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9%labels
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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
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48%\settimeformat{xxivtime} % 24 hour Format
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50\date{\today, \ \currenttime}
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55\fi
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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}
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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
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83%Subversion keywords:
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85%$LastChangedDate: 2008-08-13 05:47:22 +0000 (Wed, 13 Aug 2008) $
86%$LastChangedRevision: 5650 $
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88
89\input{copyright}
90
91
92\begin{abstract}
93\label{def:anuga}
94
95\noindent \anuga\index{\anuga} is a hydrodynamic modelling tool that
96allows users to model realistic flow problems in complex 2D geometries.
97Examples include dam breaks or the effects of natural hazards such
98as riverine flooding, storm surges and tsunami.
99
100The user must specify a study area represented by a mesh of triangular
101cells, the topography and bathymetry, frictional resistance, initial
102values for water level (called \emph{stage}\index{stage} within \anuga),
103boundary conditions and forces such as rainfall, stream flows, windstress or pressure gradients if applicable.
104
105\anuga tracks the evolution of water depth and horizontal momentum
106within each cell over time by solving the shallow water wave equation
107governing equation using a finite-volume method.
108
109\anuga also incorporates a mesh generator %, called \code{graphical
110                                %mesh generator},
111that
112allows the user to set up the geometry of the problem interactively as
113well as tools for interpolation and surface fitting, and a number of
114auxiliary tools for visualising and interrogating the model output.
115
116Most \anuga components are written in the object-oriented programming
117language Python and most users will interact with \anuga by writing
118small Python programs based on the \anuga library
119functions. Computationally intensive components are written for
120efficiency in C routines working directly with the Numerical Python
121structures.
122
123
124\end{abstract}
125
126\tableofcontents
127
128
129\chapter{Introduction}
130
131
132\section{Purpose}
133
134The purpose of this user manual is to introduce the new user to the
135inundation software, describe what it can do and give step-by-step
136instructions for setting up and running hydrodynamic simulations.
137
138\section{Scope}
139
140This manual covers only what is needed to operate the software after
141installation and configuration. It does not includes instructions
142for installing the software or detailed API documentation, both of
143which will be covered in separate publications and by documentation
144in the source code.
145
146\section{Audience}
147
148Readers are assumed to be familiar with the Python Programming language and
149its object oriented approach.
150Python tutorials include
151\url{http://docs.python.org/tut},
152\url{http://www.sthurlow.com/python}, and
153%\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}.
154\url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}.
155
156
157Readers also need to have a general understanding of scientific modelling,
158as well as
159enough programming experience to adapt the code to different
160requirements.
161
162
163
164\pagebreak
165\chapter{Background}
166
167
168Modelling the effects on the built environment of natural hazards such
169as riverine flooding, storm surges and tsunami is critical for
170understanding their economic and social impact on our urban
171communities.  Geoscience Australia and the Australian National
172University are developing a hydrodynamic inundation modelling tool
173called \anuga to help simulate the impact of these hazards.
174
175The core of \anuga is the fluid dynamics module, called \code{shallow\_water},
176which is based on a finite-volume method for solving the Shallow Water
177Wave Equation.  The study area is represented by a mesh of triangular
178cells.  By solving the governing equation within each cell, water
179depth and horizontal momentum are tracked over time.
180
181A major capability of \anuga is that it can model the process of
182wetting and drying as water enters and leaves an area.  This means
183that it is suitable for simulating water flow onto a beach or dry land
184and around structures such as buildings.  \anuga is also capable
185of modelling hydraulic jumps due to the ability of the finite-volume
186method to accommodate discontinuities in the solution.
187
188To set up a particular scenario the user specifies the geometry
189(bathymetry and topography), the initial water level (stage),
190boundary conditions such as tide, and any forcing terms that may
191drive the system such as rain_fall, abstraction of water, wind stress or atmospheric pressure
192gradients. Gravity and frictional resistance from the different
193terrains in the model are represented by predefined forcing terms.
194See section \ref{sec:forcing terms} for details on forcing terms available in ANUGA.
195
196The built-in mesh generator, called \code{graphical\_mesh\_generator},
197allows the user to set up the geometry
198of the problem interactively and to identify boundary segments and
199regions using symbolic tags.  These tags may then be used to set the
200actual boundary conditions and attributes for different regions
201(e.g.\ the Manning friction coefficient) for each simulation.
202
203Most \anuga components are written in the object-oriented programming
204language Python.  Software written in Python can be produced quickly
205and can be readily adapted to changing requirements throughout its
206lifetime.  Computationally intensive components are written for
207efficiency in C routines working directly with the Numerical Python
208structures.  The animation tool developed for \anuga is based on
209OpenSceneGraph, an Open Source Software (OSS) component allowing high
210level interaction with sophisticated graphics primitives.
211See \cite{nielsen2005} for more background on \anuga.
212
213\chapter{Restrictions and limitations on \anuga}
214\label{ch:limitations}
215
216Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a
217number of limitations that any potential user need to be aware of. They are
218
219\begin{itemize}
220  \item The mathematical model is the 2D shallow water wave equation.
221  As such it cannot resolve vertical convection and consequently not breaking
222  waves or 3D turbulence (e.g.\ vorticity).
223  %\item The surface is assumed to be open, e.g. \anuga cannot model
224  %flow under ceilings or in pipes
225  \item All spatial coordinates are assumed to be UTM (meters). As such,
226  ANUGA is unsuitable for modelling flows in areas larger than one UTM zone
227  (6 degrees wide).
