source: anuga_core/documentation/user_manual/anuga_user_manual.tex @ 5508

Last change on this file since 5508 was 5508, checked in by ole, 11 years ago

Minor fixes in the manual

  • Property svn:keywords set to LastChangedDate LastChangedRevision LastChangedBy HeadURL Id
File size: 171.9 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: 2008-07-16 02:50:05 +0000 (Wed, 16 Jul 2008) $
86%$LastChangedRevision: 5508 $
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 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
104conditions and forces such as windstress or pressure gradients if
105applicable.
106
107\anuga tracks the evolution of water depth and horizontal momentum
108within each cell over time by solving the shallow water wave equation
109governing equation using a finite-volume method.
110
111\anuga also incorporates a mesh generator %, called \code{graphical
112                                %mesh generator},
113that
114allows the user to set up the geometry of the problem interactively as
115well as tools for interpolation and surface fitting, and a number of
116auxiliary tools for visualising and interrogating the model output.
117
118Most \anuga components are written in the object-oriented programming
119language Python and most users will interact with \anuga by writing
120small Python programs based on the \anuga library
121functions. Computationally intensive components are written for
122efficiency in C routines working directly with the Numerical Python
123structures.
124
125
126\end{abstract}
127
128\tableofcontents
129
130
131\chapter{Introduction}
132
133
134\section{Purpose}
135
136The purpose of this user manual is to introduce the new user to the
137inundation software, describe what it can do and give step-by-step
138instructions for setting up and running hydrodynamic simulations.
139
140\section{Scope}
141
142This manual covers only what is needed to operate the software after
143installation and configuration. It does not includes instructions
144for installing the software or detailed API documentation, both of
145which will be covered in separate publications and by documentation
146in the source code.
147
148\section{Audience}
149
150Readers are assumed to be familiar with the Python Programming language and
151its object oriented approach.
152Python tutorials include
153\url{http://docs.python.org/tut},
154\url{http://www.sthurlow.com/python}, and
155%\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}.
156\url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}.
157
158
159Readers also need to have a general understanding of scientific modelling,
160as well as
161enough programming experience to adapt the code to different
162requirements.
163
164
165
166\pagebreak
167\chapter{Background}
168
169
170Modelling the effects on the built environment of natural hazards such
171as riverine flooding, storm surges and tsunami is critical for
172understanding their economic and social impact on our urban
173communities.  Geoscience Australia and the Australian National
174University are developing a hydrodynamic inundation modelling tool
175called \anuga to help simulate the impact of these hazards.
176
177The core of \anuga is the fluid dynamics module, called \code{shallow\_water},
178which is based on a finite-volume method for solving the Shallow Water
179Wave Equation.  The study area is represented by a mesh of triangular
180cells.  By solving the governing equation within each cell, water
181depth and horizontal momentum are tracked over time.
182
183A major capability of \anuga is that it can model the process of
184wetting and drying as water enters and leaves an area.  This means
185that it is suitable for simulating water flow onto a beach or dry land
186and around structures such as buildings.  \anuga is also capable
187of modelling hydraulic jumps due to the ability of the finite-volume
188method to accommodate discontinuities in the solution.
189
190To set up a particular scenario the user specifies the geometry
191(bathymetry and topography), the initial water level (stage),
192boundary conditions such as tide, and any forcing terms that may
193drive the system such as rain_fall, abstraction of water, wind stress or atmospheric pressure
194gradients. Gravity and frictional resistance from the different
195terrains in the model are represented by predefined forcing terms.
196See section \ref{sec:forcing terms} for details on forcing terms available in ANUGA.
197
198The built-in mesh generator, called \code{graphical\_mesh\_generator},
199allows the user to set up the geometry
200of the problem interactively and to identify boundary segments and
201regions using symbolic tags.  These tags may then be used to set the
202actual boundary conditions and attributes for different regions
203(e.g.\ the Manning friction coefficient) for each simulation.
204
205Most \anuga components are written in the object-oriented programming
206language Python.  Software written in Python can be produced quickly
207and can be readily adapted to changing requirements throughout its
208lifetime.  Computationally intensive components are written for
209efficiency in C routines working directly with the Numerical Python
210structures.  The animation tool developed for \anuga is based on
211OpenSceneGraph, an Open Source Software (OSS) component allowing high
212level interaction with sophisticated graphics primitives.
213See \cite{nielsen2005} for more background on \anuga.
214
215\chapter{Restrictions and limitations on \anuga}
216\label{ch:limitations}
217
218Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a
219number of limitations that any potential user need to be aware of. They are
220
221\begin{itemize}
222  \item The mathematical model is the 2D shallow water wave equation.
223  As such it cannot resolve vertical convection and consequently not breaking
224  waves or 3D turbulence (e.g.\ vorticity).
225  \item The surface is assumed to be open, e.g. \anuga cannot model
226  flow under ceilings or in pipes
227  \item All spatial coordinates are assumed to be UTM (meters). As such,
228  ANUGA is unsuitable for modelling flows in areas larger than one UTM zone
229  (6 degrees wide).
230  \item Fluid is assumed to be inviscid
231  \item The finite volume is a very robust and flexible numerical technique,
232  but it is not the fastest method around. If the geometry is sufficiently
233  simple and if there is no need for wetting or drying, a finite-difference
234  method may be able to solve the problem faster than \anuga.
235  %\item Mesh resolutions near coastlines with steep gradients need to be...
236  \item Frictional resistance is implemented using Manning's formula, but
237  \anuga has not yet been fully validated in regard to bottom roughness
238  \item ANUGA contains no tsunami-genic functionality relating to
239  earthquakes.
240\end{itemize}
241
242
243
244\chapter{Getting Started}
245\label{ch:getstarted}
246
247This section is designed to assist the reader to get started with
248\anuga by working through some examples. Two examples are discussed;
249the first is a simple example to illustrate many of the ideas, and
250the second is a more realistic example.
251
252\section{A Simple Example}
253\label{sec:simpleexample}
254
255\subsection{Overview}
256
257What follows is a discussion of the structure and operation of a
258script called \file{runup.py}.
259
260This example carries out the solution of the shallow-water wave
261equation in the simple case of a configuration comprising a flat
262bed, sloping at a fixed angle in one direction and having a
263constant depth across each line in the perpendicular direction.
264
265The example demonstrates the basic ideas involved in setting up a
266complex scenario. In general the user specifies the geometry
267(bathymetry and topography), the initial water level, boundary
268conditions such as tide, and any forcing terms that may drive the
269system such as rain_fall, abstraction of water, wind stress or atmospheric pressure gradients.
270Frictional resistance from the different terrains in the model is
271represented by predefined forcing terms. In this example, the
272boundary is reflective on three sides and a time dependent wave on
273one side.
274
275The present example represents a simple scenario and does not
276include any forcing terms, nor is the data taken from a file as it
277would typically be.
278
279The conserved quantities involved in the
280problem are stage (absolute height of water surface),
281$x$-momentum and $y$-momentum. Other quantities
282involved in the computation are the friction and elevation.
283
284Water depth can be obtained through the equation
285
286\begin{tabular}{rcrcl}
287  \code{depth} &=& \code{stage} &$-$& \code{elevation}
288\end{tabular}
289
290
291\subsection{Outline of the Program}
292
293In outline, \file{runup.py} performs the following steps:
294
295\begin{enumerate}
296
297   \item Sets up a triangular mesh.
298
299   \item Sets certain parameters governing the mode of
300operation of the model-specifying, for instance, where to store the model output.
301
302   \item Inputs various quantities describing physical measurements, such
303as the elevation, to be specified at each mesh point (vertex).
304
305   \item Sets up the boundary conditions.
306
307   \item Carries out the evolution of the model through a series of time
308steps and outputs the results, providing a results file that can
309be visualised.
310
311\end{enumerate}
312
313\subsection{The Code}
314
315%FIXME: we are using the \code function here.
316%This should be used wherever possible
317For reference we include below the complete code listing for
318\file{runup.py}. Subsequent paragraphs provide a
319`commentary' that describes each step of the program and explains it
320significance.
321
322\verbatiminput{demos/runup.py}
323
324\subsection{Establishing the Mesh}\index{mesh, establishing}
325
326The first task is to set up the triangular mesh to be used for the
327scenario. This is carried out through the statement:
328
329{\small \begin{verbatim}
330    points, vertices, boundary = rectangular_cross(10, 10)
331\end{verbatim}}
332
333The function \function{rectangular_cross} is imported from a module
334\module{mesh\_factory} defined elsewhere. (\anuga also contains
335several other schemes that can be used for setting up meshes, but we
336shall not discuss these.) The above assignment sets up a $10 \times
33710$ rectangular mesh, triangulated in a regular way. The assignment
338
339{\small \begin{verbatim}
340    points, vertices, boundary = rectangular_cross(m, n)
341\end{verbatim}}
342
343returns:
344
345\begin{itemize}
346
347   \item a list \code{points} giving the coordinates of each mesh point,
348
349   \item a list \code{vertices} specifying the three vertices of each triangle, and
350
351   \item a dictionary \code{boundary} that stores the edges on
352   the boundary and associates each with one of the symbolic tags \code{`left'}, \code{`right'},
353   \code{`top'} or \code{`bottom'}.
354
355\end{itemize}
356
357(For more details on symbolic tags, see page
358\pageref{ref:tagdescription}.)
359
360An example of a general unstructured mesh and the associated data
361structures \code{points}, \code{vertices} and \code{boundary} is
362given in Section \ref{sec:meshexample}.
363
364
365
366
367\subsection{Initialising the Domain}
368
369These variables are then used to set up a data structure
370\code{domain}, through the assignment:
371
372{\small \begin{verbatim}
373    domain = Domain(points, vertices, boundary)
374\end{verbatim}}
375
376This creates an instance of the \class{Domain} class, which
377represents the domain of the simulation. Specific options are set at
378this point, including the basename for the output file and the
379directory to be used for data:
380
381{\small \begin{verbatim}
382    domain.set_name('runup')
383\end{verbatim}}
384
385{\small \begin{verbatim}
386    domain.set_datadir('.')
387\end{verbatim}}
388
389In addition, the following statement now specifies that the
390quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are
391to be stored:
392
393{\small \begin{verbatim}
394    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
395    'ymomentum'])
396\end{verbatim}}
397
398
399\subsection{Initial Conditions}
400
401The next task is to specify a number of quantities that we wish to
402set for each mesh point. The class \class{Domain} has a method
403\method{set\_quantity}, used to specify these quantities. It is a
404flexible method that allows the user to set quantities in a variety
405of ways---using constants, functions, numeric arrays, expressions
406involving other quantities, or arbitrary data points with associated
407values, all of which can be passed as arguments. All quantities can
408be initialised using \method{set\_quantity}. For a conserved
409quantity (such as \code{stage, xmomentum, ymomentum}) this is called
410an \emph{initial condition}. However, other quantities that aren't
411updated by the equation are also assigned values using the same
412interface. The code in the present example demonstrates a number of
413forms in which we can invoke \method{set\_quantity}.
414
415
416\subsubsection{Elevation}
417
418The elevation, or height of the bed, is set using a function,
419defined through the statements below, which is specific to this
420example and specifies a particularly simple initial configuration
421for demonstration purposes:
422
423{\small \begin{verbatim}
424    def f(x,y):
425        return -x/2
426\end{verbatim}}
427
428This simply associates an elevation with each point \code{(x, y)} of
429the plane.  It specifies that the bed slopes linearly in the
430\code{x} direction, with slope $-\frac{1}{2}$,  and is constant in
431the \code{y} direction.
432
433Once the function \function{f} is specified, the quantity
434\code{elevation} is assigned through the simple statement:
435
436{\small \begin{verbatim}
437    domain.set_quantity('elevation', f)
438\end{verbatim}}
439
440NOTE: If using function to set \code{elevation} it must be vector
441compatible. For example square root will not work.
442
443\subsubsection{Friction}
444
445The assignment of the friction quantity (a forcing term)
446demonstrates another way we can use \method{set\_quantity} to set
447quantities---namely, assign them to a constant numerical value:
448
449{\small \begin{verbatim}
450    domain.set_quantity('friction', 0.1)
451\end{verbatim}}
452
453This specifies that the Manning friction coefficient is set to 0.1
454at every mesh point.
455
456\subsubsection{Stage}
457
458The stage (the height of the water surface) is related to the
459elevation and the depth at any time by the equation
460
461{\small \begin{verbatim}
462    stage = elevation + depth
463\end{verbatim}}
464
465
466For this example, we simply assign a constant value to \code{stage},
467using the statement
468
469{\small \begin{verbatim}
470    domain.set_quantity('stage', -.4)
471\end{verbatim}}
472
473which specifies that the surface level is set to a height of $-0.4$,
474i.e. 0.4 units (m) below the zero level.
475
476Although it is not necessary for this example, it may be useful to
477digress here and mention a variant to this requirement, which allows
478us to illustrate another way to use \method{set\_quantity}---namely,
479incorporating an expression involving other quantities. Suppose,
480instead of setting a constant value for the stage, we wished to
481specify a constant value for the \emph{depth}. For such a case we
482need to specify that \code{stage} is everywhere obtained by adding
483that value to the value already specified for \code{elevation}. We
484would do this by means of the statements:
485
486{\small \begin{verbatim}
487    h = 0.05 # Constant depth
488    domain.set_quantity('stage', expression = 'elevation + %f' %h)
489\end{verbatim}}
490
491That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus
492the value of \code{elevation} already defined.
493
494The reader will probably appreciate that this capability to
495incorporate expressions into statements using \method{set\_quantity}
496greatly expands its power.) See Section \ref{sec:initial conditions} for more
497details.
498
499\subsection{Boundary Conditions}\index{boundary conditions}
500
501The boundary conditions are specified as follows:
502
503{\small \begin{verbatim}
504    Br = Reflective_boundary(domain)
505
506    Bt = Transmissive_boundary(domain)
507
508    Bd = Dirichlet_boundary([0.2,0.,0.])
509
510    Bw = Time_boundary(domain=domain,
511                f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
512\end{verbatim}}
513
514The effect of these statements is to set up a selection of different
515alternative boundary conditions and store them in variables that can be
516assigned as needed. Each boundary condition specifies the
517behaviour at a boundary in terms of the behaviour in neighbouring
518elements. The boundary conditions introduced here may be briefly described as
519follows:
520
521\begin{itemize}
522    \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as
523      as present in its neighbour volume but momentum vector
524      reversed 180 degrees (reflected).
525      Specific to the shallow water equation as it works with the
526      momentum quantities assumed to be the second and third conserved
527      quantities. A reflective boundary condition models a solid wall.
528    \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as
529      those present in its neighbour volume. This is one way of modelling
530      outflow from a domain, but it should be used with caution if flow is
531      not steady state as replication of momentum at the boundary
532      may cause occasional spurious effects. If this occurs,
533      consider using e.g. a Dirichlet boundary condition.
534    \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies
535      constant values for stage, $x$-momentum and $y$-momentum at the boundary.
536    \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet
537      boundary but with behaviour varying with time.
538\end{itemize}
539
540\label{ref:tagdescription}Before describing how these boundary
541conditions are assigned, we recall that a mesh is specified using
542three variables \code{points}, \code{vertices} and \code{boundary}.
543In the code we are discussing, these three variables are returned by
544the function \code{rectangular}; however, the example given in
545Section \ref{sec:realdataexample} illustrates another way of
546assigning the values, by means of the function
547\code{create\_mesh\_from\_regions}.
548
549These variables store the data determining the mesh as follows. (You
550may find that the example given in Section \ref{sec:meshexample}
551helps to clarify the following discussion, even though that example
552is a \emph{non-rectangular} mesh.)
553
554\begin{itemize}
555\item The variable \code{points} stores a list of 2-tuples giving the
556coordinates of the mesh points.
557
558\item The variable \code{vertices} stores a list of 3-tuples of
559numbers, representing vertices of triangles in the mesh. In this
560list, the triangle whose vertices are \code{points[i]},
561\code{points[j]}, \code{points[k]} is represented by the 3-tuple
562\code{(i, j, k)}.
563
564\item The variable \code{boundary} is a Python dictionary that
565not only stores the edges that make up the boundary but also assigns
566symbolic tags to these edges to distinguish different parts of the
567boundary. An edge with endpoints \code{points[i]} and
568\code{points[j]} is represented by the 2-tuple \code{(i, j)}. The
569keys for the dictionary are the 2-tuples \code{(i, j)} corresponding
570to boundary edges in the mesh, and the values are the tags are used
571to label them. In the present example, the value \code{boundary[(i,
572j)]} assigned to \code{(i, j)]} is one of the four tags
573\code{`left'}, \code{`right'}, \code{`top'} or \code{`bottom'},
574depending on whether the boundary edge represented by \code{(i, j)}
575occurs at the left, right, top or bottom of the rectangle bounding
576the mesh. The function \code{rectangular} automatically assigns
577these tags to the boundary edges when it generates the mesh.
578\end{itemize}
579
580The tags provide the means to assign different boundary conditions
581to an edge depending on which part of the boundary it belongs to.
582(In Section \ref{sec:realdataexample} we describe an example that
583uses different boundary tags --- in general, the possible tags are entirely selectable by the user when generating the mesh and not
584limited to `left', `right', `top' and `bottom' as in this example.)
585All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by ANUGA.
586
587
588Using the boundary objects described above, we assign a boundary
589condition to each part of the boundary by means of a statement like
590
591{\small \begin{verbatim}
592    domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br})
593\end{verbatim}}
594
595It is critical that all tags are assoctiated with a boundary conditing in this statement. If not the program will halt with a statement like
596
597\begin{verbatim}
598
599Traceback (most recent call last):
600  File "mesh_test.py", line 114, in ?
601    domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br})
602  File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary
603    raise msg
604ERROR (domain.py): Tag "exterior" has not been bound to a boundary object.
605All boundary tags defined in domain must appear in the supplied dictionary.
606The tags are: ['ocean', 'east', 'north', 'exterior', 'south']
607\end{verbatim}
608
609
610The command \code{set\_boundary} stipulates that, in the current example, the right
611boundary varies with time, as defined by the lambda function, while the other
612boundaries are all reflective.
613
614The reader may wish to experiment by varying the choice of boundary
615types for one or more of the boundaries. (In the case of \code{Bd}
616and \code{Bw}, the three arguments in each case represent the
617\code{stage}, $x$-momentum and $y$-momentum, respectively.)
618
619{\small \begin{verbatim}
620    Bw = Time_boundary(domain=domain,
621                       f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
622\end{verbatim}}
623
624
625
626\subsection{Evolution}\index{evolution}
627
628The final statement \nopagebreak[3]
629{\small \begin{verbatim}
630    for t in domain.evolve(yieldstep = 0.1, duration = 4.0):
631        print domain.timestepping_statistics()
632\end{verbatim}}
633
634causes the configuration of the domain to `evolve', over a series of
635steps indicated by the values of \code{yieldstep} and
636\code{duration}, which can be altered as required.  The value of
637\code{yieldstep} controls the time interval between successive model
638outputs.  Behind the scenes more time steps are generally taken.
639
640
641\subsection{Output}
642
643The output is a NetCDF file with the extension \code{.sww}. It
644contains stage and momentum information and can be used with the
645ANUGA viewer \code{animate} (see Section \ref{sec:animate})
646visualisation package
647to generate a visual display. See Section \ref{sec:file formats}
648(page \pageref{sec:file formats}) for more on NetCDF and other file
649formats.
