
4204\declaremodule[generalmesh]{}{general\_mesh}
4205\label{mod:generalmesh}
4206
4207\section{\module{abstract\_2d\_finite\_volumes.neighbour\_mesh} }
4208\declaremodule[neighbourmesh]{}{neighbour\_mesh}
4209\label{mod:neighbourmesh}
4210
4211\section{\module{abstract\_2d\_finite\_volumes.domain}}
4212Generic module for 2D triangular domains for finite-volume computations of conservation laws
4213\declaremodule{}{domain}
4214\label{mod:domain}
4215
4216
4217\section{\module{abstract\_2d\_finite\_volumes.quantity}}
4218\declaremodule{}{quantity}
4219\label{mod:quantity}
4220
4221\begin{verbatim}
4222Class Quantity - Implements values at each triangular element
4223
4224To create:
4225
4226   Quantity(domain, vertex_values)
4227
4228   domain: Associated domain structure. Required.
4229
4230   vertex_values: N x 3 array of values at each vertex for each element.
4231                  Default None
4232
4233   If vertex_values are None Create array of zeros compatible with domain.
4234   Otherwise check that it is compatible with dimenions of domain.
4235   Otherwise raise an exception
4236
4237\end{verbatim}
4238
4239
4240
4241
4242\section{\module{shallow\_water}}
42432D triangular domains for finite-volume
4244computations of the shallow water wave equation.
4245This module contains a specialisation of class Domain from module domain.py consisting of methods specific to the Shallow Water
4246Wave Equation
4247\declaremodule[shallowwater]{}{shallow\_water}
4248\label{mod:shallowwater}
4249
4250
4251
4252
4253%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4254
4255\chapter{Frequently Asked Questions}
4256
4257
4258\section{General Questions}
4259
4260\subsubsection{What is \anuga?}
4261It is a software package suitable for simulating 2D water flows in
4262complex geometries.
4263
4264\subsubsection{Why is it called \anuga?}
4265The software was developed in collaboration between the
4266Australian National University (ANU) and Geoscience Australia (GA).
4267
4268\subsubsection{How do I obtain a copy of \anuga?}
4269See \url{https://datamining.anu.edu.au/anuga} for all things ANUGA.
4270
4271%\subsubsection{What developments are expected for \anuga in the future?}
4272%This
4273
4274\subsubsection{Are there any published articles about \anuga that I can reference?}
4275See \url{https://datamining.anu.edu.au/anuga} for links.
4276
4277
4278\subsubsection{How do I find out what version of \anuga I am running?}
4279Use the following code snippet
4280\begin{verbatim}
4281from anuga.utilities.system_tools import get_revision_number
4282print get_revision_number()
4283\end{verbatim}
4284This should work both for installations from SourceForge as well as when working off the repository.
4285
4286
4287
4288
4289\section{Modelling Questions}
4290
4291\subsubsection{Which type of problems are \anuga good for?}
4292General 2D waterflows in complex geometries such as
4293dam breaks, flows amoung structurs, coastal inundation etc.
4294
4295\subsubsection{Which type of problems are beyond the scope of \anuga?}
4296See Chapter \ref{ch:limitations}.
4297
4298\subsubsection{Can I start the simulation at an arbitrary time?}
4299Yes, using \code{domain.set\_time()} you can specify an arbitrary
4300starting time. This is for example useful in conjunction with a
4301file\_boundary, which may start hours before anything hits the model
4302boundary. By assigning a later time for the model to start,
4303computational resources aren't wasted.
4304
4305\subsubsection{Can I change values for any quantity during the simulation?}
4306Yes, using \code{domain.set\_quantity()} inside the domain.evolve
4307loop you can change values of any quantity. This is for example
4308useful if you wish to let the system settle for a while before
4309assigning an initial condition. Another example would be changing
4310the values for elevation to model e.g. erosion.
4311
4312\subsubsection{Can I change boundary conditions during the simulation?}
4313Yes - see example on page \pageref{sec:change boundary code} in Section
4314\ref{sec:change boundary}.
4315
4316\subsubsection{How do I access model time during the simulation?}
4317The variable \code{t} in the evolve for loop is the model time.
4318For example to change the boundary at a particular time (instead of basing this on the state of the system as in Section \ref{sec:change boundary})
4319one would write something like
4320{\small \begin{verbatim}
4321    for t in domain.evolve(yieldstep = 0.2, duration = 40.0):
4322
4323        if Numeric.allclose(t, 15):
4324            print 'Changing boundary to outflow'
4325            domain.set_boundary({'right': Bo})
4326
4327\end{verbatim}}
4328The model time can also be accessed through the public interface \code{domain.get\_time()}, or changed (at your own peril) through \code{domain.set\_time()}.