650
651The following is a listing of the screen output seen by the user
652when this example is run:
653
654\verbatiminput{examples/runupoutput.txt}
655
656
657\section{How to Run the Code}
658
659The code can be run in various ways:
660
661\begin{itemize}
662  \item{from a Windows or Unix command line} as in\ \code{python runup.py}
663  \item{within the Python IDLE environment}
664  \item{within emacs}
665  \item{within Windows, by double-clicking the \code{runup.py}
666  file.}
667\end{itemize}
668
669
670\section{Exploring the Model Output}
671
672The following figures are screenshots from the \anuga visualisation
673tool \code{animate}. Figure \ref{fig:runupstart} shows the domain
674with water surface as specified by the initial condition, $t=0$.
675Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and
676$t=4$ where the system has been evolved and the wave is encroaching
677on the previously dry bed.  All figures are screenshots from an
678interactive animation tool called animate which is part of \anuga and
679distributed as in the package anuga\_viewer.
680Animate is described in more detail is Section \ref{sec:animate}.
681
682\begin{figure}[hbt]
683
684  \centerline{\includegraphics[width=75mm, height=75mm]
685    {graphics/bedslopestart.jpg}}
686
687  \caption{Runup example viewed with the ANUGA viewer}
688  \label{fig:runupstart}
689\end{figure}
690
691
692\begin{figure}[hbt]
693
694  \centerline{
695   \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg}
696    \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg}
697   }
698
699  \caption{Runup example viewed with ANGUA viewer}
700  \label{fig:runup2}
701\end{figure}
702
703
704
705\clearpage
706
707%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
708
709\section{A slightly more complex example}
710\label{sec:channelexample}
711
712\subsection{Overview}
713
714The next example is about waterflow in a channel with varying boundary conditions and
715more complex topograhies. These examples build on the
716concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
717The example will be built up through three progressively more complex scripts.
718
719\subsection{Overview}
720As in the case of \file{runup.py}, the actions carried
721out by the program can be organised according to this outline:
722
723\begin{enumerate}
724
725   \item Set up a triangular mesh.
726
727   \item Set certain parameters governing the mode of
728operation of the model---specifying, for instance, where to store the
729model output.
730
731   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
732
733   \item Set up the boundary conditions.
734
735   \item Carry out the evolution of the model through a series of time
736steps and output the results, providing a results file that can be
737visualised.
738
739\end{enumerate}
740
741
742\subsection{The Code}
743
744Here is the code for the first version of the channel flow \file{channel1.py}:
745
746\verbatiminput{demos/channel1.py}
747
748In discussing the details of this example, we follow the outline
749given above, discussing each major step of the code in turn.
750
751\subsection{Establishing the Mesh}\index{mesh, establishing}
752
753In this example we use a similar simple structured triangular mesh as in \code{runup.py}
754for simplicity, but this time we will use a symmetric one and also
755change the physical extent of the domain. The assignment
756
757{\small \begin{verbatim}
758    points, vertices, boundary = rectangular_cross(m, n,
759                                                   len1=length, len2=width)
760\end{verbatim}}
761returns a m x n mesh similar to the one used in the previous example, except that now the
762extent in the x and y directions are given by the value of \code{length} and \code{width}
763respectively.
764
765Defining m and n in terms of the extent as in this example provides a convenient way of
766controlling 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:
767
768{\small \begin{verbatim}
769length = 10.
770width = 5.
771dx = dy = 1           # Resolution: Length of subdivisions on both axes
772
773points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
774                                               len1=length, len2=width)
775\end{verbatim}}
776which 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.
777
778The rest of this script is as in the previous example.
779% 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}:
780%{\small \begin{verbatim}
781%  domain.set_quantity('stage', expression='elevation')
782%\end{verbatim}}
783
784\section{Model Output}
785
786The following figure is a screenshot from the \anuga visualisation
787tool \code{animate} of output from this example.
788\begin{figure}[hbt]
789  \centerline{\includegraphics[height=75mm]
790    {graphics/channel1.png}}%
791
792  \caption{Simple channel example viewed with the ANUGA viewer.}
793  \label{fig:channel1}
794\end{figure}
795
796
797\subsection{Changing boundary conditions on the fly}
798\label{sec:change boundary}
799
800Here is the code for the second version of the channel flow \file{channel2.py}:
801\verbatiminput{demos/channel2.py}
802This example differs from the first version in that a constant outflow boundary condition has
803been defined
804{\small \begin{verbatim}
805    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
806\end{verbatim}}
807and that it is applied to the right hand side boundary when the water level there exceeds 0m.
808{\small \begin{verbatim}
809for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
810    domain.write_time()
811
812    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:
813        print 'Stage > 0: Changing to outflow boundary'
814        domain.set_boundary({'right': Bo})
815\end{verbatim}}
816\label{sec:change boundary code}
817
818The if statement in the timestepping loop (evolve) gets the quantity
819\code{stage} and obtain the interpolated value at the point (10m,
8202.5m) which is on the right boundary. If the stage exceeds 0m a
821message is printed and the old boundary condition at tag 'right' is
822replaced by the outflow boundary using the method
823{\small \begin{verbatim}
824    domain.set_boundary({'right': Bo})
825\end{verbatim}}
826This type of dynamically varying boundary could for example be
827used to model the
828breakdown of a sluice door when water exceeds a certain level.
829
830\subsection{Output}
831
832The text output from this example looks like this
833{\small \begin{verbatim}
834...
835Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
836Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
837Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
838Stage > 0: Changing to outflow boundary
839Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
840Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
841...
842\end{verbatim}}
843
844
845\subsection{Flow through more complex topograhies}
846
847Here is the code for the third version of the channel flow \file{channel3.py}:
848\verbatiminput{demos/channel3.py}
849
850This example differs from the first two versions in that the topography
851contains obstacles.
852
853This is accomplished here by defining the function \code{topography} as follows
854{\small \begin{verbatim}
855def topography(x,y):
856    """Complex topography defined by a function of vectors x and y
857    """
858
859    z = -x/10
860
861    N = len(x)
862    for i in range(N):
863
864        # Step
865        if 10 < x[i] < 12:
866            z[i] += 0.4 - 0.05*y[i]
867
868        # Constriction
869        if 27 < x[i] < 29 and y[i] > 3:
870            z[i] += 2
871
872        # Pole
873        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
874            z[i] += 2
875
876    return z
877\end{verbatim}}
878
879In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
880
881A screenshot of this model at time == 15s is
882\begin{figure}[hbt]
883
884  \centerline{\includegraphics[height=75mm]
885    {graphics/channel3.png}}
886
887  \caption{More complex flow in a channel}
888  \label{fig:channel3}
889\end{figure}
890
891
892
893
894\clearpage
895
896%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
897
898\section{An Example with Real Data}
899\label{sec:realdataexample} The following discussion builds on the
900concepts introduced through the \file{runup.py} example and
901introduces a second example, \file{runcairns.py}.  This refers to
902a {\bf hypothetical} scenario using real-life data,
903in which the domain of interest surrounds the
904Cairns region. Two scenarios are given; firstly, a
905hypothetical tsunami wave is generated by a submarine mass failure
906situated on the edge of the continental shelf, and secondly, a fixed wave
907of given amplitude and period is introduced through the boundary.
908
909{\bf
910Each scenario has been designed to generate a tsunami which will
911inundate the Cairns region. To achieve this, suitably large
912parameters were chosen and were not based on any known tsunami sources
913or realistic amplitudes.
914}
915
916\subsection{Overview}
917As in the case of \file{runup.py}, the actions carried
918out by the program can be organised according to this outline:
919
920\begin{enumerate}
921
922   \item Set up a triangular mesh.
923
924   \item Set certain parameters governing the mode of
925operation of the model---specifying, for instance, where to store the
926model output.
927
928   \item Input various quantities describing physical measurements, such
929as the elevation, to be specified at each mesh point (vertex).
930
931   \item Set up the boundary conditions.
932
933   \item Carry out the evolution of the model through a series of time
934steps and output the results, providing a results file that can be
935visualised.
936
937\end{enumerate}
938
939
940
941\subsection{The Code}
942
943Here is the code for \file{runcairns.py}:
944
945\verbatiminput{demos/cairns/runcairns.py}
946
947In discussing the details of this example, we follow the outline
948given above, discussing each major step of the code in turn.
949
950\subsection{Establishing the Mesh}\index{mesh, establishing}
951
952One obvious way that the present example differs from
953\file{runup.py} is in the use of a more complex method to
954create the mesh. Instead of imposing a mesh structure on a
955rectangular grid, the technique used for this example involves
956building mesh structures inside polygons specified by the user,
957using a mesh-generator.
958
959In its simplest form, the mesh-generator creates the mesh within a single
960polygon whose vertices are at geographical locations specified by
961the user. The user specifies the \emph{resolution}---that is, the
962maximal area of a triangle used for triangulation---and a triangular
963mesh is created inside the polygon using a mesh generation engine.
964On any given platform, the same mesh will be returned.
965%Figure
966%\ref{fig:pentagon} shows a simple example of this, in which the
967%triangulation is carried out within a pentagon.
968
969
970%\begin{figure}[hbt]
971
972%  \caption{Mesh points are created inside the polygon}
973  %\label{fig:pentagon}
974%\end{figure}
975
976Boundary tags are not restricted to \code{`left'}, \code{`bottom'},
977\code{`right'} and \code{`top'}, as in the case of
978\file{runup.py}. Instead the user specifies a list of
979tags appropriate to the configuration being modelled.
980
981In addition, the mesh-generator provides a way to adapt to geographic or
982other features in the landscape, whose presence may require an
983increase in resolution. This is done by allowing the user to specify
984a number of \emph{interior polygons}, each with a specified
985resolution. It is also
986possible to specify one or more `holes'---that is, areas bounded by
987polygons in which no triangulation is required.
988
989%\begin{figure}[hbt]
990%  \caption{Interior meshes with individual resolution}
991%  \label{fig:interior meshes}
992%\end{figure}
993
994In its general form, the mesh-generator takes for its input a bounding
995polygon and (optionally) a list of interior polygons. The user
996specifies resolutions, both for the bounding polygon and for each of
997the interior polygons. Given this data, the mesh-generator first creates a
998triangular mesh with varying resolution.
999
1000The function used to implement this process is
1001\function{create\_mesh\_from\_regions}. Its arguments include the
1002bounding polygon and its resolution, a list of boundary tags, and a
1003list of pairs \code{[polygon, resolution]}, specifying the interior
1004polygons and their resolutions.
1005
1006The resulting mesh is output to a \emph{mesh file}\index{mesh
1007file}\label{def:mesh file}. This term is used to describe a file of
1008a specific format used to store the data specifying a mesh. (There
1009are in fact two possible formats for such a file: it can either be a
1010binary file, with extension \code{.msh}, or an ASCII file, with
1011extension \code{.tsh}. In the present case, the binary file format
1012\code{.msh} is used. See Section \ref{sec:file formats} (page
1013\pageref{sec:file formats}) for more on file formats.)
1014
1015In practice, the details of the polygons used are read from a
1016separate file \file{project.py}. Here is a complete listing of
1017\file{project.py}:
1018
1019\verbatiminput{demos/cairns/project.py}
1020
1021Figure \ref{fig:cairns3d} illustrates the landscape of the region
1022for the Cairns example. Understanding the landscape is important in
1023determining the location and resolution of interior polygons. The
1024supporting data is found in the ASCII grid, \code{cairns.asc}, which
1025has been sourced from the publically available Australian Bathymetry
1026and Topography Grid 2005, \cite{grid250}. The required resolution
1027for inundation modelling will depend on the underlying topography and
1028bathymetry; as the terrain becomes more complex, the desired resolution
1029would decrease to the order of tens of metres.
1030
1031\begin{figure}[hbt]
1032\centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}}
1033\caption{Landscape of the Cairns scenario.}
1034\label{fig:cairns3d}
1035
1036\end{figure}
1037The following statements are used to read in the specific polygons
1038from \code{project.cairns} and assign a defined resolution to
1039each polygon.
1040
1041{\small \begin{verbatim}
1042    islands_res = 100000
1043    cairns_res = 100000
1044    shallow_res = 500000
1045    interior_regions = [[project.poly_cairns, cairns_res],
1046                        [project.poly_island0, islands_res],
1047                        [project.poly_island1, islands_res],
1048                        [project.poly_island2, islands_res],
1049                        [project.poly_island3, islands_res],
1050                        [project.poly_shallow, shallow_res]]
1051\end{verbatim}}
1052
1053Figure \ref{fig:cairnspolys}
1054illustrates the polygons used for the Cairns scenario.
1055
1056\begin{figure}[hbt]
1057
1058  \centerline{\includegraphics[scale=0.5]
1059      {graphics/cairnsmodel.jpg}}
1060  \caption{Interior and bounding polygons for the Cairns example.}
1061  \label{fig:cairnspolys}
1062\end{figure}
1063
1064The statement
1065
1066
1067{\small \begin{verbatim}
1068remainder_res = 10000000
1069create_mesh_from_regions(project.bounding_polygon,
1070                         boundary_tags={'top': [0],
1071                                        'ocean_east': [1],
1072                                        'bottom': [2],
1073                                        'onshore': [3]},
1074                         maximum_triangle_area=remainder_res,
1075                         filename=meshname,
1076                         interior_regions=interior_regions,
1077                         use_cache=True,
1078                         verbose=True)
1079\end{verbatim}}
1080is then used to create the mesh, taking the bounding polygon to be
1081the polygon \code{bounding\_polygon} specified in \file{project.py}.
1082The argument \code{boundary\_tags} assigns a dictionary, whose keys
1083are the names of the boundary tags used for the bounding
1084polygon---\code{`top'}, \code{`ocean\_east'}, \code{`bottom'}, and
1085\code{`onshore'}--- and whose values identify the indices of the
1086segments associated with each of these tags.
1087The polygon may be arranged either clock-wise or counter clock-wise and the
1088indices 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.
1089(Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges)
1090If polygons intersect, or edges coincide the resolution may be undefined in some regions.
1091Use the underlying mesh interface for such cases. See Section
1092\ref{sec:mesh interface}.
1093
1094Note that every point on each polygon defining the mesh will be used as vertices in triangles.
1095Consequently, polygons with points very close together will cause triangles with very small
1096areas to be generated irrespective of the requested resolution.
1097Make sure points on polygons are spaced to be no closer than the smallest resolution requested.
1098
1099
1100\subsection{Initialising the Domain}
1101
1102As with \file{runup.py}, once we have created the mesh, the next
1103step is to create the data structure \code{domain}. We did this for
1104\file{runup.py} by inputting lists of points and triangles and
1105specifying the boundary tags directly. However, in the present case,
1106we use a method that works directly with the mesh file
1107\code{meshname}, as follows:
1108
1109
1110{\small \begin{verbatim}
1111    domain = Domain(meshname, use_cache=True, verbose=True)
1112\end{verbatim}}
1113
1114Providing a filename instead of the lists used in \file{runup.py}
1115above causes \code{Domain} to convert a mesh file \code{meshname}
1116into an instance of \code{Domain}, allowing us to use methods like
1117\method{set\_quantity} to set quantities and to apply other
1118operations.
1119
1120%(In principle, the
1121%second argument of \function{pmesh\_to\_domain\_instance} can be any
1122%subclass of \class{Domain}, but for applications involving the
1123%shallow-water wave equation, the second argument of
1124%\function{pmesh\_to\_domain\_instance} can always be set simply to
1125%\class{Domain}.)
1126
1127The following statements specify a basename and data directory, and
1128identify quantities to be stored. For the first two, values are
1129taken from \file{project.py}.
1130
1131{\small \begin{verbatim}
1132    domain.set_name(project.basename)
1133    domain.set_datadir(project.outputdir)
1134    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
1135        'ymomentum'])
1136\end{verbatim}}
1137
1138
1139\subsection{Initial Conditions}
1140Quantities for \file{runcairns.py} are set
1141using similar methods to those in \file{runup.py}. However,
1142in this case, many of the values are read from the auxiliary file
1143\file{project.py} or, in the case of \code{elevation}, from an
1144ancillary points file.
1145
1146
1147
1148\subsubsection{Stage}
1149
1150For the scenario we are modelling in this case, we use a callable
1151object \code{tsunami\_source}, assigned by means of a function
1152\function{slide\_tsunami}. This is similar to how we set elevation in
1153\file{runup.py} using a function---however, in this case the
1154function is both more complex and more interesting.
1155
1156The function returns the water displacement for all \code{x} and
1157\code{y} in the domain. The water displacement is a double Gaussian
1158function that depends on the characteristics of the slide (length,
1159width, thickness, slope, etc), its location (origin) and the depth at that
1160location. For this example, we choose to apply the slide function
1161at a specified time into the simulation. {\bf Note, the parameters used
1162in this example have been deliberately chosen to generate a suitably
1163large amplitude tsunami which would inundate the Cairns region.}
1164
1165\subsubsection{Friction}
1166
1167We assign the friction exactly as we did for \file{runup.py}:
1168
1169{\small \begin{verbatim}
1170    domain.set_quantity('friction', 0.0)
1171\end{verbatim}}
1172
1173
1174\subsubsection{Elevation}
1175
1176The elevation is specified by reading data from a file:
1177
1178{\small \begin{verbatim}
1179    domain.set_quantity('elevation',
1180                        filename = project.dem_name + '.pts',
1181                        use_cache = True,
1182                        verbose = True)
1183\end{verbatim}}
1184
1185%However, before this step can be executed, some preliminary steps
1186%are needed to prepare the file from which the data is taken. Two
1187%source files are used for this data---their names are specified in
1188%the file \file{project.py}, in the variables \code{coarsedemname}
1189%and \code{finedemname}. They contain `coarse' and `fine' data,
1190%respectively---that is, data sampled at widely spaced points over a
1191%large region and data sampled at closely spaced points over a
1192%smaller subregion. The data in these files is combined through the
1193%statement
1194
1195%{\small \begin{verbatim}
1196%combine_rectangular_points_files(project.finedemname + '.pts',
1197%                                 project.coarsedemname + '.pts',
1198%                                 project.combineddemname + '.pts')
1199%\end{verbatim}}
1200%The effect of this is simply to combine the datasets by eliminating
1201%any coarse data associated with points inside the smaller region
1202%common to both datasets. The name to be assigned to the resulting
1203%dataset is also derived from the name stored in the variable
1204%\code{combinedname} in the file \file{project.py}.
1205
1206\subsection{Boundary Conditions}\index{boundary conditions}
1207
1208Setting boundaries follows a similar pattern to the one used for
1209\file{runup.py}, except that in this case we need to associate a
1210boundary type with each of the
1211boundary tag names introduced when we established the mesh. In place of the four
1212boundary types introduced for \file{runup.py}, we use the reflective
1213boundary for each of the
1214eight tagged segments defined by \code{create_mesh_from_regions}:
1215
1216{\small \begin{verbatim}
1217Bd = Dirichlet_boundary([0.0,0.0,0.0])
1218domain.set_boundary( {'ocean_east': Bd, 'bottom': Bd, 'onshore': Bd,
1219                          'top': Bd} )
1220\end{verbatim}}
1221
1222\subsection{Evolution}
1223
1224With the basics established, the running of the `evolve' step is
1225very similar to the corresponding step in \file{runup.py}. For the slide
1226scenario,
1227the simulation is run for 5000 seconds with the output stored every ten seconds.
1228For this example, we choose to apply the slide at 60 seconds into the simulation.
1229
1230{\small \begin{verbatim}
1231    import time t0 = time.time()
1232
1233
1234    for t in domain.evolve(yieldstep = 10, finaltime = 60):
1235            domain.write_time()
1236            domain.write_boundary_statistics(tags = 'ocean_east')
1237
1238        # add slide
1239        thisstagestep = domain.get_quantity('stage')
1240        if allclose(t, 60):
1241            slide = Quantity(domain)
1242            slide.set_values(tsunami_source)
1243            domain.set_quantity('stage', slide + thisstagestep)
1244
1245        for t in domain.evolve(yieldstep = 10, finaltime = 5000,
1246                               skip_initial_step = True):
1247            domain.write_time()
1248        domain.write_boundary_statistics(tags = 'ocean_east')
1249\end{verbatim}}
1250
1251For the fixed wave scenario, the simulation is run to 10000 seconds,
1252with the first half of the simulation stored at two minute intervals,
1253and the second half of the simulation stored at ten second intervals.
1254This functionality is especially convenient as it allows the detailed
1255parts of the simulation to be viewed at higher time resolution.
1256
1257
1258{\small \begin{verbatim}
1259
1260# save every two mins leading up to wave approaching land
1261    for t in domain.evolve(yieldstep = 120, finaltime = 5000):
1262        domain.write_time()
1263        domain.write_boundary_statistics(tags = 'ocean_east')
1264
1265    # save every 30 secs as wave starts inundating ashore
1266    for t in domain.evolve(yieldstep = 10, finaltime = 10000,
1267                           skip_initial_step = True):
1268        domain.write_time()
1269        domain.write_boundary_statistics(tags = 'ocean_east')
1270
1271\end{verbatim}}
1272
1273\section{Exploring the Model Output}
1274
1275Now that the scenario has been run, the user can view the output in a number of ways.
1276As described earlier, the user may run animate to view a three-dimensional representation
1277of the simulation.
1278
1279The user may also be interested in a maximum inundation map. This simply shows the
1280maximum water depth over the domain and is achieved with the function sww2dem (described in
1281Section \ref{sec:basicfileconversions}).
1282\file{ExportResults.py} demonstrates how this function can be used:
1283
1284\verbatiminput{demos/cairns/ExportResults.py}
1285
1286The script generates an maximum water depth ASCII grid at a defined
1287resolution (here 100 m$^2$) which can then be viewed in a GIS environment, for
1288example. The parameters used in the function are defined in \file{project.py}.
1289Figures \ref{fig:maxdepthcairnsslide} and \ref{fig:maxdepthcairnsfixedwave} show
1290the maximum water depth within the defined region for the slide and fixed wave scenario
1291respectively. {\bf Note, these inundation maps have been based on purely hypothetical
1292scenarios and were designed explicitly for demonstration purposes only.}
1293The user could develop a maximum absolute momentum or other expressions which can be
1294derived from the quantities.
1295It must be noted here that depth is more meaningful when the elevation is positive
1296(\code{depth} = \code{stage} $-$ \code{elevation}) as it describes the water height
1297above the available elevation. When the elevation is negative, depth is meauring the
1298water height from the sea floor. With this in mind, maximum inundation maps are
1299typically "clipped" to the coastline. However, the data input here did not contain a
1300coastline.
1301
1302\begin{figure}[hbt]
1303\centerline{\includegraphics[scale=0.5]{graphics/slidedepth.jpg}}
1304\caption{Maximum inundation map for the Cairns slide scenario. \bf Note, this
1305inundaiton map has been based on a purely hypothetical scenario which was
1306designed explictiy for demonstration purposes only.}
1307\label{fig:maxdepthcairnsslide}
1308\end{figure}
1309
1310\begin{figure}[hbt]
1311\centerline{\includegraphics[scale=0.5]{graphics/fixedwavedepth.jpg}}
1312\caption{Maximum inundation map for the Cairns fixed wave scenario.
1313\bf Note, this
1314inundaiton map has been based on a purely hypothetical scenario which was
1315designed explictiy for demonstration purposes only.}
1316\label{fig:maxdepthcairnsfixedwave}
1317\end{figure}
1318
1319The user may also be interested in interrogating the solution at a particular spatial
1320location to understand the behaviour of the system through time. To do this, the user
1321must first define the locations of interest. A number of locations have been
1322identified for the Cairns scenario, as shown in Figure \ref{fig:cairnsgauges}.
1323
1324\begin{figure}[hbt]
1325\centerline{\includegraphics[scale=0.5]{graphics/cairnsgauges.jpg}}
1326\caption{Point locations to show time series information for the Cairns scenario.}
1327\label{fig:cairnsgauges}
1328\end{figure}
1329
1330These locations
1331must be stored in either a .csv or .txt file. The corresponding .csv file for
1332the gauges shown in Figure \ref{fig:cairnsgauges} is \file{gauges.csv}
1333
1334\verbatiminput{demos/cairns/gauges.csv}
1335
1336Header information has been included to identify the location in terms of eastings and
1337northings, and each gauge is given a name. The elevation column can be zero here.
1338This information is then passed to the function \code{sww2csv_gauges} (shown in
1339\file{GetTimeseries.py} which generates the csv files for each point location. The csv files
1340can then be used in \code{csv2timeseries_graphs} to create the timeseries plot for each desired
1341quantity. \code{csv2timeseries_graphs} relies on \code{pylab} to be installed which is not part
1342of the standard \code{anuga} release, however it can be downloaded and installed from \code{http://matplotlib.sourceforge.net/}
1343
1344\verbatiminput{demos/cairns/GetTimeseries.py}
1345
1346Here, the time series for the quantities stage, depth and speed will be generated for
1347each gauge defined in the gauge file. As described earlier, depth is more meaningful
1348for onshore gauges, and stage is more appropriate for offshore gauges.
1349
1350As an example output,
1351Figure \ref{fig:reef} shows the time series for the quantity stage for the
1352Elford Reef location for each scenario (the elevation at this location is negative,
1353therefore stage is the more appropriate quantity to plot). Note the large negative stage value when the slide was
1354introduced. This is due to the double gaussian form of the initial surface
1355displacement of the slide. By contrast, the time series for depth is shown for the onshore location of the Cairns
1356Airport in Figure \ref{fig:airportboth}.
1357
1358\begin{figure}[hbt]
1359\centerline{\includegraphics[scale=0.5]{graphics/gaugeElfordReefstage.png}}
1360\caption{Time series information of the quantity stage for the Elford Reef location for the
1361fixed wave and slide scenario.}
1362\label{fig:reef}
1363\end{figure}
1364
1365\begin{figure}[hbt]
1366\centerline{\includegraphics[scale=0.5]{graphics/gaugeCairnsAirportdepth.png}}
1367\caption{Time series information of the quantity depth for the Cairns Airport
1368location for the slide and fixed wave scenario.}
1369\label{fig:airportboth}
1370\end{figure}
1371
1372
1373%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1374%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1375
1376\chapter{\anuga Public Interface}
1377\label{ch:interface}
1378
1379This chapter gives an overview of the features of \anuga available
1380to the user at the public interface. These are grouped under the
1381following headings, which correspond to the outline of the examples
1382described in Chapter \ref{ch:getstarted}:
1383
1384\begin{itemize}
1385    \item Establishing the Mesh: Section \ref{sec:establishing the mesh}
1386    \item Initialising the Domain: Section \ref{sec:initialising the domain}
1387    \item Specifying the Quantities: Section \ref{sec:quantitis}
1388    \item Initial Conditions: Section \ref{sec:initial conditions}
1389    \item Boundary Conditions: Section \ref{sec:boundary conditions}
1390    \item Forcing Terms: Section \ref{sec:forcing terms}
1391    \item Evolution: Section \ref{sec:evolution}
1392\end{itemize}
1393
1394The listings are intended merely to give the reader an idea of what
1395each feature is, where to find it and how it can be used---they do
1396not give full specifications; for these the reader
1397may consult the code. The code for every function or class contains
1398a documentation string, or `docstring', that specifies the precise
1399syntax for its use. This appears immediately after the line
1400introducing the code, between two sets of triple quotes.
1401
1402Each listing also describes the location of the module in which
1403the code for the feature being described can be found. All modules
1404are in the folder \file{inundation} or one of its subfolders, and the
1405location of each module is described relative to \file{inundation}. Rather
1406than using pathnames, whose syntax depends on the operating system,
1407we use the format adopted for importing the function or class for
1408use in Python code. For example, suppose we wish to specify that the
1409function \function{create\_mesh\_from\_regions} is in a module called
1410\module{mesh\_interface} in a subfolder of \module{inundation} called
1411\code{pmesh}. In Linux or Unix syntax, the pathname of the file
1412containing the function, relative to \file{inundation}, would be
1413
1414\begin{center}
1415%    \code{pmesh/mesh\_interface.py}
1416    \code{pmesh}$\slash$\code{mesh\_interface.py}
1417\end{center}
1418\label{sec:mesh interface}
1419
1420while in Windows syntax it would be
1421
1422\begin{center}
1423    \code{pmesh}$\backslash$\code{mesh\_interface.py}
1424\end{center}
1425
1426Rather than using either of these forms, in this chapter we specify
1427the location simply as \code{pmesh.mesh\_interface}, in keeping with
1428the usage in the Python statement for importing the function,
1429namely:
1430\begin{center}
1431    \code{from pmesh.mesh\_interface import create\_mesh\_from\_regions}
1432\end{center}
1433
1434Each listing details the full set of parameters for the class or
1435function; however, the description is generally limited to the most
1436important parameters and the reader is again referred to the code
1437for more details.
1438
1439The following parameters are common to many functions and classes
1440and are omitted from the descriptions given below:
1441
1442%\begin{center}
1443\begin{tabular}{ll}  %\hline
1444%\textbf{Name } & \textbf{Description}\\
1445%\hline
1446\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\\
1447\emph{verbose} & If \code{True}, provides detailed terminal output
1448to the user\\  % \hline
1449\end{tabular}
1450%\end{center}
1451
1452\section{Mesh Generation}\index{Mesh!generation}
1453\label{sec:establishing the mesh}
1454Before discussing the part of the interface relating to mesh
1455generation, we begin with a description of a simple example of a
1456mesh and use it to describe how mesh data is stored.
1457
1458\label{sec:meshexample} Figure \ref{fig:simplemesh} represents a
1459very simple mesh comprising just 11 points and 10 triangles.
1460
1461
1462\begin{figure}[h]
1463  \begin{center}
1464    \includegraphics[width=90mm, height=90mm]{triangularmesh.jpg}
1465  \end{center}
1466
1467  \caption{A simple mesh}
1468  \label{fig:simplemesh}
1469\end{figure}
1470
1471
1472The variables \code{points}, \code{vertices} and \code{boundary}
1473represent the data displayed in Figure \ref{fig:simplemesh} as
1474follows. The list \code{points} stores the coordinates of the
1475points, and may be displayed schematically as in Table
1476\ref{tab:points}.
1477
1478
1479\begin{table}
1480  \begin{center}
1481    \begin{tabular}[t]{|c|cc|} \hline
1482      index & \code{x} & \code{y}\\  \hline
1483      0 & 1 & 1\\
1484      1 & 4 & 2\\
1485      2 & 8 & 1\\
1486      3 & 1 & 3\\
1487      4 & 5 & 5\\
1488      5 & 8 & 6\\
1489      6 & 11 & 5\\
1490      7 & 3 & 6\\
1491      8 & 1 & 8\\
1492      9 & 4 & 9\\
1493      10 & 10 & 7\\  \hline
1494    \end{tabular}
1495  \end{center}
1496
1497  \caption{Point coordinates for mesh in
1498    Figure \protect \ref{fig:simplemesh}}
1499  \label{tab:points}
1500\end{table}
1501
1502The list \code{vertices} specifies the triangles that make up the
1503mesh. It does this by specifying, for each triangle, the indices
1504(the numbers shown in the first column above) that correspond to the
1505three points at its vertices, taken in an anti-clockwise order
1506around the triangle. Thus, in the example shown in Figure
1507\ref{fig:simplemesh}, the variable \code{vertices} contains the
1508entries shown in Table \ref{tab:vertices}. The starting point is
1509arbitrary so triangle $(0,1,3)$ is considered the same as $(1,3,0)$
1510and $(3,0,1)$.
1511
1512
1513\begin{table}
1514  \begin{center}
1515    \begin{tabular}{|c|ccc|} \hline
1516      index & \multicolumn{3}{c|}{\code{vertices}}\\ \hline
1517      0 & 0 & 1 & 3\\
1518      1 & 1 & 2 & 4\\
1519      2 & 2 & 5 & 4\\
1520      3 & 2 & 6 & 5\\
1521      4 & 4 & 5 & 9\\
1522      5 & 4 & 9 & 7\\
1523      6 & 3 & 4 & 7\\
1524      7 & 7 & 9 & 8\\
1525      8 & 1 & 4 & 3\\
1526      9 & 5 & 10 & 9\\  \hline
1527    \end{tabular}
1528  \end{center}
1529
1530  \caption{Vertices for mesh in Figure \protect \ref{fig:simplemesh}}
1531  \label{tab:vertices}
1532\end{table}
1533
1534Finally, the variable \code{boundary} identifies the boundary
1535triangles and associates a tag with each.
1536
1537\refmodindex[pmesh.meshinterface]{pmesh.mesh\_interface}\label{sec:meshgeneration}
1538
1539\begin{funcdesc}  {create\_mesh\_from\_regions}{bounding_polygon,
1540                             boundary_tags,
1541                             maximum_triangle_area,
1542                             filename=None,
1543                             interior_regions=None,
1544                             poly_geo_reference=None,
1545                             mesh_geo_reference=None,
1546                             minimum_triangle_angle=28.0}
1547Module: \module{pmesh.mesh\_interface}
1548
1549This function allows a user to initiate the automatic creation of a
1550mesh inside a specified polygon (input \code{bounding_polygon}).
1551Among the parameters that can be set are the \emph{resolution}
1552(maximal area for any triangle in the mesh) and the minimal angle
1553allowable in any triangle. The user can specify a number of internal
1554polygons within each of which the resolution of the mesh can be
1555specified. \code{interior_regions} is a paired list containing the
1556interior polygon and its resolution.  Additionally, the user specifies
1557a list of boundary tags, one for each edge of the bounding polygon.
1558
1559\textbf{WARNING}. Note that the dictionary structure used for the
1560parameter \code{boundary\_tags} is different from that used for the
1561variable \code{boundary} that occurs in the specification of a mesh.
1562In the case of \code{boundary}, the tags are the \emph{values} of
1563the dictionary, whereas in the case of \code{boundary_tags}, the
1564tags are the \emph{keys} and the \emph{value} corresponding to a
1565particular tag is a list of numbers identifying boundary edges
1566labelled with that tag. Because of this, it is theoretically
1567possible to assign the same edge to more than one tag. However, an
1568attempt to do this will cause an error.
1569
1570\textbf{WARNING}. Do not have polygon lines cross or be on-top of each
1571    other. This can result in regions of unspecified resolutions. Do
1572    not have polygon close to each other. This can result in the area
1573    between the polygons having small triangles.  For more control
1574    over the mesh outline use the methods described below.
1575
1576\end{funcdesc}
1577
1578
1579
1580\subsection{Advanced mesh generation}
1581
1582For more control over the creation of the mesh outline, use the
1583methods of the class \class{Mesh}.
1584
1585
1586\begin{classdesc}  {Mesh}{userSegments=None,
1587                 userVertices=None,
1588                 holes=None,
1589                 regions=None}
1590Module: \module{pmesh.mesh}
1591
1592A class used to build a mesh outline and generate a two-dimensional
1593triangular mesh. The mesh outline is used to describe features on the
1594mesh, such as the mesh boundary. Many of this classes methods are used
1595to build a mesh outline, such as \code{add\_vertices} and
1596\code{add\_region\_from\_polygon}.
1597
1598\end{classdesc}
1599
1600
1601\subsubsection{Key Methods of Class Mesh}
1602
1603
1604\begin{methoddesc} {add\_hole}{x,y}
1605Module: \module{pmesh.mesh},  Class: \class{Mesh}
1606
1607This method is used to build the mesh outline.  It defines a hole,
1608when the boundary of the hole has already been defined, by selecting a
1609point within the boundary.
1610
1611\end{methoddesc}
1612
1613
1614\begin{methoddesc}  {add\_hole\_from\_polygon}{self, polygon, tags=None}
1615Module: \module{pmesh.mesh},  Class: \class{Mesh}
1616
1617This method is used to add a `hole' within a region ---that is, to
1618define a interior region where the triangular mesh will not be
1619generated---to a \class{Mesh} instance. The region boundary is described by
1620the polygon passed in.  Additionally, the user specifies a list of
1621boundary tags, one for each edge of the bounding polygon.
1622\end{methoddesc}
1623
1624
1625\begin{methoddesc}  {add\_points_and_segments}{self, points, segments,
1626    segment\_tags=None}
1627Module: \module{pmesh.mesh},  Class: \class{Mesh}
1628
1629This method is used to build the mesh outline. It adds points and
1630segments connecting the points.  A tag for each segment can optionally
1631be added.
1632
1633\end{methoddesc}
1634
1635\begin{methoddesc} {add\_region}{x,y}
1636Module: \module{pmesh.mesh},  Class: \class{Mesh}
1637
1638This method is used to build the mesh outline.  It defines a region,
1639when the boundary of the region has already been defined, by selecting
1640a point within the boundary.  A region instance is returned.  This can
1641be used to set the resolution.
1642
1643\end{methoddesc}
1644
1645\begin{methoddesc}  {add\_region\_from\_polygon}{self, polygon,
1646segment_tags=None, region_tag=None
1647                                max_triangle_area=None}
1648Module: \module{pmesh.mesh},  Class: \class{Mesh}
1649
1650This method is used to build the mesh outline.  It adds a region to a
1651\class{Mesh} instance.  Regions are commonly used to describe an area
1652with an increased density of triangles, by setting
1653\code{max_triangle_area}.  The
1654region boundary is described by the input \code{polygon}.  Additionally, the
1655user specifies a list of segment tags, one for each edge of the
1656bounding polygon.  The regional tag is set using  \code{region}.
1657
1658\end{methoddesc}
1659
1660
1661
1662
1663
1664\begin{methoddesc} {add\_vertices}{point_data}
1665Module: \module{pmesh.mesh},  Class: \class{Mesh}
1666
1667Add user vertices. The point_data can be a list of (x,y) values, a numeric
1668array or a geospatial_data instance.
1669\end{methoddesc}
1670
1671\begin{methoddesc} {auto\_segment}{raw_boundary=raw_boundary,
1672                    remove_holes=remove_holes,
1673                    smooth_indents=smooth_indents,
1674                    expand_pinch=expand_pinch}
1675Module: \module{pmesh.mesh},  Class: \class{Mesh}
1676
1677Add segments between some of the user vertices to give the vertices an
1678outline.  The outline is an alpha shape. This method is
1679useful since a set of user vertices need to be outlined by segments
1680before generate_mesh is called.