4329
4330
4331\subsubsection{Why does a file\_function return a list of numbers when evaluated?}
4332Currently, file\_function works by returning values for the conserved
4333quantities \code{stage}, \code{xmomentum} and \code{ymomentum} at a given point in time
4334and space as a triplet. To access e.g.\ \code{stage} one must specify element 0 of the
4335triplet returned by file\_function, to access \code{xmomentum} one must specify element 1 of the triplet etc.
4336
4337\subsubsection{Which diagnostics are available to troubleshoot a simulation?}
4338
4339\subsubsection{How do I use a DEM in my simulation?}
4340You use \code{dem2pts} to convert your DEM to the required .pts format. This .pts file is then called
4341when setting the elevation data to the mesh in \code{domain.set_quantity}
4342
4343\subsubsection{What sort of DEM resolution should I use?}
4344Try and work with the \emph{best} you have available. Onshore DEMs
4345are typically available in 25m, 100m and 250m grids. Note, offshore
4346data is often sparse, or non-existent.
4347
4348Note that onshore DEMS can be much finer as the underlying datasets from which they
4349are created often contain several datapoints per m$^2$.
4350It may be necessary to thin out the data so that it can be imported
4351without exceeding available memory. One tool available on the net is called 'decimate'. %FIXME: (Need reference?). 
4352
4353
4354\subsubsection{What sort of mesh resolution should I use?}
4355The mesh resolution should be commensurate with your DEM - it does not make sense to put in place a mesh which is finer than your DEM. As an example,
4356if your DEM is on a 25m grid, then the cell resolution should be of the order of 315$m^2$ (this represents half the area of the square grid). Ideally,
4357you need a fine mesh over regions where the DEM changes rapidly, and other areas of significant interest, such as the coast.
4358If meshes are too coarse, discretisation errors in both stage and momentum may lead to unrealistic results. All studies should include sensitivity and convergence studies based on different resolutions.
4359
4360
4361\subsubsection{How do I tag interior polygons?}
4362At the moment create_mesh_from_regions does not allow interior
4363polygons with symbolic tags. If tags are needed, the interior
4364polygons must be created subsequently. For example, given a filename
4365of polygons representing solid walls (in Arc Ungenerate format) can
4366be tagged as such using the code snippet:
4367\begin{verbatim}
4368  # Create mesh outline with tags
4369  mesh = create_mesh_from_regions(bounding_polygon,
4370                                  boundary_tags=boundary_tags)
4371  # Add buildings outlines with tags set to 'wall'. This would typically
4372  # bind to a Reflective boundary
4373  mesh.import_ungenerate_file(buildings_filename, tag='wall')
4374
4375  # Generate and write mesh to file
4376  mesh.generate_mesh(maximum_triangle_area=max_area)
4377  mesh.export_mesh_file(mesh_filename)
4378\end{verbatim}
4379
4380Note that a mesh object is returned from \code{create_mesh_from_regions}
4381when file name is omitted.
4382
4383\subsubsection{How often should I store the output?}
4384This will depend on what you are trying to answer with your model and how much memory you have available on your machine. If you need
4385to look in detail at the evolution, then you will need to balance your storage requirements and the duration of the simulation.
4386If the SWW file exceeds 1Gb, another SWW file will be created until the end of the simulation. As an example, to store all the conserved
4387quantities on a mesh with approximately 300000 triangles on a 2 min interval for 5 hours will result in approximately 350Mb SWW file
4388(as for the \file{run\_sydney\_smf.py} example).
4389
4390\subsubsection{How can I set the friction in different areas in the domain?}
4391The model area will typically be estimating the water height and momentum over varying
4392topographies which will have different friction values. One way of assigning
4393different friction values is to create polygons (say \code{poly1, poly2 and poly3}) describing each
4394area and then set the corresponding friction values in the following way
4395
4396\code{domain.set_quantity('friction',Polygon_function([(poly1,f1),(poly2,f2),
4397(poly3,f3))]))}
4398
4399The values of \code{f1,f2} and \code{f3} could be constant or functions
4400as determined by the user.
4401
4402\subsubsection{How can I combine data sets?}
4403
4404A user may have access to a range of different resolution DEMs and raw data points (such
4405as beach profiles, spot heights, single or multi-beam data etc) and will need
4406to combine them to create an overall elevation data set.