1681
1682\end{methoddesc}
1683
1684\begin{methoddesc}  {export\_mesh_file}{self,ofile}
1685Module: \module{pmesh.mesh},  Class: \class{Mesh}
1686
1687This method is used to save the mesh to a file. \code{ofile} is the
1688name of the mesh file to be written, including the extension.  Use
1689the extension \code{.msh} for the file to be in NetCDF format and
1690\code{.tsh} for the file to be ASCII format.
1691\end{methoddesc}
1692
1693\begin{methoddesc}  {generate\_mesh}{self,
1694                      maximum_triangle_area=None,
1695                      minimum_triangle_angle=28.0,
1696                      verbose=False}
1697Module: \module{pmesh.mesh},  Class: \class{Mesh}
1698
1699This method is used to generate the triangular mesh.  The  maximal
1700area of any triangle in the mesh can be specified, which is used to
1701control the triangle density, along with the
1702minimum angle in any triangle.
1703\end{methoddesc}
1704
1705
1706
1707\begin{methoddesc}  {import_ungenerate_file}{self,ofile, tag=None,
1708region_tag=None}
1709Module: \module{pmesh.mesh},  Class: \class{Mesh}
1710
1711This method is used to import a polygon file in the ungenerate format,
1712which is used by arcGIS. The polygons from the file are converted to
1713vertices and segments. \code{ofile} is the name of the polygon file.
1714\code{tag} is the tag given to all the polygon's segments.
1715\code{region_tag} is the tag given to all the polygon's segments.  If
1716it is a string the one value will be assigned to all regions.  If it
1717is a list the first value in the list will be applied to the first
1718polygon etc.
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} 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
2089The model time stored within the file function can be accessed using
2090the method \code{f.get\_time()}
2091
2092
2093The underlying algorithm used is as follows:\\
2094Given a time series (i.e.\ a series of values associated with
2095different times), whose values are either just numbers or a set of
2096 numbers defined at the vertices of a triangular mesh (such as those
2097 stored in SWW files), \code{Interpolation\_function} is used to
2098 create a callable object that interpolates a value for an arbitrary
2099 time \code{t} within the model limits and possibly a point \code{(x,
2100 y)} within a mesh region.
2101
2102 The actual time series at which data is available is specified by
2103 means of an array \code{time} of monotonically increasing times. The
2104 quantities containing the values to be interpolated are specified in
2105 an array---or dictionary of arrays (used in conjunction with the
2106 optional argument \code{quantity\_names}) --- called
2107 \code{quantities}. The optional arguments \code{vertex\_coordinates}
2108 and \code{triangles} represent the spatial mesh associated with the
2109 quantity arrays. If omitted the function created by
2110 \code{Interpolation\_function} will be a function of \code{t} only.
2111
2112 Since, in practice, values need to be computed at specified points,
2113 the syntax allows the user to specify, once and for all, a list
2114 \code{interpolation\_points} of points at which values are required.
2115 In this case, the function may be called using the form \code{f(t,
2116 id)}, where \code{id} is an index for the list
2117 \code{interpolation\_points}.
2118
2119
2120\end{funcdesc}
2121
2122%%%
2123%% \begin{classdesc}{Interpolation\_function}{self,
2124%%     time,
2125%%     quantities,
2126%%     quantity_names = None,
2127%%     vertex_coordinates = None,
2128%%     triangles = None,
2129%%     interpolation_points = None,
2130%%     verbose = False}
2131%% Module: \module{abstract\_2d\_finite\_volumes.least\_squares}
2132
2133%% Given a time series (i.e.\ a series of values associated with
2134%% different times), whose values are either just numbers or a set of
2135%% numbers defined at the vertices of a triangular mesh (such as those
2136%% stored in SWW files), \code{Interpolation\_function} is used to
2137%% create a callable object that interpolates a value for an arbitrary
2138%% time \code{t} within the model limits and possibly a point \code{(x,
2139%% y)} within a mesh region.
2140
2141%% The actual time series at which data is available is specified by
2142%% means of an array \code{time} of monotonically increasing times. The
2143%% quantities containing the values to be interpolated are specified in
2144%% an array---or dictionary of arrays (used in conjunction with the
2145%% optional argument \code{quantity\_names}) --- called
2146%% \code{quantities}. The optional arguments \code{vertex\_coordinates}
2147%% and \code{triangles} represent the spatial mesh associated with the
2148%% quantity arrays. If omitted the function created by
2149%% \code{Interpolation\_function} will be a function of \code{t} only.
2150
2151%% Since, in practice, values need to be computed at specified points,
2152%% the syntax allows the user to specify, once and for all, a list
2153%% \code{interpolation\_points} of points at which values are required.
2154%% In this case, the function may be called using the form \code{f(t,
2155%% id)}, where \code{id} is an index for the list
2156%% \code{interpolation\_points}.
2157
2158%% \end{classdesc}
2159
2160%%%
2161%\begin{funcdesc}{set\_region}{functions}
2162%[Low priority. Will be merged into set\_quantity]
2163
2164%Module:\module{abstract\_2d\_finite\_volumes.domain}
2165%\end{funcdesc}
2166
2167
2168
2169%%%%%%
2170\section{Boundary Conditions}\index{boundary conditions}
2171\label{sec:boundary conditions}
2172
2173\anuga provides a large number of predefined boundary conditions,
2174represented by objects such as \code{Reflective\_boundary(domain)} and
2175\code{Dirichlet\_boundary([0.2, 0.0, 0.0])}, described in the examples
2176in Chapter 2. Alternatively, you may prefer to ``roll your own'',
2177following the method explained in Section \ref{sec:roll your own}.
2178
2179These boundary objects may be used with the function \code{set\_boundary} described below
2180to assign boundary conditions according to the tags used to label boundary segments.
2181
2182\begin{methoddesc}{set\_boundary}{boundary_map}
2183Module: \module{abstract\_2d\_finite\_volumes.domain}
2184
2185This function allows you to assign a boundary object (corresponding to a
2186pre-defined or user-specified boundary condition) to every boundary segment that
2187has been assigned a particular tag.
2188
2189This is done by specifying a dictionary \code{boundary\_map}, whose values are the boundary objects
2190and whose keys are the symbolic tags.
2191
2192\end{methoddesc}
2193
2194\begin{methoddesc} {get\_boundary\_tags}{}
2195Module: \module{abstract\_2d\_finite\_volumes.domain}
2196
2197Returns a list of the available boundary tags.
2198\end{methoddesc}
2199
2200%%%
2201\subsection{Predefined boundary conditions}
2202
2203\begin{classdesc}{Reflective\_boundary}{Boundary}
2204Module: \module{shallow\_water}
2205
2206Reflective boundary returns same conserved quantities as those present in
2207the neighbouring volume but reflected.
2208
2209This class is specific to the shallow water equation as it works with the
2210momentum quantities assumed to be the second and third conserved quantities.
2211\end{classdesc}
2212
2213%%%
2214\begin{classdesc}{Transmissive\_boundary}{domain = None}
2215Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2216
2217A transmissive boundary returns the same conserved quantities as
2218those present in the neighbouring volume.
2219
2220The underlying domain must be specified when the boundary is instantiated.
2221\end{classdesc}
2222
2223%%%
2224\begin{classdesc}{Dirichlet\_boundary}{conserved_quantities=None}
2225Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2226
2227A Dirichlet boundary returns constant values for each of conserved
2228quantities. In the example of \code{Dirichlet\_boundary([0.2, 0.0, 0.0])},
2229the \code{stage} value at the boundary is 0.2 and the \code{xmomentum} and
2230\code{ymomentum} at the boundary are set to 0.0. The list must contain
2231a value for each conserved quantity.
2232\end{classdesc}
2233
2234%%%
2235\begin{classdesc}{Time\_boundary}{domain = None, f = None}
2236Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2237
2238A time-dependent boundary returns values for the conserved
2239quantities as a function \code{f(t)} of time. The user must specify
2240the domain to get access to the model time.
2241\end{classdesc}
2242
2243%%%
2244\begin{classdesc}{File\_boundary}{Boundary}
2245Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2246
2247This method may be used if the user wishes to apply a SWW file or
2248a time series file to a boundary segment or segments.
2249The boundary values are obtained from a file and interpolated to the
2250appropriate segments for each conserved quantity.
2251\end{classdesc}
2252
2253
2254
2255%%%
2256\begin{classdesc}{Transmissive\_Momentum\_Set\_Stage\_boundary}{Boundary}
2257Module: \module{shallow\_water}
2258
2259This boundary returns same momentum conserved quantities as
2260those present in its neighbour volume but sets stage as in a Time\_boundary.
2261The underlying domain must be specified when boundary is instantiated
2262
2263This type of boundary is useful when stage is known at the boundary as a
2264function of time, but momenta (or speeds) aren't.
2265
2266This class is specific to the shallow water equation as it works with the
2267momentum quantities assumed to be the second and third conserved quantities.
2268\end{classdesc}
2269
2270
2271\begin{classdesc}{Dirichlet\_Discharge\_boundary}{Boundary}
2272Module: \module{shallow\_water}
2273
2274Sets stage (stage0)
2275Sets momentum (wh0) in the inward normal direction.
2276\end{classdesc}
2277
2278
2279
2280\subsection{User-defined boundary conditions}
2281\label{sec:roll your own}
2282
2283All boundary classes must inherit from the generic boundary class
2284\code{Boundary} and have a method called \code{evaluate} which must
2285take as inputs \code{self, vol\_id, edge\_id} where self refers to the
2286object itself and vol\_id and edge\_id are integers referring to
2287particular edges. The method must return a list of three floating point
2288numbers representing values for \code{stage},
2289\code{xmomentum} and \code{ymomentum}, respectively.
2290
2291The constructor of a particular boundary class may be used to specify
2292particular values or flags to be used by the \code{evaluate} method.
2293Please refer to the source code for the existing boundary conditions
2294for examples of how to implement boundary conditions.
2295
2296
2297
2298\section{Forcing Terms}\index{Forcing terms}
2299\label{sec:forcing terms}
2300
2301\anuga provides a number of predefined forcing functions to be used with simulations.
2302Gravity and friction are always calculated using the elevation and friction quantities, but the user may additionally add forcing terms to the list
2303\code{domain.forcing\_terms} and have them affect the model.
2304 
2305Currently, predefined forcing terms are
2306
2307\begin{funcdesc}{General\_forcing}{}
2308  Module: \module{shallow\_water.shallow\_water\_domain}
2309
2310  This is a general class to modify any quantity according to a given rate of change.
2311  Other specific forcing terms are based on this class but it can be used by itself as well (e.g.\ to modify momentum).
2312 
2313  The General\_forcing class takes as input:
2314  \begin{itemize} 
2315    \item \code{domain}: a reference to the domain being evolved
2316    \item \code{quantity\_name}: The name of the quantity that will be affected by this forcing term
2317    \item \code{rate}: The rate at which the quantity should change. The parameter \code{rate} can be eithe a constant or a
2318                function of time. Positive values indicate increases,
2319                negative values indicate decreases.
2320                The parametr \code{rate} can be \code{None} at initialisation but must be specified
2321                before forcing term is applied (i.e. simulation has started).
2322                The default value is 0.0 - i.e.\ no forcing.
2323    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2324    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2325  \end{itemize}
2326  Note specifying both center, radius and polygon will cause an exception to be thrown.
2327
2328  \bigskip 
2329  Example:
2330  {\scriptsize \begin{verbatim} 
2331    P = [[x0, y0], [x1, y0], [x1, y1], [x0, y1]] # Square polygon
2332 
2333    xmom = General_forcing(domain, 'xmomentum', polygon=P)
2334    ymom = General_forcing(domain, 'ymomentum', polygon=P)
2335
2336    xmom.rate = f
2337    ymom.rate = g
2338 
2339    domain.forcing_terms.append(xmom)
2340    domain.forcing_terms.append(ymom)   
2341  \end{verbatim}}
2342  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.
2343  P is assumed to be polygon, specified as a list of points.
2344 
2345\end{funcdesc} 
2346
2347
2348\begin{funcdesc}{Inflow}{}
2349  Module: \module{shallow\_water.shallow\_water\_domain}
2350
2351  This is a general class for infiltration and abstraction of water according to a given rate of change.
2352  This class will always modify the \code{stage} quantity.
2353 
2354  Inflow is based on the General_forcing class so the functionality is similar.
2355 
2356  The Inflow class takes as input:
2357  \begin{itemize} 
2358    \item \code{domain}: a reference to the domain being evolved
2359    \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
2360                function of time. Positive values indicate inflow,
2361                negative values indicate outflow.
2362               
2363                Note: The specified flow will be divided by the area of
2364                the inflow region and then applied to update the
2365                stage quantity.     
2366    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2367    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2368  \end{itemize}
2369
2370  \bigskip     
2371  Example:
2372  {\scriptsize \begin{verbatim} 
2373    hydrograph = Inflow(center=(320, 300), radius=10,
2374                        rate=file_function('QPMF_Rot_Sub13.tms'))
2375
2376    domain.forcing_terms.append(hydrograph)
2377  \end{verbatim}}
2378  Here, \code{'QPMF_Rot_Sub13.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for a hydrograph.
2379\end{funcdesc} 
2380
2381
2382\begin{funcdesc}{Rainfall}{}
2383  Module: \module{shallow\_water.shallow\_water\_domain}
2384
2385  This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon.
2386  This class will always modify the \code{stage} quantity.
2387 
2388  Rainfall is based on the General_forcing class so the functionality is similar.
2389 
2390  The Rainfall class takes as input:
2391  \begin{itemize} 
2392    \item \code{domain}: a reference to the domain being evolved
2393    \item \code{rate}: Total rain rate over the specified domain. 
2394                  Note: Raingauge Data needs to reflect the time step.
2395                  For example: if rain gauge is mm read every \code{dt} seconds, then the input
2396                  here is as \code{mm/dt} so 10 mm in 5 minutes becomes
2397                  10/(5x60) = 0.0333mm/s.
2398       
2399                  This parameter can be either a constant or a
2400                  function of time. Positive values indicate rain being added (or be used for general infiltration),
2401                  negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction).
2402    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2403    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2404  \end{itemize}
2405 
2406  \bigskip   
2407  Example:
2408  {\scriptsize \begin{verbatim} 
2409 
2410    catchmentrainfall = Rainfall(rain=file_function('Q100_2hr_Rain.tms')) 
2411    domain.forcing_terms.append(catchmentrainfall)
2412
2413  \end{verbatim}}
2414  Here, \code{'Q100_2hr_Rain.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for the rainfall.
2415\end{funcdesc} 
2416
2417
2418
2419\begin{funcdesc}{Culvert\_flow}{}
2420  Module: \module{culver\_flows.culvert\_class}
2421
2422  This is a general class for implementing flow through a culvert.
2423  This class modifies the quantities \code{stage, xmomentum, ymomentum} in areas at both ends of the culvert.
2424 
2425  The Culvert\_flow forcing term uses \code{Inflow} and {General\_forcing} to update the quantities. The flow drection is determined on-the-fly so
2426  openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow and Outflow.
2427 
2428  The Culvert\_flow class takes as input:
2429  \begin{itemize} 
2430    \item \code{domain}: a reference to the domain being evolved
2431    \item \code{label}: Short text naming the culvert
2432    \item \code{description}: Text describing it
2433    \item \code{end_point0}: Coordinates of one opening
2434    \item \code{end_point1}: Coordinates of other opening
2435    \item \code{width}:
2436    \item \code{height}:
2437    \item \code{diameter}:
2438    \item \code{manning}: Mannings Roughness for Culvert
2439    \item \code{invert_level0}: Invert level if not the same as the Elevation on the Domain
2440    \item \code{invert_level1}: Invert level if not the same as the Elevation on the Domain
2441    \item \code{culvert_routine}: Function specifying the calculation of flow based on energy difference between the two openings (see below)
2442  \end{itemize}
2443
2444  The user can specify different culvert routines. Hower ANUGA currently specifies one, namely the \code{boyd\_generalised\_culvert\_model} as used in the example below.
2445     
2446  \bigskip       
2447  Example:
2448  {\scriptsize \begin{verbatim} 
2449    from anuga.culvert_flows.culvert_class import Culvert_flow
2450    from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model 
2451
2452    culvert1 = Culvert_flow(domain,
2453                           label='Culvert No. 1',
2454                           description='This culvert is a test unit 1.2m Wide by 0.75m High',   
2455                           end_point0=[9.0, 2.5],
2456                           end_point1=[13.0, 2.5],
2457                           width=1.20,height=0.75,
2458                           culvert_routine=boyd_generalised_culvert_model,       
2459                           verbose=True)
2460
2461    culvert2 = Culvert_flow(domain,
2462                           label='Culvert No. 2',
2463                           description='This culvert is a circular test with d=1.2m',   
2464                           end_point0=[9.0, 1.5],
2465                           end_point1=[30.0, 3.5],
2466                           diameter=1.20,
2467                           invert_level0=7,
2468                           culvert_routine=boyd_generalised_culvert_model,       
2469                           verbose=True)
2470                           
2471    domain.forcing_terms.append(culvert1)
2472    domain.forcing_terms.append(culvert2)
2473
2474   
2475  \end{verbatim}}
2476\end{funcdesc} 
2477
2478
2479
2480
2481
2482
2483\section{Evolution}\index{evolution}
2484\label{sec:evolution}
2485
2486  \begin{methoddesc}{evolve}{yieldstep = None, finaltime = None, duration = None, skip_initial_step = False}
2487
2488  Module: \module{abstract\_2d\_finite\_volumes.domain}
2489
2490  This function (a method of \class{domain}) is invoked once all the
2491  preliminaries have been completed, and causes the model to progress
2492  through successive steps in its evolution, storing results and
2493  outputting statistics whenever a user-specified period
2494  \code{yieldstep} is completed (generally during this period the
2495  model will evolve through several steps internally
2496  as the method forces the water speed to be calculated
2497  on successive new cells). The user
2498  specifies the total time period over which the evolution is to take
2499  place, by specifying values (in seconds) for either \code{duration}
2500  or \code{finaltime}, as well as the interval in seconds after which
2501  results are to be stored and statistics output.
2502
2503  You can include \method{evolve} in a statement of the type:
2504
2505  {\small \begin{verbatim}
2506      for t in domain.evolve(yieldstep, finaltime):
2507          <Do something with domain and t>
2508  \end{verbatim}}
2509
2510  \end{methoddesc}
2511
2512
2513
2514\subsection{Diagnostics}
2515\label{sec:diagnostics}
2516
2517
2518  \begin{funcdesc}{statistics}{}
2519  Module: \module{abstract\_2d\_finite\_volumes.domain}
2520
2521  \end{funcdesc}
2522
2523  \begin{funcdesc}{timestepping\_statistics}{}
2524  Module: \module{abstract\_2d\_finite\_volumes.domain}
2525
2526  Returns a string of the following type for each
2527  timestep:
2528
2529  \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12
2530  (12)}
2531
2532  Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and
2533  the number of first-order steps, respectively.\\
2534
2535  The optional keyword argument \code{track_speeds=True} will
2536  generate a histogram of speeds generated by each triangle. The
2537  speeds relate to the size of the timesteps used by ANUGA and
2538  this diagnostics may help pinpoint problem areas where excessive speeds
2539  are generated.