4407
4408If there are multiple DEMs, say of 10m and 25m resolution, then the technique is similar to
4409that defined in the Cairns example described earlier, that is
4410
4411{\small \begin{verbatim}
4412convert_dem_from_ascii2netcdf(10m_dem_name, use_cache=True, verbose=True)
4413convert_dem_from_ascii2netcdf(25m_dem_name, use_cache=True, verbose=True)
4414\end{verbatim}}
4415followed by
4416{\small \begin{verbatim}
4417dem2pts(10m_dem_name, use_cache=True, verbose=True)
4418dem2pts(25m_dem_name, use_cache=True, verbose=True)
4419\end{verbatim}}
4420These data sets can now be combined by
4421{\small \begin{verbatim}
4422from anuga.geospatial_data.geospatial_data import *
4423G1 = Geospatial_data(file_name = 10m_dem_name + '.pts')
4424G2 = Geospatial_data(file_name = 25m_dem_name + '.pts')
4425G = G1 + G2
4426G.export_points_file(combined_dem_name + ᅵ.ptsᅵ)
4427\end{verbatim}}
4428this is the basic way of combining data sets, however, the user will need to
4429assess the boundaries of each data set and whether they overlap. For example, consider
4430if the 10m DEM is describing by \code{poly1} and the 25m DEM is described by \code{poly2}
4431with \code{poly1} completely enclosed in \code{poly2} as shown in Figure \ref{fig:polydata}
4432\begin{figure}[hbt]
4433  \centerline{\includegraphics{graphics/polyanddata.jpg}}
4434  \caption{Polygons describing the extent of the 10m and 25m DEM.}
4435  \label{fig:polydata}
4436\end{figure}
4437To combine the data sets, the geospatial addition is updated to
4438{\small \begin{verbatim}
4439G = G1 + G2.clip_outside(Geospatial_data(poly1))
4440\end{verbatim}}
4441For this example, we assume that \code{poly2} is the domain, otherwise an additional dataset
4442would be required for the remainder of the domain.
4443
4444This technique can be expanded to handle point data sets as well. In the case
4445of a bathymetry data set available in text format in an \code{.csv} file, then
4446the geospatial addition is updated to
4447{\small \begin{verbatim}
4448G3 = Geospatial_data(file_name = bathy_data_name + '.csv')
4449G = G1 + G2.clip_outside(Geospatial_data(poly1)) + G3
4450\end{verbatim}}
4451The \code{.csv} file has the data stored as \code{x,y,elevation} with the text \code{elevation}
4452on the first line.
4453
4454The coastline could be included
4455as part of the clipping polygon to separate the offshore and onshore datasets if required.
4456Assume that \code{poly1} crosses the coastline
4457In this case, two new polygons could be created out of \code{poly1} which uses the coastline
4458as the divider. As shown in Figure \ref{fig:polycoast}, \code{poly3} describes the
4459onshore data and \code{poly4} describes the offshore data.
4460\begin{figure}[hbt]
4461  \centerline{\includegraphics{graphics/polyanddata2.jpg}}
4462  \caption{Inclusion of new polygons separating the 10m DEM area into an
4463  onshore (poly3) and offshore (poly4) data set.}
4464  \label{fig:polycoast}
4465\end{figure}
4466Let's include the bathymetry
4467data described above, so to combine the datasets in this case,
4468{\small \begin{verbatim}
4469G = G1.clip(Geospatial_data(poly3)) + G2.clip_outside(Geospatial_data(poly1)) + G3
4470\end{verbatim}}
4471
4472Finally, to fit the elevation data to the mesh, the script is adjusted in this way
4473{\small \begin{verbatim}
4474    domain.set_quantity('elevation',
4475                        filename = combined_dem_name + '.pts',
4476                        use_cache = True,
4477                        verbose = True)
4478\end{verbatim}}
4479\subsection{Boundary Conditions}
4480
4481\subsubsection{How do I create a Dirichlet boundary condition?}
4482
4483A Dirichlet boundary condition sets a constant value for the
4484conserved quantities at the boundaries. A list containing
4485the constant values for stage, xmomentum and ymomentum is constructed
4486and used in the function call, e.g. \code{Dirichlet_boundary([0.2,0.,0.])}
4487
4488\subsubsection{How do I know which boundary tags are available?}
4489The method \code{domain.get\_boundary\_tags()} will return a list of
4490available tags for use with
4491\code{domain.set\_boundary\_condition()}.
4492
4493\subsubsection{What is the difference between file_boundary and field_boundary?}
4494The only difference is field_boundary will allow you to change the level of the stage height when you read in the boundary condition.