2540
2541  \end{funcdesc}
2542
2543
2544  \begin{funcdesc}{boundary\_statistics}{quantities = None, tags = None}
2545  Module: \module{abstract\_2d\_finite\_volumes.domain}
2546
2547  Returns a string of the following type when \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']}:
2548
2549  {\small \begin{verbatim}
2550 Boundary values at time 0.5000:
2551    top:
2552        stage in [ -0.25821218,  -0.02499998]
2553    bottom:
2554        stage in [ -0.27098821,  -0.02499974]
2555  \end{verbatim}}
2556
2557  \end{funcdesc}
2558
2559
2560  \begin{funcdesc}{get\_quantity}{name, location='vertices', indices = None}
2561  Module: \module{abstract\_2d\_finite\_volumes.domain}
2562
2563  Allow access to individual quantities and their methods
2564
2565  \end{funcdesc}
2566
2567
2568  \begin{funcdesc}{set\_quantities\_to\_be\_monitored}{}
2569  Module: \module{abstract\_2d\_finite\_volumes.domain}
2570
2571  Selects quantities and derived quantities for which extrema attained at internal timesteps
2572  will be collected.
2573
2574  Information can be tracked in the evolve loop by printing \code{quantity\_statistics} and
2575  collected data will be stored in the sww file.
2576
2577  Optional parameters \code{polygon} and \code{time\_interval} may be specified to restrict the
2578  extremum computation.
2579  \end{funcdesc}
2580
2581  \begin{funcdesc}{quantity\_statistics}{}
2582  Module: \module{abstract\_2d\_finite\_volumes.domain}
2583
2584  Reports on extrema attained by selected quantities.
2585
2586  Returns a string of the following type for each
2587  timestep:
2588
2589  \begin{verbatim}
2590  Monitored quantities at time 1.0000:
2591    stage-elevation:
2592      values since time = 0.00 in [0.00000000, 0.30000000]
2593      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2594      maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667)
2595    ymomentum:
2596      values since time = 0.00 in [0.00000000, 0.06241221]
2597      minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667)
2598      maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667)
2599    xmomentum:
2600      values since time = 0.00 in [-0.06062178, 0.47886313]
2601      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2602      maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667)
2603  \end{verbatim}
2604
2605  The quantities (and derived quantities) listed here must be selected at model
2606  initialisation using the method \code{domain.set_quantities_to_be_monitored}.\\
2607
2608  The optional keyword argument \code{precision='\%.4f'} will
2609  determine the precision used for floating point values in the output.
2610  This diagnostics helps track extrema attained by the selected quantities
2611  at every internal timestep.
2612
2613  These values are also stored in the sww file for post processing.
2614
2615  \end{funcdesc}
2616
2617
2618
2619  \begin{funcdesc}{get\_values}{location='vertices', indices = None}
2620  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2621
2622  Extract values for quantity as an array
2623
2624  \end{funcdesc}
2625
2626
2627  \begin{funcdesc}{get\_integral}{}
2628  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2629
2630  Return computed integral over entire domain for this quantity
2631
2632  \end{funcdesc}
2633
2634
2635
2636
2637  \begin{funcdesc}{get\_maximum\_value}{indices = None}
2638  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2639
2640  Return maximum value of quantity (on centroids)
2641
2642  Optional argument indices is the set of element ids that
2643  the operation applies to. If omitted all elements are considered.
2644
2645  We do not seek the maximum at vertices as each vertex can
2646  have multiple values - one for each triangle sharing it.
2647  \end{funcdesc}
2648
2649
2650
2651  \begin{funcdesc}{get\_maximum\_location}{indices = None}
2652  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2653
2654  Return location of maximum value of quantity (on centroids)
2655
2656  Optional argument indices is the set of element ids that
2657  the operation applies to.
2658
2659  We do not seek the maximum at vertices as each vertex can
2660  have multiple values - one for each triangle sharing it.
2661
2662  If there are multiple cells with same maximum value, the
2663  first cell encountered in the triangle array is returned.
2664  \end{funcdesc}
2665
2666
2667
2668  \begin{funcdesc}{get\_wet\_elements}{indices=None}
2669  Module: \module{shallow\_water.shallow\_water\_domain}
2670
2671  Return indices for elements where h $>$ minimum_allowed_height
2672  Optional argument indices is the set of element ids that the operation applies to.
2673  \end{funcdesc}
2674
2675
2676  \begin{funcdesc}{get\_maximum\_inundation\_elevation}{indices=None}
2677  Module: \module{shallow\_water.shallow\_water\_domain}
2678
2679  Return highest elevation where h $>$ 0.\\
2680  Optional argument indices is the set of element ids that the operation applies to.\\
2681
2682  Example to find maximum runup elevation:\\
2683     z = domain.get_maximum_inundation_elevation()
2684  \end{funcdesc}
2685
2686
2687  \begin{funcdesc}{get\_maximum\_inundation\_location}{indices=None}
2688  Module: \module{shallow\_water.shallow\_water\_domain}
2689
2690  Return location (x,y) of highest elevation where h $>$ 0.\\
2691  Optional argument indices is the set of element ids that the operation applies to.\\
2692
2693  Example to find maximum runup location:\\
2694     x, y = domain.get_maximum_inundation_location()
2695  \end{funcdesc}
2696
2697
2698\section{Queries of SWW model output files}
2699After a model has been run, it is often useful to extract various information from the sww
2700output file (see Section \ref{sec:sww format}). This is typically more convenient than using the
2701diagnostics described in Section \ref{sec:diagnostics} which rely on the model running - something
2702that can be very time consuming. The sww files are easy and quick to read and offer much information
2703about the model results such as runup heights, time histories of selected quantities,
2704flow through cross sections and much more.
2705
2706\begin{funcdesc}{get\_maximum\_inundation\_elevation}{filename, polygon=None,
2707    time_interval=None, verbose=False}
2708  Module: \module{shallow\_water.data\_manager}
2709
2710  Return highest elevation where depth is positive ($h > 0$)
2711
2712  Example to find maximum runup elevation:\\
2713  max_runup = get_maximum_inundation_elevation(filename,
2714  polygon=None,
2715  time_interval=None,
2716  verbose=False)
2717
2718
2719  filename is a NetCDF sww file containing ANUGA model output.
2720  Optional arguments polygon and time_interval restricts the maximum runup calculation
2721  to a points that lie within the specified polygon and time interval.
2722
2723  If no inundation is found within polygon and time_interval the return value
2724  is None signifying "No Runup" or "Everything is dry".
2725
2726  See doc string for general function get_maximum_inundation_data for details.
2727\end{funcdesc}
2728
2729
2730\begin{funcdesc}{get\_maximum\_inundation\_location}{filename, polygon=None,
2731    time_interval=None, verbose=False}
2732  Module: \module{shallow\_water.data\_manager}
2733
2734  Return location (x,y) of highest elevation where depth is positive ($h > 0$)
2735
2736  Example to find maximum runup location:\\
2737  max_runup_location = get_maximum_inundation_location(filename,
2738  polygon=None,
2739  time_interval=None,
2740  verbose=False)
2741
2742
2743  filename is a NetCDF sww file containing ANUGA model output.
2744  Optional arguments polygon and time_interval restricts the maximum runup calculation
2745  to a points that lie within the specified polygon and time interval.
2746
2747  If no inundation is found within polygon and time_interval the return value
2748  is None signifying "No Runup" or "Everything is dry".
2749
2750  See doc string for general function get_maximum_inundation_data for details.
2751\end{funcdesc}
2752
2753
2754\begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report = None, reportname = None,
2755plot_quantity = None, generate_fig = False, surface = None, time_min = None, time_max = None, time_thinning = 1,
2756time_unit = None, title_on = None, use_cache = False, verbose = False}
2757
2758  Module: \module{anuga.abstract\_2d\_finite\_volumes.util}
2759
2760  Return csv files for the location in the \code{gauge_filename} and can also return plots of them
2761
2762  See doc string for general function sww2timeseries for details.
2763
2764\end{funcdesc}
2765
2766
2767\begin{funcdesc}{get\_flow\_through\_cross\_section}{filename, cross\_section, verbose=False}
2768  Module: \module{shallow\_water.data\_manager}
2769
2770  Obtain flow $[m^2]$ perpendicular to specified cross section.
2771
2772  Inputs:
2773  \begin{itemize} 
2774        \item filename: Name of sww file containing ANUGA model output.
2775        \item polyline: Representation of desired cross section - it may contain multiple
2776          sections allowing for complex shapes. Assume absolute UTM coordinates.
2777  \end{itemize} 
2778
2779  Output:
2780  \begin{itemize}
2781    \item time: All stored times in sww file
2782    \item Q: Hydrograph of total flow across given segments for all stored times.
2783  \end{itemize} 
2784 
2785  The normal flow is computed for each triangle intersected by the polyline and
2786  added up.  Multiple segments at different angles are specified the normal flows
2787  may partially cancel each other.
2788 
2789  Example to find flow through cross section:
2790 
2791  \begin{verbatim} 
2792  cross_section = [[x, 0], [x, width]]
2793  time, Q = get_flow_through_cross_section(filename,
2794                                           cross_section,
2795                                           verbose=False)
2796  \end{verbatim} 
2797
2798
2799  See doc string for general function get_maximum_inundation_data for details.
2800 
2801\end{funcdesc}
2802
2803
2804
2805\section{Other}
2806
2807  \begin{funcdesc}{domain.create\_quantity\_from\_expression}{string}
2808
2809  Handy for creating derived quantities on-the-fly as for example
2810  \begin{verbatim}
2811  Depth = domain.create_quantity_from_expression('stage-elevation')
2812
2813  exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5')
2814  Absolute_momentum = domain.create_quantity_from_expression(exp)
2815  \end{verbatim}
2816
2817  %See also \file{Analytical\_solution\_circular\_hydraulic\_jump.py} for an example of use.
2818  \end{funcdesc}
2819
2820
2821
2822
2823
2824%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2825%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2826
2827\chapter{\anuga System Architecture}
2828
2829
2830\section{File Formats}
2831\label{sec:file formats}
2832
2833\anuga makes use of a number of different file formats. The
2834following table lists all these formats, which are described in more
2835detail in the paragraphs below.
2836
2837\bigskip
2838
2839\begin{center}
2840
2841\begin{tabular}{|ll|}  \hline
2842
2843\textbf{Extension} & \textbf{Description} \\
2844\hline\hline
2845
2846\code{.sww} & NetCDF format for storing model output
2847\code{f(t,x,y)}\\
2848
2849\code{.tms} & NetCDF format for storing time series \code{f(t)}\\
2850
2851\code{.csv/.txt} & ASCII format called points csv for storing
2852arbitrary points and associated attributes\\
2853
2854\code{.pts} & NetCDF format for storing arbitrary points and
2855associated attributes\\
2856
2857\code{.asc} & ASCII format of regular DEMs as output from ArcView\\
2858
2859\code{.prj} & Associated ArcView file giving more metadata for
2860\code{.asc} format\\
2861
2862\code{.ers} & ERMapper header format of regular DEMs for ArcView\\
2863
2864\code{.dem} & NetCDF representation of regular DEM data\\
2865
2866\code{.tsh} & ASCII format for storing meshes and associated
2867boundary and region info\\
2868
2869\code{.msh} & NetCDF format for storing meshes and associated
2870boundary and region info\\
2871
2872\code{.nc} & Native ferret NetCDF format\\
2873
2874\code{.geo} & Houdinis ASCII geometry format (?) \\  \par \hline
2875%\caption{File formats used by \anuga}
2876\end{tabular}
2877
2878
2879\end{center}
2880
2881The above table shows the file extensions used to identify the
2882formats of files. However, typically, in referring to a format we
2883capitalise the extension and omit the initial full stop---thus, we
2884refer, for example, to `SWW files' or `PRJ files'.
2885
2886\bigskip
2887
2888A typical dataflow can be described as follows:
2889
2890\subsection{Manually Created Files}
2891
2892\begin{tabular}{ll}
2893ASC, PRJ & Digital elevation models (gridded)\\
2894NC & Model outputs for use as boundary conditions (e.g. from MOST)
2895\end{tabular}
2896
2897\subsection{Automatically Created Files}
2898
2899\begin{tabular}{ll}
2900ASC, PRJ  $\rightarrow$  DEM  $\rightarrow$  PTS & Convert
2901DEMs to native \code{.pts} file\\
2902
2903NC $\rightarrow$ SWW & Convert MOST boundary files to
2904boundary \code{.sww}\\
2905
2906PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\
2907
2908TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using
2909\code{animate}\\
2910
2911TSH + Boundary SWW $\rightarrow$ SWW & Simulation using
2912\code{\anuga}\\
2913
2914Polygonal mesh outline $\rightarrow$ & TSH or MSH
2915\end{tabular}
2916
2917
2918
2919
2920\bigskip
2921
2922\subsection{SWW and TMS Formats}
2923\label{sec:sww format}
2924
2925The SWW and TMS formats are both NetCDF formats, and are of key
2926importance for \anuga.
2927
2928An SWW file is used for storing \anuga output and therefore pertains
2929to a set of points and a set of times at which a model is evaluated.
2930It contains, in addition to dimension information, the following
2931variables:
2932
2933\begin{itemize}
2934    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2935    \item \code{elevation}, a Numeric array storing bed-elevations
2936    \item \code{volumes}, a list specifying the points at the vertices of each of the
2937    triangles
2938    % Refer here to the example to be provided in describing the simple example
2939    \item \code{time}, a Numeric array containing times for model
2940    evaluation
2941\end{itemize}
2942
2943
2944The contents of an SWW file may be viewed using the anuga viewer
2945\code{animate}, which creates an on-screen geometric
2946representation. See section \ref{sec:animate} (page
2947\pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more
2948on \code{animate}.
2949
2950Alternatively, there are tools, such as \code{ncdump}, that allow
2951you to convert an NetCDF file into a readable format such as the
2952Class Definition Language (CDL). The following is an excerpt from a
2953CDL representation of the output file \file{runup.sww} generated
2954from running the simple example \file{runup.py} of
2955Chapter \ref{ch:getstarted}:
2956
2957\verbatiminput{examples/bedslopeexcerpt.cdl}
2958
2959The SWW format is used not only for output but also serves as input
2960for functions such as \function{file\_boundary} and
2961\function{file\_function}, described in Chapter \ref{ch:interface}.
2962
2963A TMS file is used to store time series data that is independent of
2964position.
2965
2966
2967\subsection{Mesh File Formats}
2968
2969A mesh file is a file that has a specific format suited to
2970triangular meshes and their outlines. A mesh file can have one of
2971two formats: it can be either a TSH file, which is an ASCII file, or
2972an MSH file, which is a NetCDF file. A mesh file can be generated
2973from the function \function{create\_mesh\_from\_regions} (see
2974Section \ref{sec:meshgeneration}) and used to initialise a domain.
2975
2976A mesh file can define the outline of the mesh---the vertices and
2977line segments that enclose the region in which the mesh is
2978created---and the triangular mesh itself, which is specified by
2979listing the triangles and their vertices, and the segments, which
2980are those sides of the triangles that are associated with boundary
2981conditions.
2982
2983In addition, a mesh file may contain `holes' and/or `regions'. A
2984hole represents an area where no mesh is to be created, while a
2985region is a labelled area used for defining properties of a mesh,
2986such as friction values.  A hole or region is specified by a point
2987and bounded by a number of segments that enclose that point.
2988
2989A mesh file can also contain a georeference, which describes an
2990offset to be applied to $x$ and $y$ values---eg to the vertices.
2991
2992
2993\subsection{Formats for Storing Arbitrary Points and Attributes}
2994
2995
2996A CSV/TXT file is used to store data representing
2997arbitrary numerical attributes associated with a set of points.
2998
2999The format for an CSV/TXT file is:\\
3000%\begin{verbatim}
3001
3002            first line:     \code{[column names]}\\
3003            other lines:  \code{[x value], [y value], [attributes]}\\
3004
3005            for example:\\
3006            \code{x, y, elevation, friction}\\
3007            \code{0.6, 0.7, 4.9, 0.3}\\
3008            \code{1.9, 2.8, 5, 0.3}\\
3009            \code{2.7, 2.4, 5.2, 0.3}
3010
3011        The delimiter is a comma. The first two columns are assumed to
3012        be x, y coordinates.
3013       
3014
3015A PTS file is a NetCDF representation of the data held in an points CSV
3016file. If the data is associated with a set of $N$ points, then the
3017data is stored using an $N \times 2$ Numeric array of float
3018variables for the points and an $N \times 1$ Numeric array for each
3019attribute.
3020
3021%\end{verbatim}
3022
3023\subsection{ArcView Formats}
3024
3025Files of the three formats ASC, PRJ and ERS are all associated with
3026data from ArcView.
3027
3028An ASC file is an ASCII representation of DEM output from ArcView.
3029It contains a header with the following format:
3030
3031\begin{tabular}{l l}
3032\code{ncols}      &   \code{753}\\
3033\code{nrows}      &   \code{766}\\
3034\code{xllcorner}  &   \code{314036.58727982}\\
3035\code{yllcorner}  & \code{6224951.2960092}\\
3036\code{cellsize}   & \code{100}\\
3037\code{NODATA_value} & \code{-9999}
3038\end{tabular}
3039
3040The remainder of the file contains the elevation data for each grid point
3041in the grid defined by the above information.
3042
3043A PRJ file is an ArcView file used in conjunction with an ASC file
3044to represent metadata for a DEM.
3045
3046
3047\subsection{DEM Format}
3048
3049A DEM file is a NetCDF representation of regular DEM data.
3050
3051
3052\subsection{Other Formats}
3053
3054
3055
3056
3057\subsection{Basic File Conversions}
3058\label{sec:basicfileconversions}
3059
3060  \begin{funcdesc}{sww2dem}{basename_in, basename_out = None,
3061            quantity = None,
3062            timestep = None,
3063            reduction = None,
3064            cellsize = 10,
3065            NODATA_value = -9999,
3066            easting_min = None,
3067            easting_max = None,
3068            northing_min = None,
3069            northing_max = None,
3070            expand_search = False,
3071            verbose = False,
3072            origin = None,
3073            datum = 'WGS84',
3074            format = 'ers'}
3075  Module: \module{shallow\_water.data\_manager}
3076
3077  Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or
3078  ERS) of a desired grid size \code{cellsize} in metres.
3079  The easting and northing values are used if the user wished to clip the output
3080  file to a specified rectangular area. The \code{reduction} input refers to a function
3081  to reduce the quantities over all time step of the SWW file, example, maximum.
3082  \end{funcdesc}
3083
3084
3085  \begin{funcdesc}{dem2pts}{basename_in, basename_out=None,
3086            easting_min=None, easting_max=None,
3087            northing_min=None, northing_max=None,
3088            use_cache=False, verbose=False}
3089  Module: \module{shallow\_water.data\_manager}
3090
3091  Takes DEM data (a NetCDF file representation of data from a regular Digital
3092  Elevation Model) and converts it to PTS format.
3093  \end{funcdesc}
3094
3095
3096
3097%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3098%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3099
3100\chapter{\anuga mathematical background}
3101\label{cd:mathematical background}
3102
3103\section{Introduction}
3104
3105This chapter outlines the mathematics underpinning \anuga.
3106
3107
3108
3109\section{Model}
3110\label{sec:model}
3111
3112The shallow water wave equations are a system of differential
3113conservation equations which describe the flow of a thin layer of
3114fluid over terrain. The form of the equations are:
3115\[
3116\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
3117x}+\frac{\partial \GG}{\partial y}=\SSS
3118\]
3119where $\UU=\left[ {{\begin{array}{*{20}c}
3120 h & {uh} & {vh} \\
3121\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
3122$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
3123entering the system are bed elevation $z$ and stage (absolute water
3124level) $w$, where the relation $w = z + h$ holds true at all times.
3125The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
3126by
3127\[
3128\EE=\left[ {{\begin{array}{*{20}c}
3129 {uh} \hfill \\
3130 {u^2h+gh^2/2} \hfill \\
3131 {uvh} \hfill \\
3132\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
3133 {vh} \hfill \\
3134 {vuh} \hfill \\
3135 {v^2h+gh^2/2} \hfill \\
3136\end{array} }} \right]
3137\]
3138and the source term (which includes gravity and friction) is given
3139by
3140\[
3141\SSS=\left[ {{\begin{array}{*{20}c}
3142 0 \hfill \\
3143 -{gh(z_{x} + S_{fx} )} \hfill \\
3144 -{gh(z_{y} + S_{fy} )} \hfill \\
3145\end{array} }} \right]
3146\]
3147where $S_f$ is the bed friction. The friction term is modelled using
3148Manning's resistance law
3149\[
3150S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
3151=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
3152\]
3153in which $\eta$ is the Manning resistance coefficient.
3154
3155As demonstrated in our papers, \cite{ZR1999,nielsen2005} these
3156equations provide an excellent model of flows associated with
3157inundation such as dam breaks and tsunamis.
3158
3159\section{Finite Volume Method}
3160\label{sec:fvm}
3161
3162We use a finite-volume method for solving the shallow water wave
3163equations \cite{ZR1999}. The study area is represented by a mesh of
3164triangular cells as in Figure~\ref{fig:mesh} in which the conserved
3165quantities of  water depth $h$, and horizontal momentum $(uh, vh)$,
3166in each volume are to be determined. The size of the triangles may
3167be varied within the mesh to allow greater resolution in regions of
3168particular interest.
3169
3170\begin{figure}
3171\begin{center}
3172\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five}
3173\caption{Triangular mesh used in our finite volume method. Conserved
3174quantities $h$, $uh$ and $vh$ are associated with the centroid of
3175each triangular cell.} \label{fig:mesh}
3176\end{center}
3177\end{figure}
3178
3179The equations constituting the finite-volume method are obtained by
3180integrating the differential conservation equations over each
3181triangular cell of the mesh. Introducing some notation we use $i$ to
3182refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the
3183set of indices referring to the cells neighbouring the $i$th cell.
3184Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is
3185the length of the edge between the $i$th and $j$th cells.
3186
3187By applying the divergence theorem we obtain for each volume an
3188equation which describes the rate of change of the average of the
3189conserved quantities within each cell, in terms of the fluxes across
3190the edges of the cells and the effect of the source terms. In
3191particular, rate equations associated with each cell have the form
3192$$
3193 \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i
3194$$
3195where
3196\begin{itemize}
3197\item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell,
3198\item $\SSS_i$ is the source term associated with the $i$th cell,
3199and
3200\item $\HH_{ij}$ is the outward normal flux of
3201material across the \textit{ij}th edge.
3202\end{itemize}
3203
3204
3205%\item $l_{ij}$ is the length of the edge between the $i$th and $j$th
3206%cells
3207%\item $m_{ij}$ is the midpoint of
3208%the \textit{ij}th edge,
3209%\item
3210%$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing
3211%normal along the \textit{ij}th edge, and The
3212
3213The flux $\HH_{ij}$ is evaluated using a numerical flux function
3214$\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow
3215water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$
3216$$
3217H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 .
3218$$
3219
3220Then
3221$$
3222\HH_{ij}  = \HH(\UU_i(m_{ij}),
3223\UU_j(m_{ij}); \mathbf{n}_{ij})
3224$$
3225where $m_{ij}$ is the midpoint of the \textit{ij}th edge and
3226$\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the
3227\textit{ij}th edge. The function $\UU_i(x)$ for $x \in
3228T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and
3229neighbouring  cells.
3230
3231We use a second order reconstruction to produce a piece-wise linear
3232function construction of the conserved quantities for  all $x \in
3233T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This
3234function is allowed to be discontinuous across the edges of the
3235cells, but the slope of this function is limited to avoid
3236artificially introduced oscillations.
3237
3238Godunov's method (see \cite{Toro1992}) involves calculating the
3239numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly
3240solving the corresponding one dimensional Riemann problem normal to
3241the edge. We use the central-upwind scheme of \cite{KurNP2001} to
3242calculate an approximation of the flux across each edge.
3243
3244\begin{figure}
3245\begin{center}
3246\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct}
3247\caption{From the values of the conserved quantities at the centroid
3248of the cell and its neighbouring cells, a discontinuous piecewise
3249linear reconstruction of the conserved quantities is obtained.}
3250\label{fig:mesh:reconstruct}
3251\end{center}
3252\end{figure}
3253
3254In the computations presented in this paper we use an explicit Euler
3255time stepping method with variable timestepping adapted to the
3256observed CFL condition.
3257
3258
3259\section{Flux limiting}
3260
3261The shallow water equations are solved numerically using a
3262finite volume method on unstructured triangular grid.
3263The upwind central scheme due to Kurganov and Petrova is used as an
3264approximate Riemann solver for the computation of inviscid flux functions.
3265This makes it possible to handle discontinuous solutions.
3266
3267To alleviate the problems associated with numerical instabilities due to
3268small water depths near a wet/dry boundary we employ a new flux limiter that
3269ensures that unphysical fluxes are never encounted.
3270
3271
3272Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction,
3273$w$ the absolute water level (stage) and
3274$z$ the bed elevation. The latter are assumed to be relative to the
3275same height datum.
3276The conserved quantities tracked by ANUGA are momentum in the
3277$x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$)
3278and depth ($h = w-z$).
3279
3280The flux calculation requires access to the velocity vector $(u, v)$
3281where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively.
3282In the presence of very small water depths, these calculations become
3283numerically unreliable and will typically cause unphysical speeds.
3284
3285We have employed a flux limiter which replaces the calculations above with
3286the limited approximations.
3287\begin{equation}
3288  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
3289\end{equation}
3290where $h_0$ is a regularisation parameter that controls the minimal
3291magnitude of the denominator. Taking the limits we have for $\hat{u}$
3292\[
3293  \lim_{h \rightarrow 0} \hat{u} =
3294  \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0
3295\]
3296and
3297\[
3298  \lim_{h \rightarrow \infty} \hat{u} =
3299  \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u
3300\]
3301with similar results for $\hat{v}$.
3302
3303The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator)
3304\[
3305  1 - h_0/h^2 = 0
3306\]
3307or
3308\[
3309  h_0 = h^2
3310\]
3311
3312
3313ANUGA has a global parameter $H_0$ that controls the minimal depth which
3314is considered in the various equations. This parameter is typically set to
3315$10^{-3}$. Setting
3316\[
3317  h_0 = H_0^2
3318\]
3319provides a reasonable balance between accurracy and stability. In fact,
3320setting $h=H_0$ will scale the predicted speed by a factor of $0.5$:
3321\[
3322  \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \frac{\mu}{2 H_0}
3323\]
3324In general, for multiples of the minimal depth $N H_0$ one obtains
3325\[
3326  \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
3327  \frac{\mu}{H_0 (1 + 1/N^2)}
3328\]
3329which converges quadratically to the true value with the multiple N.
3330
3331
3332%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.
3333
3334
3335
3336
3337
3338\section{Slope limiting}
3339A 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.
3340
3341However 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.
3342
3343
3344Let $w, z, h$  be the stage, bed elevation and depth at the centroid and
3345let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$.
3346Define the minimal depth across all vertices as $\hmin$ as
3347\[
3348  \hmin = \min_i h_i
3349\]
3350
3351Let $\tilde{w_i}$ be the stage obtained from a gradient limiter
3352limiting on stage only. The corresponding depth is then defined as
3353\[
3354  \tilde{h_i} = \tilde{w_i} - z_i
3355\]
3356We would use this limiter in deep water which we will define (somewhat boldly)
3357as
3358\[
3359  \hmin \ge \epsilon
3360\]
3361
3362
3363Similarly, let $\bar{w_i}$ be the stage obtained from a gradient
3364limiter limiting on depth respecting the bed slope.
3365The corresponding depth is defined as
3366\[
3367  \bar{h_i} = \bar{w_i} - z_i
3368\]
3369
3370
3371We introduce the concept of a balanced stage $w_i$ which is obtained as
3372the linear combination
3373
3374\[
3375  w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i}
3376\]
3377or
3378\[
3379  w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i}
3380\]
3381where $\alpha \in [0, 1]$.
3382
3383Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope
3384is ignored we have immediately that
3385\[
3386  \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0
3387\]
3388%where the maximal bed elevation range $dz$ is defined as
3389%\[
3390%  dz = \max_i |z_i - z|
3391%\]
3392
3393If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that
3394no negative depths occur. Formally, we will require that
3395\[
3396  \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i
3397\]
3398or
3399\begin{equation}
3400  \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i
3401  \label{eq:limiter bound}
3402\end{equation}
3403
3404There are two cases:
3405\begin{enumerate}
3406  \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage)
3407  vertex is at least as far away from the bed than the shallow water
3408  (limited using depth). In this case we won't need any contribution from
3409  $\bar{h_i}$ and can accept any $\alpha$.
3410
3411  E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to
3412  \[
3413    \tilde{h_i} > \epsilon
3414  \]
3415  whereas $\alpha=0$ yields
3416  \[
3417    \bar{h_i} > \epsilon
3418  \]
3419  all well and good.
3420  \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is
3421  closer to the bed than the shallow water vertex or even below the bed.
3422  In this case we need to find an $\alpha$ that will ensure a positive depth.
3423  Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one
3424  obtains the bound
3425  \[
3426    \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i
3427  \]
3428\end{enumerate}
3429
3430Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one
3431arrives at the definition
3432\[
3433  \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}}
3434\]
3435which will guarantee that no vertex 'cuts' through the bed. Finally, should
3436$\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting
3437$\alpha=0$ and similarly capping $\alpha$ at 1 just in case.
3438
3439%Furthermore,
3440%dropping the $\epsilon$ ensures that alpha is always positive and also
3441%provides a numerical safety {??)
3442
3443
3444
3445
3446
3447%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3448%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3449
3450\chapter{Basic \anuga Assumptions}
3451
3452
3453Physical model time cannot be earlier than 1 Jan 1970 00:00:00.
3454If one wished to recreate scenarios prior to that date it must be done
3455using some relative time (e.g. 0).
3456
3457
3458All spatial data relates to the WGS84 datum (or GDA94) and has been
3459projected into UTM with false easting of 500000 and false northing of
34601000000 on the southern hemisphere (0 on the northern).
3461
3462It is assumed that all computations take place within one UTM zone and
3463all locations must consequently be specified in Cartesian coordinates
3464(eastings, northings) or (x,y) where the unit is metres.
3465
3466DEMs, meshes and boundary conditions can have different origins within
3467one UTM zone. However, the computation will use that of the mesh for
3468numerical stability.
3469
3470When generating a mesh it is assumed that polygons do not cross.
3471Having polygons tht cross can cause the mesh generation to fail or bad
3472meshes being produced.
3473
3474
3475%OLD
3476%The dataflow is: (See data_manager.py and from scenarios)
3477%
3478%
3479%Simulation scenarios
3480%--------------------%
3481%%
3482%
3483%Sub directories contain scrips and derived files for each simulation.
3484%The directory ../source_data contains large source files such as
3485%DEMs provided externally as well as MOST tsunami simulations to be used
3486%as boundary conditions.
3487%
3488%Manual steps are:
3489%  Creation of DEMs from argcview (.asc + .prj)
3490%  Creation of mesh from pmesh (.tsh)
3491%  Creation of tsunami simulations from MOST (.nc)
3492%%
3493%
3494%Typical scripted steps are%
3495%
3496%  prepare_dem.py:  Convert asc and prj files supplied by arcview to
3497%                   native dem and pts formats%
3498%
3499%  prepare_pts.py: Convert netcdf output from MOST to an sww file suitable
3500%                  as boundary condition%
3501%
3502%  prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares
3503%                   smoothing. The outputs are tsh files with elevation data.%
3504%
3505%  run_simulation.py: Use the above together with various parameters to
3506%                     run inundation simulation.
3507
3508
3509%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3510%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3511
3512\appendix
3513
3514\chapter{Supporting Tools}
3515\label{ch:supportingtools}
3516
3517This section describes a number of supporting tools, supplied with \anuga, that offer a
3518variety of types of functionality and enhance the basic capabilities of \anuga.
3519
3520\section{caching}
3521\label{sec:caching}
3522
3523The \code{cache} function is used to provide supervised caching of function
3524results. A Python function call of the form
3525
3526      {\small \begin{verbatim}
3527      result = func(arg1,...,argn)
3528      \end{verbatim}}
3529
3530  can be replaced by
3531
3532      {\small \begin{verbatim}
3533      from caching import cache
3534      result = cache(func,(arg1,...,argn))
3535      \end{verbatim}}
3536
3537  which returns the same output but reuses cached
3538  results if the function has been computed previously in the same context.
3539  \code{result} and the arguments can be simple types, tuples, list, dictionaries or
3540  objects, but not unhashable types such as functions or open file objects.
3541  The function \code{func} may be a member function of an object or a module.
3542
3543  This type of caching is particularly useful for computationally intensive
3544  functions with few frequently used combinations of input arguments. Note that
3545  if the inputs or output are very large caching may not save time because
3546  disc access may dominate the execution time.
3547
3548  If the function definition changes after a result has been cached, this will be
3549  detected by examining the functions \code{bytecode (co\_code, co\_consts,
3550  func\_defaults, co\_argcount)} and the function will be recomputed.
3551  However, caching will not detect changes in modules used by \code{func}.
3552  In this case cache must be cleared manually.
3553
3554  Options are set by means of the function \code{set\_option(key, value)},
3555  where \code{key} is a key associated with a
3556  Python dictionary \code{options}. This dictionary stores settings such as the name of
3557  the directory used, the maximum
3558  number of cached files allowed, and so on.
3559
3560  The \code{cache} function allows the user also to specify a list of dependent files. If any of these
3561  have been changed, the function is recomputed and the results stored again.
3562
3563  %Other features include support for compression and a capability to \ldots
3564
3565
3566   \textbf{USAGE:} \nopagebreak
3567
3568    {\small \begin{verbatim}
3569    result = cache(func, args, kwargs, dependencies, cachedir, verbose,
3570                   compression, evaluate, test, return_filename)
3571    \end{verbatim}}
3572
3573
3574\section{ANUGA viewer - animate}
3575\label{sec:animate}
3576 The output generated by \anuga may be viewed by
3577means of the visualisation tool \code{animate}, which takes the
3578\code{SWW} file output by \anuga and creates a visual representation
3579of the data. Examples may be seen in Figures \ref{fig:runupstart}
3580and \ref{fig:runup2}. To view an \code{SWW} file with
3581\code{animate} in the Windows environment, you can simply drag the
3582icon representing the file over an icon on the desktop for the
3583\code{animate} executable file (or a shortcut to it), or set up a
3584file association to make files with the extension \code{.sww} open
3585with \code{animate}. Alternatively, you can operate \code{animate}
3586from the command line, in both Windows and Linux environments.
3587
3588On successful operation, you will see an interactive moving-picture
3589display. You can use keys and the mouse to slow down, speed up or
3590stop the display, change the viewing position or carry out a number
3591of other simple operations. Help is also displayed when you press
3592the \code{h} key.
3593
3594The main keys operating the interactive screen are:\\
3595
3596\begin{center}
3597\begin{tabular}{|ll|}   \hline
3598
3599\code{w} & toggle wireframe \\
3600
3601space bar & start/stop\\
3602
3603up/down arrows & increase/decrease speed\\
3604
3605left/right arrows & direction in time \emph{(when running)}\\
3606& step through simulation \emph{(when stopped)}\\
3607
3608left mouse button & rotate\\
3609
3610middle mouse button & pan\\
3611
3612right mouse button & zoom\\  \hline
3613
3614\end{tabular}
3615\end{center}
3616
3617\vfill
3618
3619The following table describes how to operate animate from the command line:
3620
3621Usage: \code{animate [options] swwfile \ldots}\\  \nopagebreak
3622Options:\\  \nopagebreak
3623\begin{tabular}{ll}
3624  \code{--display <type>} & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\
3625                                    & \code{HEAD\_MOUNTED\_DISPLAY}\\
3626  \code{--rgba} & Request a RGBA colour buffer visual\\
3627  \code{--stencil} & Request a stencil buffer visual\\
3628  \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\
3629                                    & overridden by environmental variable\\
3630  \code{--stereo <mode>} & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\
3631                                    & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\
3632                                     & \code{ON | OFF} \\
3633  \code{-alphamax <float 0-1>} & Maximum transparency clamp value\\
3634  \code{-alphamin <float 0-1>} & Transparency value at \code{hmin}\\
3635\end{tabular}
3636
3637\begin{tabular}{ll}
3638  \code{-cullangle <float angle 0-90>} & Cull triangles steeper than this value\\
3639  \code{-help} & Display this information\\
3640  \code{-hmax <float>} & Height above which transparency is set to
3641                                     \code{alphamax}\\
3642\end{tabular}
3643
3644\begin{tabular}{ll}
3645
3646  \code{-hmin <float>} & Height below which transparency is set to
3647                                     zero\\
3648\end{tabular}
3649
3650\begin{tabular}{ll}
3651  \code{-lightpos <float>,<float>,<float>} & $x,y,z$ of bedslope directional light ($z$ is
3652                                     up, default is overhead)\\
3653\end{tabular}
3654
3655\begin{tabular}{ll}
3656  \code{-loop}  & Repeated (looped) playback of \code{.swm} files\\
3657
3658\end{tabular}
3659
3660\begin{tabular}{ll}
3661  \code{-movie <dirname>} & Save numbered images to named directory and
3662                                     quit\\
3663
3664  \code{-nosky} & Omit background sky\\
3665
3666
3667  \code{-scale <float>} & Vertical scale factor\\
3668  \code{-texture <file>} & Image to use for bedslope topography\\
3669  \code{-tps <rate>} & Timesteps per second\\
3670  \code{-version} & Revision number and creation (not compile)
3671                                     date\\
3672\end{tabular}
3673
3674\section{utilities/polygons}
3675
3676  \declaremodule{standard}{utilities.polygon}
3677  \refmodindex{utilities.polygon}
3678
3679  \begin{classdesc}{Polygon\_function}{regions, default=0.0, geo_reference=None}
3680  Module: \code{utilities.polygon}
3681
3682  Creates a callable object that returns one of a specified list of values when
3683  evaluated at a point \code{x, y}, depending on which polygon, from a specified list of polygons, the
3684  point belongs to. The parameter \code{regions} is a list of pairs
3685  \code{(P, v)}, where each \code{P} is a polygon and each \code{v}
3686  is either a constant value or a function of coordinates \code{x}
3687  and \code{y}, specifying the return value for a point inside \code{P}. The
3688  optional parameter \code{default} may be used to specify a value
3689  (or a function)
3690  for a point not lying inside any of the specified polygons. When a
3691  point lies in more than one polygon, the return value is taken to
3692  be the value for whichever of these polygon appears later in the
3693  list.