4495This is very useful when running different tide heights in the same area as you need only to convert
4496one boundary condition to a SWW file, ideally for tide height of 0 m (saving disk space). Then you can
4497use field_boundary to read this SWW file and change the stage height (tide) on the fly depending on the scenario.
4498
4499
4500
4501
4502\subsection{Analysing Results}
4503
4504\subsubsection{How do I easily plot "tide gauges" timeseries graphs from a SWW file?}
4505
4506There is two ways to do this.
4507
45081) Create csv files from the sww file using \code{anuga.abstract_2d_finite_volumes.util sww2csv_gauges}
4509and then use \code{anuga.abstract_2d_finite_volumes.util csv2timeseries_graphs} to
4510create the plots. This code is newer, has unit tests and might be easier to use. Read doc strings for more information and
4511review section 4.7 of this manual.
4512
4513Or
4514
45152) Use \code{anuga.abstract_2d_finite_volumes.util sww2timeseries} to do the whole thing
4516however this doesn't have a much control on the file name and plots. Plus there is no unit tests yet.
4517
4518Read the doc string for more information.
4519
4520\subsubsection{How do I extract elevation and other quantities from a SWW file?}
4521
4522The function \code{sww2dem} can extract any quantity, or expression using
4523quantities, from a SWW file as used in
4524the Cairns example described earlier. This function is used in \code{ExportResults.py}
4525in the Cairns demo folder where stage, absolute momentum, depth, speed and elevation
4526can be exported from the input sww file. Note that depth, absolute momentum and speed
4527are expressions and stage and elevation are quantities. In addition to extracting a particular
4528quantity or expression, the user can define a region to extract these values by
4529defining the minimum and maximum of both the easting and northing coordinates. The function
4530also calls for a grid resolution, or cell size, to extract these values at. It is
4531recommended to align this resolution with the mesh resolution in the desired region and to not
4532generate a fine grid where the model output cannot support that resolution.
4533
4534 
4535
4536\chapter{Glossary}
4537
4538\begin{tabular}{|lp{10cm}|c|}  \hline
4539%\begin{tabular}{|llll|}  \hline
4540    \emph{Term} & \emph{Definition} & \emph{Page}\\  \hline
4541
4542    \indexedbold{\anuga} & Name of software (joint development between ANU and
4543    GA) & \pageref{def:anuga}\\
4544
4545    \indexedbold{bathymetry} & offshore elevation &\\
4546
4547    \indexedbold{conserved quantity} & conserved (stage, x and y
4548    momentum) & \\
4549
4550%    \indexedbold{domain} & The domain of a function is the set of all input values to the
4551%    function.&\\
4552
4553    \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations,
4554sampled systematically at equally spaced intervals.& \\
4555
4556    \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation
4557 that specifies the values the solution is to take on the boundary of the
4558 domain. & \pageref{def:dirichlet boundary}\\
4559
4560    \indexedbold{edge} & A triangular cell within the computational mesh can be depicted
4561    as a set of vertices joined by lines (the edges). & \\
4562
4563    \indexedbold{elevation} & refers to bathymetry and topography &\\
4564
4565    \indexedbold{evolution} & integration of the shallow water wave equations
4566    over time &\\
4567
4568    \indexedbold{finite volume method} & The method evaluates the terms in the shallow water
4569    wave equation as fluxes at the surfaces of each finite volume. Because the
4570    flux entering a given volume is identical to that leaving the adjacent volume,
4571    these methods are conservative. Another advantage of the finite volume method is
4572    that it is easily formulated to allow for unstructured meshes. The method is used
4573    in many computational fluid dynamics packages. & \\
4574
4575    \indexedbold{forcing term} & &\\
4576
4577    \indexedbold{flux} & the amount of flow through the volume per unit
4578    time & \\
4579
4580    \indexedbold{grid} & Evenly spaced mesh & \\
4581
4582    \indexedbold{latitude} & The angular distance on a mericlear north and south of the
4583    equator, expressed in degrees and minutes. & \\
4584
4585    \indexedbold{longitude} & The angular distance east or west, between the meridian
4586    of a particular place on Earth and that of the Prime Meridian (located in Greenwich,
4587    England) expressed in degrees or time.& \\
4588
4589    \indexedbold{Manning friction coefficient} & &\\
4590
4591    \indexedbold{mesh} & Triangulation of domain &\\
4592
4593    \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\
4594
4595    \indexedbold{NetCDF} & &\\
4596
4597    \indexedbold{node} & A point at which edges meet & \\
4598
4599    \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance
4600    north from a north-south reference line, usually a meridian used as the axis of
4601    origin within a map zone or projection. Northing is a UTM (Universal Transverse