3694  %FIXME (Howard): CAN x, y BE VECTORS?
3695  The optional parameter geo\_reference refers to the status of points
3696  that are passed into the function. Typically they will be relative to
3697  some origin. In ANUGA, a typical call will take the form:
3698  {\small \begin{verbatim}
3699     set_quantity('elevation',
3700                  Polygon_function([(P1, v1), (P2, v2)],
3701                                   default=v3,
3702                                   geo_reference=domain.geo_reference))
3703  \end{verbatim}}
3704 
3705
3706  \end{classdesc}
3707
3708  \begin{funcdesc}{read\_polygon}{filename}
3709  Module: \code{utilities.polygon}
3710
3711  Reads the specified file and returns a polygon. Each
3712  line of the file must contain exactly two numbers, separated by a comma, which are interpreted
3713  as coordinates of one vertex of the polygon.
3714  \end{funcdesc}
3715
3716  \begin{funcdesc}{populate\_polygon}{polygon, number_of_points, seed = None, exclude = None}
3717  Module: \code{utilities.polygon}
3718
3719  Populates the interior of the specified polygon with the specified number of points,
3720  selected by means of a uniform distribution function.
3721  \end{funcdesc}
3722
3723  \begin{funcdesc}{point\_in\_polygon}{polygon, delta=1e-8}
3724  Module: \code{utilities.polygon}
3725
3726  Returns a point inside the specified polygon and close to the edge. The distance between
3727  the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the
3728  second argument \code{delta}, which is taken as $10^{-8}$ by default.
3729  \end{funcdesc}
3730
3731  \begin{funcdesc}{inside\_polygon}{points, polygon, closed = True, verbose = False}
3732  Module: \code{utilities.polygon}
3733
3734  Used to test whether the members of a list of points
3735  are inside the specified polygon. Returns a Numeric
3736  array comprising the indices of the points in the list that lie inside the polygon.
3737  (If none of the points are inside, returns \code{zeros((0,), 'l')}.)
3738  Points on the edges of the polygon are regarded as inside if
3739  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3740  \end{funcdesc}
3741
3742  \begin{funcdesc}{outside\_polygon}{points, polygon, closed = True, verbose = False}
3743  Module: \code{utilities.polygon}
3744
3745  Exactly like \code{inside\_polygon}, but with the words `inside' and `outside' interchanged.
3746  \end{funcdesc}
3747
3748  \begin{funcdesc}{is\_inside\_polygon}{point, polygon, closed=True, verbose=False}
3749  Module: \code{utilities.polygon}
3750
3751  Returns \code{True} if \code{point} is inside \code{polygon} or
3752  \code{False} otherwise. Points on the edges of the polygon are regarded as inside if
3753  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3754  \end{funcdesc}
3755
3756  \begin{funcdesc}{is\_outside\_polygon}{point, polygon, closed=True, verbose=False}
3757  Module: \code{utilities.polygon}
3758
3759  Exactly like \code{is\_outside\_polygon}, but with the words `inside' and `outside' interchanged.
3760  \end{funcdesc}
3761
3762  \begin{funcdesc}{point\_on\_line}{x, y, x0, y0, x1, y1}
3763  Module: \code{utilities.polygon}
3764
3765  Returns \code{True} or \code{False}, depending on whether the point with coordinates
3766  \code{x, y} is on the line passing through the points with coordinates \code{x0, y0}
3767  and \code{x1, y1} (extended if necessary at either end).
3768  \end{funcdesc}
3769
3770  \begin{funcdesc}{separate\_points\_by\_polygon}{points, polygon, closed = True, verbose = False}
3771    \indexedcode{separate\_points\_by\_polygon}
3772  Module: \code{utilities.polygon}
3773
3774  \end{funcdesc}
3775
3776  \begin{funcdesc}{polygon\_area}{polygon}
3777  Module: \code{utilities.polygon}
3778
3779  Returns area of arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html)
3780  \end{funcdesc}
3781
3782  \begin{funcdesc}{plot\_polygons}{polygons, style, figname, verbose = False}
3783    Module: \code{utilities.polygon}
3784 
3785    Plots each polygon contained in input polygon list, e.g.
3786   \code{polygons = [poly1, poly2, poly3]} where \code{poly1 = [[x11,y11],[x12,y12],[x13,y13]]}
3787   etc.  Each polygon can be closed for plotting purposes by assigning the style type to each
3788   polygon in the list, e.g. \code{style = ['line','line','line']}. The default will be a line
3789   type when \code{style = None}.
3790   The subsequent plot will be saved to \code{figname} or defaulted to \code{test_image.png}.
3791    The function returns a list containing the minimum and maximum of \code{x} and \code{y},
3792    i.e. \code{[x_{min}, x_{max}, y_{min}, y_{max}]}.
3793  \end{funcdesc}
3794
3795\section{coordinate\_transforms}
3796
3797\section{geospatial\_data}
3798\label{sec:geospatial}
3799
3800This describes a class that represents arbitrary point data in UTM
3801coordinates along with named attribute values.
3802
3803%FIXME (Ole): This gives a LaTeX error
3804%\declaremodule{standard}{geospatial_data}
3805%\refmodindex{geospatial_data}
3806
3807
3808
3809\begin{classdesc}{Geospatial\_data}
3810  {data_points = None,
3811    attributes = None,
3812    geo_reference = None,
3813    default_attribute_name = None,
3814    file_name = None}
3815Module: \code{geospatial\_data}
3816
3817This class is used to store a set of data points and associated
3818attributes, allowing these to be manipulated by methods defined for
3819the class.
3820
3821The data points are specified either by reading them from a NetCDF
3822or CSV file, identified through the parameter \code{file\_name}, or
3823by providing their \code{x}- and \code{y}-coordinates in metres,
3824either as a sequence of 2-tuples of floats or as an $M \times 2$
3825Numeric array of floats, where $M$ is the number of points.
3826Coordinates are interpreted relative to the origin specified by the
3827object \code{geo\_reference}, which contains data indicating the UTM
3828zone, easting and northing. If \code{geo\_reference} is not
3829specified, a default is used.
3830
3831Attributes are specified through the parameter \code{attributes},
3832set either to a list or array of length $M$ or to a dictionary whose
3833keys are the attribute names and whose values are lists or arrays of
3834length $M$. One of the attributes may be specified as the default
3835attribute, by assigning its name to \code{default\_attribute\_name}.
3836If no value is specified, the default attribute is taken to be the
3837first one.
3838\end{classdesc}
3839
3840
3841\begin{methoddesc}{import\_points\_file}{delimiter = None, verbose = False}
3842
3843\end{methoddesc}
3844
3845
3846\begin{methoddesc}{export\_points\_file}{ofile, absolute=False}
3847
3848\end{methoddesc}
3849
3850
3851\begin{methoddesc}{get\_data\_points}{absolute = True, as\_lat\_long =
3852    False}
3853    If \code{as\_lat\_long} is\code{True} the point information
3854    returned will be in Latitudes and Longitudes.
3855
3856\end{methoddesc}
3857
3858
3859\begin{methoddesc}{set\_attributes}{attributes}
3860
3861\end{methoddesc}
3862
3863
3864\begin{methoddesc}{get\_attributes}{attribute_name = None}
3865
3866\end{methoddesc}
3867
3868
3869\begin{methoddesc}{get\_all\_attributes}{}
3870
3871\end{methoddesc}
3872
3873
3874\begin{methoddesc}{set\_default\_attribute\_name}{default_attribute_name}
3875
3876\end{methoddesc}
3877
3878
3879\begin{methoddesc}{set\_geo\_reference}{geo_reference}
3880
3881\end{methoddesc}
3882
3883
3884\begin{methoddesc}{add}{}
3885
3886\end{methoddesc}
3887
3888
3889\begin{methoddesc}{clip}{}
3890Clip geospatial data by a polygon
3891
3892Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3893a Geospatial data object and \code{closed}(optional) which determines
3894whether points on boundary should be regarded as belonging to the polygon
3895(\code{closed=True}) or not (\code{closed=False}).
3896Default is \code{closed=True}.
3897
3898Returns new Geospatial data object representing points
3899inside specified polygon.
3900\end{methoddesc}
3901
3902
3903\begin{methoddesc}{clip_outside}{}
3904Clip geospatial data by a polygon
3905
3906Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3907a Geospatial data object and \code{closed}(optional) which determines
3908whether points on boundary should be regarded as belonging to the polygon
3909(\code{closed=True}) or not (\code{closed=False}).
3910Default is \code{closed=True}.
3911
3912Returns new Geospatial data object representing points
3913\emph{out}side specified polygon.
3914\end{methoddesc}
3915
3916\begin{methoddesc}{split}{factor=0.5, seed_num=None, verbose=False}
3917Returns two geospatial_data object, first is the size of the 'factor'
3918smaller the original and the second is the remainder. The two
3919new object are disjoin set of each other.
3920       
3921Points of the two new geospatial_data object are selected RANDOMLY.
3922       
3923Input - the (\code{factor}) which to split the object, if 0.1 then 10% of the
3924together object will be returned
3925       
3926Output - two geospatial_data objects that are disjoint sets of the original
3927\end{methoddesc}
3928
3929\begin{methoddesc}{find_optimal_smoothing_parameter}{data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000,
3930north_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}
3931
3932Removes a small random sample of points from 'data_file'. Creates
3933models from resulting points in 'data_file' with different alpha values from 'alpha_list' and cross validates
3934the predicted value to the previously removed point data. Returns the
3935alpha value which has the smallest covariance.
3936
3937data_file: must not contain points outside the boundaries defined
3938and it either a pts, txt or csv file.
3939   
3940alpha_list: the alpha values to test in a single list
3941   
3942mesh_file: name of the created mesh file or if passed in will read it.
3943NOTE, if there is a mesh file mesh_resolution, north_boundary, south... etc will be ignored.
3944   
3945mesh_resolution: the maximum area size for a triangle
3946   
3947north_boundary... west_boundary: the value of the boundary
3948   
3949plot_name: the name for the plot contain the results
3950   
3951seed_num: the seed to the random number generator
3952   
3953USAGE:
3954convariance_value, alpha = find_optimal_smoothing_parameter(data_file=fileName,
3955                                             alpha_list=[0.0001, 0.01, 1],
3956                                             mesh_file=None,
3957                                             mesh_resolution=3,
3958                                             north_boundary=5,
3959                                             south_boundary=-5,
3960                                             east_boundary=5,
3961                                             west_boundary=-5,
3962                                             plot_name='all_alphas',
3963                                             seed_num=100000,
3964                                             verbose=False)
3965   
3966OUTPUT: returns the minumum normalised covalance calculate AND the
3967alpha that created it. PLUS writes a plot of the results
3968           
3969NOTE: code will not work if the data_file extent is greater than the
3970boundary_polygon or any of the boundaries, eg north_boundary...west_boundary
3971\end{methoddesc}
3972
3973
3974
3975\section{Graphical Mesh Generator GUI}
3976The program \code{graphical\_mesh\_generator.py} in the pmesh module
3977allows the user to set up the mesh of the problem interactively.
3978It can be used to build the outline of a mesh or to visualise a mesh
3979automatically generated.
3980
3981Graphical Mesh Generator will let the user select various modes. The
3982current allowable modes are vertex, segment, hole or region.  The mode
3983describes what sort of object is added or selected in response to
3984mouse clicks.  When changing modes any prior selected objects become
3985deselected.
3986
3987In general the left mouse button will add an object and the right
3988mouse button will select an object.  A selected object can de deleted
3989by pressing the the middle mouse button (scroll bar).
3990
3991\section{alpha\_shape}
3992\emph{Alpha shapes} are used to generate close-fitting boundaries
3993around sets of points. The alpha shape algorithm produces a shape
3994that approximates to the `shape formed by the points'---or the shape
3995that would be seen by viewing the points from a coarse enough
3996resolution. For the simplest types of point sets, the alpha shape
3997reduces to the more precise notion of the convex hull. However, for
3998many sets of points the convex hull does not provide a close fit and
3999the alpha shape usually fits more closely to the original point set,
4000offering a better approximation to the shape being sought.
4001
4002In \anuga, an alpha shape is used to generate a polygonal boundary
4003around a set of points before mesh generation. The algorithm uses a
4004parameter $\alpha$ that can be adjusted to make the resultant shape
4005resemble the shape suggested by intuition more closely. An alpha
4006shape can serve as an initial boundary approximation that the user
4007can adjust as needed.
4008
4009The following paragraphs describe the class used to model an alpha
4010shape and some of the important methods and attributes associated
4011with instances of this class.
4012
4013\begin{classdesc}{Alpha\_Shape}{points, alpha = None}
4014Module: \code{alpha\_shape}
4015
4016To instantiate this class the user supplies the points from which
4017the alpha shape is to be created (in the form of a list of 2-tuples
4018\code{[[x1, y1],[x2, y2]}\ldots\code{]}, assigned to the parameter
4019\code{points}) and, optionally, a value for the parameter
4020\code{alpha}. The alpha shape is then computed and the user can then
4021retrieve details of the boundary through the attributes defined for
4022the class.
4023\end{classdesc}
4024
4025
4026\begin{funcdesc}{alpha\_shape\_via\_files}{point_file, boundary_file, alpha= None}
4027Module: \code{alpha\_shape}
4028
4029This function reads points from the specified point file
4030\code{point\_file}, computes the associated alpha shape (either
4031using the specified value for \code{alpha} or, if no value is
4032specified, automatically setting it to an optimal value) and outputs
4033the boundary to a file named \code{boundary\_file}. This output file
4034lists the coordinates \code{x, y} of each point in the boundary,
4035using one line per point.
4036\end{funcdesc}
4037
4038
4039\begin{methoddesc}{set\_boundary\_type}{self,raw_boundary=True,
4040                          remove_holes=False,
4041                          smooth_indents=False,
4042                          expand_pinch=False,
4043                          boundary_points_fraction=0.2}
4044Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4045
4046This function sets flags that govern the operation of the algorithm
4047that computes the boundary, as follows:
4048
4049\code{raw\_boundary = True} returns raw boundary, i.e. the regular edges of the
4050                alpha shape.\\
4051\code{remove\_holes = True} removes small holes (`small' is defined by
4052\code{boundary\_points\_fraction})\\
4053\code{smooth\_indents = True} removes sharp triangular indents in
4054boundary\\
4055\code{expand\_pinch = True} tests for pinch-off and
4056corrects---preventing a boundary vertex from having more than two edges.
4057\end{methoddesc}
4058
4059
4060\begin{methoddesc}{get\_boundary}{}
4061Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4062
4063Returns a list of tuples representing the boundary of the alpha
4064shape. Each tuple represents a segment in the boundary by providing
4065the indices of its two endpoints.
4066\end{methoddesc}
4067
4068
4069\begin{methoddesc}{write\_boundary}{file_name}
4070Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4071
4072Writes the list of 2-tuples returned by \code{get\_boundary} to the
4073file \code{file\_name}, using one line per tuple.
4074\end{methoddesc}
4075
4076\section{Numerical Tools}
4077
4078The following table describes some useful numerical functions that
4079may be found in the module \module{utilities.numerical\_tools}:
4080
4081\begin{tabular}{|p{8cm} p{8cm}|}  \hline
4082\code{angle(v1, v2=None)} & Angle between two-dimensional vectors
4083\code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if
4084\code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\
4085
4086\code{normal\_vector(v)} & Normal vector to \code{v}.\\
4087
4088\code{mean(x)} & Mean value of a vector \code{x}.\\
4089
4090\code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}.
4091If \code{y} is \code{None}, returns \code{cov(x, x)}.\\
4092
4093\code{err(x, y=0, n=2, relative=True)} & Relative error of
4094$\parallel$\code{x}$-$\code{y}$\parallel$ to
4095$\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm
4096if \code{n} = \code{None}). If denominator evaluates to zero or if
4097\code{y}
4098is omitted or if \code{relative = False}, absolute error is returned.\\
4099
4100\code{norm(x)} & 2-norm of \code{x}.\\
4101
4102\code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If
4103\code{y} is \code{None} returns autocorrelation of \code{x}.\\
4104
4105\code{ensure\_numeric(A, typecode = None)} & Returns a Numeric array
4106for any sequence \code{A}. If \code{A} is already a Numeric array it
4107will be returned unaltered. Otherwise, an attempt is made to convert
4108it to a Numeric array. (Needed because \code{array(A)} can
4109cause memory overflow.)\\
4110
4111\code{histogram(a, bins, relative=False)} & Standard histogram. If
4112\code{relative} is \code{True}, values will be normalised against
4113the total and thus represent frequencies rather than counts.\\
4114
4115\code{create\_bins(data, number\_of\_bins = None)} & Safely create
4116bins for use with histogram. If \code{data} contains only one point
4117or is constant, one bin will be created. If \code{number\_of\_bins}
4118is omitted, 10 bins will be created.\\  \hline
4119
4120\section{Finding the Optimal Alpha Value}
4121
4122The function ????
4123more to come very soon
4124
4125\end{tabular}
4126
4127
4128\chapter{Modules available in \anuga}
4129
4130
4131\section{\module{abstract\_2d\_finite\_volumes.general\_mesh} }
4132\declaremodule[generalmesh]{}{general\_mesh}
4133\label{mod:generalmesh}
4134
4135\section{\module{abstract\_2d\_finite\_volumes.neighbour\_mesh} }
4136\declaremodule[neighbourmesh]{}{neighbour\_mesh}
4137\label{mod:neighbourmesh}
4138
4139\section{\module{abstract\_2d\_finite\_volumes.domain} --- Generic module for 2D triangular domains for finite-volume computations of conservation laws}
4140\declaremodule{}{domain}
4141\label{mod:domain}
4142
4143
4144\section{\module{abstract\_2d\_finite\_volumes.quantity}}
4145\declaremodule{}{quantity}
4146\label{mod:quantity}
4147
4148\begin{verbatim}
4149Class Quantity - Implements values at each triangular element
4150
4151To create:
4152
4153   Quantity(domain, vertex_values)
4154
4155   domain: Associated domain structure. Required.
4156
4157   vertex_values: N x 3 array of values at each vertex for each element.
4158                  Default None
4159
4160   If vertex_values are None Create array of zeros compatible with domain.
4161   Otherwise check that it is compatible with dimenions of domain.
4162   Otherwise raise an exception
4163
4164\end{verbatim}
4165
4166
4167
4168
4169\section{\module{shallow\_water} --- 2D triangular domains for finite-volume
4170computations of the shallow water wave equation. This module contains a specialisation
4171of class Domain from module domain.py consisting of methods specific to the Shallow Water
4172Wave Equation
4173}
4174\declaremodule[shallowwater]{}{shallow\_water}
4175\label{mod:shallowwater}
4176
4177
4178
4179
4180%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4181
4182\chapter{Frequently Asked Questions}
4183
4184
4185\section{General Questions}
4186
4187\subsubsection{What is \anuga?}
4188It is a software package suitable for simulating 2D water flows in
4189complex geometries.
4190
4191\subsubsection{Why is it called \anuga?}
4192The software was developed in collaboration between the
4193Australian National University (ANU) and Geoscience Australia (GA).
4194
4195\subsubsection{How do I obtain a copy of \anuga?}
4196See \url{https://datamining.anu.edu.au/anuga} for all things ANUGA.
4197
4198%\subsubsection{What developments are expected for \anuga in the future?}
4199%This
4200
4201\subsubsection{Are there any published articles about \anuga that I can reference?}
4202See \url{https://datamining.anu.edu.au/anuga} for links.
4203
4204
4205\subsubsection{How do I find out what version of \anuga I am running?}
4206Use the following code snippet
4207\begin{verbatim}
4208from anuga.utilities.system_tools import get_revision_number
4209print get_revision_number()
4210\end{verbatim}
4211This should work both for installations from SourceForge as well as when working off the repository.
4212
4213
4214
4215
4216\section{Modelling Questions}
4217
4218\subsubsection{Which type of problems are \anuga good for?}
4219General 2D waterflows in complex geometries such as
4220dam breaks, flows amoung structurs, coastal inundation etc.
4221
4222\subsubsection{Which type of problems are beyond the scope of \anuga?}
4223See Chapter \ref{ch:limitations}.
4224
4225\subsubsection{Can I start the simulation at an arbitrary time?}
4226Yes, using \code{domain.set\_time()} you can specify an arbitrary
4227starting time. This is for example useful in conjunction with a
4228file\_boundary, which may start hours before anything hits the model
4229boundary. By assigning a later time for the model to start,
4230computational resources aren't wasted.
4231
4232\subsubsection{Can I change values for any quantity during the simulation?}
4233Yes, using \code{domain.set\_quantity()} inside the domain.evolve
4234loop you can change values of any quantity. This is for example
4235useful if you wish to let the system settle for a while before
4236assigning an initial condition. Another example would be changing
4237the values for elevation to model e.g. erosion.
4238
4239\subsubsection{Can I change boundary conditions during the simulation?}
4240Yes - see example on page \pageref{sec:change boundary code} in Section
4241\ref{sec:change boundary}.
4242
4243\subsubsection{How do I access model time during the simulation?}
4244The variable \code{t} in the evolve for loop is the model time.
4245For 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})
4246one would write something like
4247{\small \begin{verbatim}
4248    for t in domain.evolve(yieldstep = 0.2, duration = 40.0):
4249
4250        if Numeric.allclose(t, 15):
4251            print 'Changing boundary to outflow'
4252            domain.set_boundary({'right': Bo})
4253
4254\end{verbatim}}
4255The 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()}.
4256
4257
4258\subsubsection{Why does a file\_function return a list of numbers when evaluated?}
4259Currently, file\_function works by returning values for the conserved
4260quantities \code{stage}, \code{xmomentum} and \code{ymomentum} at a given point in time
4261and space as a triplet. To access e.g.\ \code{stage} one must specify element 0 of the
4262triplet returned by file\_function.
4263
4264\subsubsection{Which diagnostics are available to troubleshoot a simulation?}
4265
4266\subsubsection{How do I use a DEM in my simulation?}
4267You use \code{dem2pts} to convert your DEM to the required .pts format. This .pts file is then called
4268when setting the elevation data to the mesh in \code{domain.set_quantity}
4269
4270\subsubsection{What sort of DEM resolution should I use?}
4271Try and work with the \emph{best} you have available. Onshore DEMs
4272are typically available in 25m, 100m and 250m grids. Note, offshore
4273data is often sparse, or non-existent.
4274
4275\subsubsection{What sort of mesh resolution should I use?}
4276The 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,
4277if 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,
4278you need a fine mesh over regions where the DEM changes rapidly, and other areas of significant interest, such as the coast.
4279If meshes are too coarse, discretisation errors in both stage and momentum may lead to unphysical results. All studies should include sensitivity and convergence studies based on different resolutions.
4280
4281
4282\subsubsection{How do I tag interior polygons?}
4283At the moment create_mesh_from_regions does not allow interior
4284polygons with symbolic tags. If tags are needed, the interior
4285polygons must be created subsequently. For example, given a filename
4286of polygons representing solid walls (in Arc Ungenerate format) can
4287be tagged as such using the code snippet:
4288\begin{verbatim}
4289  # Create mesh outline with tags
4290  mesh = create_mesh_from_regions(bounding_polygon,
4291                                  boundary_tags=boundary_tags)
4292  # Add buildings outlines with tags set to 'wall'. This would typically
4293  # bind to a Reflective boundary
4294  mesh.import_ungenerate_file(buildings_filename, tag='wall')
4295
4296  # Generate and write mesh to file
4297  mesh.generate_mesh(maximum_triangle_area=max_area)
4298  mesh.export_mesh_file(mesh_filename)
4299\end{verbatim}
4300
4301Note that a mesh object is returned from \code{create_mesh_from_regions}
4302when file name is omitted.
4303
4304\subsubsection{How often should I store the output?}
4305This 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
4306to look in detail at the evolution, then you will need to balance your storage requirements and the duration of the simulation.
4307If 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
4308quantities on a mesh with approximately 300000 triangles on a 2 min interval for 5 hours will result in approximately 350Mb SWW file
4309(as for the \file{run\_sydney\_smf.py} example).
4310
4311\subsubsection{How can I set the friction in different areas in the domain?}
4312The model area will typically be estimating the water height and momentum over varying
4313topographies which will have different friction values. One way of assigning
4314different friction values is to create polygons (say \code{poly1, poly2 and poly3}) describing each
4315area and then set the corresponding friction values in the following way
4316
4317\code{domain.set_quantity('friction',Polygon_function([(poly1,f1),(poly2,f2),
4318(poly3,f3))]))}
4319
4320The values of \code{f1,f2} and \code{f3} could be constant or functions
4321as determined by the user.
4322
4323\subsubsection{How can I combine data sets?}
4324
4325A user may have access to a range of different resolution DEMs and raw data points (such
4326as beach profiles, spot heights, single or multi-beam data etc) and will need
4327to combine them to create an overall elevation data set.
4328
4329If there are multiple DEMs, say of 10m and 25m resolution, then the technique is similar to
4330that defined in the Cairns example described earlier, that is
4331
4332{\small \begin{verbatim}
4333convert_dem_from_ascii2netcdf(10m_dem_name, use_cache=True, verbose=True)
4334convert_dem_from_ascii2netcdf(25m_dem_name, use_cache=True, verbose=True)
4335\end{verbatim}}
4336followed by
4337{\small \begin{verbatim}
4338dem2pts(10m_dem_name, use_cache=True, verbose=True)
4339dem2pts(25m_dem_name, use_cache=True, verbose=True)
4340\end{verbatim}}
4341These data sets can now be combined by
4342{\small \begin{verbatim}
4343from anuga.geospatial_data.geospatial_data import *
4344G1 = Geospatial_data(file_name = 10m_dem_name + '.pts')
4345G2 = Geospatial_data(file_name = 25m_dem_name + '.pts')
4346G = G1 + G2
4347G.export_points_file(combined_dem_name + ‘.pts’)
4348\end{verbatim}}
4349this is the basic way of combining data sets, however, the user will need to
4350assess the boundaries of each data set and whether they overlap. For example, consider
4351if the 10m DEM is describing by \code{poly1} and the 25m DEM is described by \code{poly2}
4352with \code{poly1} completely enclosed in \code{poly2} as shown in Figure \ref{fig:polydata}
4353\begin{figure}[hbt]
4354  \centerline{\includegraphics{graphics/polyanddata.jpg}}
4355  \caption{Polygons describing the extent of the 10m and 25m DEM.}
4356  \label{fig:polydata}
4357\end{figure}
4358To combine the data sets, the geospatial addition is updated to
4359{\small \begin{verbatim}
4360G = G1 + G2.clip_outside(Geospatial_data(poly1))
4361\end{verbatim}}
4362For this example, we assume that \code{poly2} is the domain, otherwise an additional dataset
4363would be required for the remainder of the domain.
4364
4365This technique can be expanded to handle point data sets as well. In the case
4366of a bathymetry data set available in text format in an \code{.csv} file, then
4367the geospatial addition is updated to
4368{\small \begin{verbatim}
4369G3 = Geospatial_data(file_name = bathy_data_name + '.csv')
4370G = G1 + G2.clip_outside(Geospatial_data(poly1)) + G3
4371\end{verbatim}}
4372The \code{.csv} file has the data stored as \code{x,y,elevation} with the text \code{elevation}
4373on the first line.
4374
4375The coastline could be included
4376as part of the clipping polygon to separate the offshore and onshore datasets if required.
4377Assume that \code{poly1} crosses the coastline
4378In this case, two new polygons could be created out of \code{poly1} which uses the coastline
4379as the divider. As shown in Figure \ref{fig:polycoast}, \code{poly3} describes the
4380onshore data and \code{poly4} describes the offshore data.
4381\begin{figure}[hbt]
4382  \centerline{\includegraphics{graphics/polyanddata2.jpg}}
4383  \caption{Inclusion of new polygons separating the 10m DEM area into an
4384  onshore (poly3) and offshore (poly4) data set.}
4385  \label{fig:polycoast}
4386\end{figure}
4387Let's include the bathymetry
4388data described above, so to combine the datasets in this case,
4389{\small \begin{verbatim}
4390G = G1.clip(Geospatial_data(poly3)) + G2.clip_outside(Geospatial_data(poly1)) + G3
4391\end{verbatim}}
4392
4393Finally, to fit the elevation data to the mesh, the script is adjusted in this way
4394{\small \begin{verbatim}
4395    domain.set_quantity('elevation',
4396                        filename = combined_dem_name + '.pts',
4397                        use_cache = True,
4398                        verbose = True)
4399\end{verbatim}}
4400\subsection{Boundary Conditions}
4401
4402\subsubsection{How do I create a Dirichlet boundary condition?}
4403
4404A Dirichlet boundary condition sets a constant value for the
4405conserved quantities at the boundaries. A list containing
4406the constant values for stage, xmomentum and ymomentum is constructed
4407and used in the function call, e.g. \code{Dirichlet_boundary([0.2,0.,0.])}
4408
4409\subsubsection{How do I know which boundary tags are available?}
4410The method \code{domain.get\_boundary\_tags()} will return a list of
4411available tags for use with
4412\code{domain.set\_boundary\_condition()}.
4413
4414\subsubsection{What is the difference between file_boundary and field_boundary?}
4415The only difference is field_boundary will allow you to change the level of the stage height when you read in the boundary condition.
4416This is very useful when running different tide heights in the same area as you need only to convert
4417one boundary condition to a SWW file, ideally for tide height of 0 m (saving disk space). Then you can
4418use field_boundary to read this SWW file and change the stage height (tide) on the fly depending on the scenario.
4419
4420
4421
4422
4423\subsection{Analysing Results}
4424
4425\subsubsection{How do I easily plot "tide gauges" timeseries graphs from a SWW file?}
4426
4427There is two ways to do this.
4428
44291) Create csv files from the sww file using \code{anuga.abstract_2d_finite_volumes.util sww2csv_gauges}
4430and then use \code{anuga.abstract_2d_finite_volumes.util csv2timeseries_graphs} to
4431create the plots. This code is newer, has unit tests and might be easier to use. Read doc strings for more information and
4432review section 4.7 of this manual.
4433
4434Or
4435
44362) Use \code{anuga.abstract_2d_finite_volumes.util sww2timeseries} to do the whole thing
4437however this doesn't have a much control on the file name and plots. Plus there is no unit tests yet.
4438
4439Read the doc string for more information.
4440
4441\subsubsection{How do I extract elevation and other quantities from a SWW file?}
4442
4443The function \code{sww2dem} can extract any quantity, or expression using
4444quantities, from a SWW file as used in
4445the Cairns example described earlier. This function is used in \code{ExportResults.py}
4446in the Cairns demo folder where stage, absolute momentum, depth, speed and elevation
4447can be exported from the input sww file. Note that depth, absolute momentum and speed
4448are expressions and stage and elevation are quantities. In addition to extracting a particular
4449quantity or expression, the user can define a region to extract these values by
4450defining the minimum and maximum of both the easting and northing coordinates. The function
4451also calls for a grid resolution, or cell size, to extract these values at. It is
4452recommended to align this resolution with the mesh resolution in the desired region and to not
4453generate a fine grid where the model output cannot support that resolution.
4454
4455 
4456
4457\chapter{Glossary}
4458
4459\begin{tabular}{|lp{10cm}|c|}  \hline
4460%\begin{tabular}{|llll|}  \hline
4461    \emph{Term} & \emph{Definition} & \emph{Page}\\  \hline
4462
4463    \indexedbold{\anuga} & Name of software (joint development between ANU and
4464    GA) & \pageref{def:anuga}\\
4465
4466    \indexedbold{bathymetry} & offshore elevation &\\
4467
4468    \indexedbold{conserved quantity} & conserved (stage, x and y
4469    momentum) & \\
4470
4471%    \indexedbold{domain} & The domain of a function is the set of all input values to the
4472%    function.&\\
4473
4474    \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations,
4475sampled systematically at equally spaced intervals.& \\
4476
4477    \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation
4478 that specifies the values the solution is to take on the boundary of the
4479 domain. & \pageref{def:dirichlet boundary}\\
4480
4481    \indexedbold{edge} & A triangular cell within the computational mesh can be depicted
4482    as a set of vertices joined by lines (the edges). & \\
4483
4484    \indexedbold{elevation} & refers to bathymetry and topography &\\
4485
4486    \indexedbold{evolution} & integration of the shallow water wave equations
4487    over time &\\
4488
4489    \indexedbold{finite volume method} & The method evaluates the terms in the shallow water
4490    wave equation as fluxes at the surfaces of each finite volume. Because the
4491    flux entering a given volume is identical to that leaving the adjacent volume,
4492    these methods are conservative. Another advantage of the finite volume method is
4493    that it is easily formulated to allow for unstructured meshes. The method is used
4494    in many computational fluid dynamics packages. & \\
4495
4496    \indexedbold{forcing term} & &\\
4497
4498    \indexedbold{flux} & the amount of flow through the volume per unit
4499    time & \\
4500
4501    \indexedbold{grid} & Evenly spaced mesh & \\
4502
4503    \indexedbold{latitude} & The angular distance on a mericlear north and south of the
4504    equator, expressed in degrees and minutes. & \\
4505
4506    \indexedbold{longitude} & The angular distance east or west, between the meridian
4507    of a particular place on Earth and that of the Prime Meridian (located in Greenwich,
4508    England) expressed in degrees or time.& \\
4509
4510    \indexedbold{Manning friction coefficient} & &\\
4511
4512    \indexedbold{mesh} & Triangulation of domain &\\
4513
4514    \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\
4515
4516    \indexedbold{NetCDF} & &\\
4517
4518    \indexedbold{node} & A point at which edges meet & \\
4519
4520    \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance
4521    north from a north-south reference line, usually a meridian used as the axis of
4522    origin within a map zone or projection. Northing is a UTM (Universal Transverse
4523    Mercator) coordinate. & \\
4524
4525
4526    \indexedbold{points file} & A PTS or CSV file & \\  \hline
4527
4528    \end{tabular}
4529
4530    \begin{tabular}{|lp{10cm}|c|}  \hline
4531
4532    \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon
4533    either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$
4534    Numeric array, where $N$ is the number of points.
4535
4536    The unit square, for example, would be represented either as
4537    \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1],
4538    [0,1] )}.
4539
4540    NOTE: For details refer to the module \module{utilities/polygon.py}. &
4541    \\     \indexedbold{resolution} &  The maximal area of a triangular cell in a
4542    mesh & \\
4543
4544
4545    \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved
4546    quantities as those present in the neighbouring volume but reflected. Specific to the
4547    shallow water equation as it works with the momentum quantities assumed to be the
4548    second and third conserved quantities. & \pageref{def:reflective boundary}\\
4549
4550    \indexedbold{stage} & &\\
4551
4552%    \indexedbold{try this}
4553
4554    \indexedbold{animate} & visualisation tool used with \anuga &
4555    \pageref{sec:animate}\\
4556
4557    \indexedbold{time boundary} & Returns values for the conserved
4558quantities as a function of time. The user must specify
4559the domain to get access to the model time. & \pageref{def:time boundary}\\
4560
4561    \indexedbold{topography} & onshore elevation &\\
4562
4563    \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\
4564
4565    \indexedbold{vertex} & A point at which edges meet. & \\
4566
4567    \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say
4568    only \code{x} and \code{y} and NOT \code{z}) &\\
4569
4570    \indexedbold{ymomentum}  & conserved quantity & \\  \hline
4571
4572    \end{tabular}
4573
4574
4575%The \code{\e appendix} markup need not be repeated for additional
4576%appendices.
4577
4578
4579%
4580%  The ugly "%begin{latexonly}" pseudo-environments are really just to
4581%  keep LaTeX2HTML quiet during the \renewcommand{} macros; they're
4582%  not really valuable.
4583%
4584%  If you don't want the Module Index, you can remove all of this up
4585%  until the second \input line.
4586%
4587
4588%begin{latexonly}
4589%\renewcommand{\indexname}{Module Index}
4590%end{latexonly}
4591\input{mod\jobname.ind}        % Module Index
4592%
4593%begin{latexonly}
4594%\renewcommand{\indexname}{Index}
4595%end{latexonly}
4596\input{\jobname.ind}            % Index
4597
4598
4599
4600\begin{thebibliography}{99}
4601\bibitem[nielsen2005]{nielsen2005}
4602{\it Hydrodynamic modelling of coastal inundation}.
4603Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman.
4604In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on
4605Modelling and Simulation. Modelling and Simulation Society of Australia and
4606New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\
4607http://www.mssanz.org.au/modsim05/papers/nielsen.pdf
4608
4609\bibitem[grid250]{grid250}
4610Australian Bathymetry and Topography Grid, June 2005.
4611Webster, M.A. and Petkovic, P.
4612Geoscience Australia Record 2005/12. ISBN: 1-920871-46-2.\\
4613http://www.ga.gov.au/meta/ANZCW0703008022.html
4614
4615\bibitem[ZR1999]{ZR1999}
4616\newblock {Catastrophic Collapse of Water Supply Reservoirs in Urban Areas}.
4617\newblock C.~Zoppou and S.~Roberts.
4618\newblock {\em ASCE J. Hydraulic Engineering}, 125(7):686--695, 1999.
4619
4620\bibitem[Toro1999]{Toro1992}
4621\newblock Riemann problems and the waf method for solving the two-dimensional
4622  shallow water equations.
4623\newblock E.~F. Toro.
4624\newblock {\em Philosophical Transactions of the Royal Society, Series A},
4625  338:43--68, 1992.
4626
4627\bibitem{KurNP2001}
4628\newblock Semidiscrete central-upwind schemes for hyperbolic conservation laws
4629  and hamilton-jacobi equations.
4630\newblock A.~Kurganov, S.~Noelle, and G.~Petrova.
4631\newblock {\em SIAM Journal of Scientific Computing}, 23(3):707--740, 2001.
4632\end{thebibliography}{99}
4633
4634\end{document}
Note: See TracBrowser for help on using the repository browser.