4602    Mercator) coordinate. & \\
4603
4604
4605    \indexedbold{points file} & A PTS or CSV file & \\  \hline
4606
4607    \end{tabular}
4608
4609    \begin{tabular}{|lp{10cm}|c|}  \hline
4610
4611    \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon
4612    either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$
4613    Numeric array, where $N$ is the number of points.
4614
4615    The unit square, for example, would be represented either as
4616    \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1],
4617    [0,1] )}.
4618
4619    NOTE: For details refer to the module \module{utilities/polygon.py}. &
4620    \\     \indexedbold{resolution} &  The maximal area of a triangular cell in a
4621    mesh & \\
4622
4623
4624    \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved
4625    quantities as those present in the neighbouring volume but reflected. Specific to the
4626    shallow water equation as it works with the momentum quantities assumed to be the
4627    second and third conserved quantities. & \pageref{def:reflective boundary}\\
4628
4629    \indexedbold{stage} & &\\
4630
4631%    \indexedbold{try this}
4632
4633    \indexedbold{animate} & visualisation tool used with \anuga &
4634    \pageref{sec:animate}\\
4635
4636    \indexedbold{time boundary} & Returns values for the conserved
4637quantities as a function of time. The user must specify
4638the domain to get access to the model time. & \pageref{def:time boundary}\\
4639
4640    \indexedbold{topography} & onshore elevation &\\
4641
4642    \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\
4643
4644    \indexedbold{vertex} & A point at which edges meet. & \\
4645
4646    \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say
4647    only \code{x} and \code{y} and NOT \code{z}) &\\
4648
4649    \indexedbold{ymomentum}  & conserved quantity & \\  \hline
4650
4651    \end{tabular}
4652
4653
4654%The \code{\e appendix} markup need not be repeated for additional
4655%appendices.
4656
4657
4658%
4659%  The ugly "%begin{latexonly}" pseudo-environments are really just to
4660%  keep LaTeX2HTML quiet during the \renewcommand{} macros; they're
4661%  not really valuable.
4662%
4663%  If you don't want the Module Index, you can remove all of this up
4664%  until the second \input line.
4665%
4666
4667%begin{latexonly}
4668%\renewcommand{\indexname}{Module Index}
4669%end{latexonly}
4670\input{mod\jobname.ind}        % Module Index
4671%
4672%begin{latexonly}
4673%\renewcommand{\indexname}{Index}
4674%end{latexonly}
4675\input{\jobname.ind}            % Index
4676
4677
4678
4679\begin{thebibliography}{99}
4680\bibitem[nielsen2005]{nielsen2005}
4681{\it Hydrodynamic modelling of coastal inundation}.
4682Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman.
4683In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on
4684Modelling and Simulation. Modelling and Simulation Society of Australia and
4685New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\
4686http://www.mssanz.org.au/modsim05/papers/nielsen.pdf
4687
4688\bibitem[grid250]{grid250}
4689Australian Bathymetry and Topography Grid, June 2005.
4690Webster, M.A. and Petkovic, P.
4691Geoscience Australia Record 2005/12. ISBN: 1-920871-46-2.\\
4692http://www.ga.gov.au/meta/ANZCW0703008022.html
4693
4694\bibitem[ZR1999]{ZR1999}
4695\newblock {Catastrophic Collapse of Water Supply Reservoirs in Urban Areas}.
4696\newblock C.~Zoppou and S.~Roberts.
4697\newblock {\em ASCE J. Hydraulic Engineering}, 125(7):686--695, 1999.
4698
4699\bibitem[Toro1999]{Toro1992}
4700\newblock Riemann problems and the waf method for solving the two-dimensional
4701  shallow water equations.
4702\newblock E.~F. Toro.
4703\newblock {\em Philosophical Transactions of the Royal Society, Series A},
4704  338:43--68, 1992.
4705
4706\bibitem{KurNP2001}
4707\newblock Semidiscrete central-upwind schemes for hyperbolic conservation laws
4708  and hamilton-jacobi equations.
4709\newblock A.~Kurganov, S.~Noelle, and G.~Petrova.
4710\newblock {\em SIAM Journal of Scientific Computing}, 23(3):707--740, 2001.
4711\end{thebibliography}{99}
4712
4713\end{document}
Note: See TracBrowser for help on using the repository browser.