228  \item Fluid is assumed to be inviscid - i.e.\ no kinematic viscosity included.
229  \item The finite volume is a very robust and flexible numerical technique,
230  but it is not the fastest method around. If the geometry is sufficiently
231  simple and if there is no need for wetting or drying, a finite-difference
232  method may be able to solve the problem faster than \anuga.
233  %\item Mesh resolutions near coastlines with steep gradients need to be...
234  \item Frictional resistance is implemented using Manning's formula, but
235  \anuga has not yet been fully validated in regard to bottom roughness
236  %\item ANUGA contains no tsunami-genic functionality relating to
237  %earthquakes.
238\end{itemize}
239
240
241
242\chapter{Getting Started}
243\label{ch:getstarted}
244
245This section is designed to assist the reader to get started with
246\anuga by working through some examples. Two examples are discussed;
247the first is a simple example to illustrate many of the concepts, and
248the second is a more realistic example.
249
250\section{A Simple Example}
251\label{sec:simpleexample}
252
253\subsection{Overview}
254
255What follows is a discussion of the structure and operation of a
256script called \file{runup.py}.
257
258This example carries out the solution of the shallow-water wave
259equation in the simple case of a configuration comprising a flat
260bed, sloping at a fixed angle in one direction and having a
261constant depth across each line in the perpendicular direction.
262
263The example demonstrates the basic ideas involved in setting up a
264complex scenario. In general the user specifies the geometry
265(bathymetry and topography), the initial water level, boundary
266conditions such as tide, and any forcing terms that may drive the
267system such as rain_fall, abstraction of water, wind stress or atmospheric pressure gradients.
268Frictional resistance from the different terrains in the model is
269represented by predefined forcing terms. In this example, the
270boundary is reflective on three sides and a time dependent wave on
271one side.
272
273The present example represents a simple scenario and does not
274include any forcing terms, nor is the data taken from a file as it
275would typically be.
276
277The conserved quantities involved in the
278problem are stage (absolute height of water surface),
279$x$-momentum and $y$-momentum. Other quantities
280involved in the computation are the friction and elevation.
281
282Water depth can be obtained through the equation
283
284\begin{tabular}{rcrcl}
285  \code{depth} &=& \code{stage} &$-$& \code{elevation}
286\end{tabular}
287
288
289\subsection{Outline of the Program}
290
291In outline, \file{runup.py} performs the following steps:
292
293\begin{enumerate}
294
295   \item Sets up a triangular mesh.
296
297   \item Sets certain parameters governing the mode of
298operation of the model-specifying, for instance, where to store the model output.
299
300   \item Inputs various quantities describing physical measurements, such
301as the elevation, to be specified at each mesh point (vertex).
302
303   \item Sets up the boundary conditions.
304
305   \item Carries out the evolution of the model through a series of time
306steps and outputs the results, providing a results file that can
307be visualised.
308
309\end{enumerate}
310
311\subsection{The Code}
312
313%FIXME: we are using the \code function here.
314%This should be used wherever possible
315For reference we include below the complete code listing for
316\file{runup.py}. Subsequent paragraphs provide a
317`commentary' that describes each step of the program and explains it
318significance.
319
320\verbatiminput{demos/runup.py}
321
322\subsection{Establishing the Mesh}\index{mesh, establishing}
323
324The first task is to set up the triangular mesh to be used for the
325scenario. This is carried out through the statement:
326
327{\small \begin{verbatim}
328    points, vertices, boundary = rectangular_cross(10, 10)
329\end{verbatim}}
330
331The function \function{rectangular_cross} is imported from a module
332\module{mesh\_factory} defined elsewhere. (\anuga also contains
333several other schemes that can be used for setting up meshes, but we
334shall not discuss these.) The above assignment sets up a $10 \times
33510$ rectangular mesh, triangulated in a regular way. The assignment
336
337{\small \begin{verbatim}
338    points, vertices, boundary = rectangular_cross(m, n)
339\end{verbatim}}
340
341returns:
342
343\begin{itemize}
344
345   \item a list \code{points} giving the coordinates of each mesh point,
346
347   \item a list \code{vertices} specifying the three vertices of each triangle, and
348
349   \item a dictionary \code{boundary} that stores the edges on
350   the boundary and associates each with one of the symbolic tags \code{`left'}, \code{`right'},
351   \code{`top'} or \code{`bottom'}.
352
353\end{itemize}
354
355(For more details on symbolic tags, see page
356\pageref{ref:tagdescription}.)
357
358An example of a general unstructured mesh and the associated data
359structures \code{points}, \code{vertices} and \code{boundary} is
360given in Section \ref{sec:meshexample}.
361
362
363
364
365\subsection{Initialising the Domain}
366
367These variables are then used to set up a data structure
368\code{domain}, through the assignment:
369
370{\small \begin{verbatim}
371    domain = Domain(points, vertices, boundary)
372\end{verbatim}}
373
374This creates an instance of the \class{Domain} class, which
375represents the domain of the simulation. Specific options are set at
376this point, including the basename for the output file and the
377directory to be used for data:
378
379{\small \begin{verbatim}
380    domain.set_name('runup')
381\end{verbatim}}
382
383{\small \begin{verbatim}
384    domain.set_datadir('.')
385\end{verbatim}}
386
387In addition, the following statement now specifies that the
388quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are
389to be stored:
390
391{\small \begin{verbatim}
392    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
393    'ymomentum'])
394\end{verbatim}}
395
396
397\subsection{Initial Conditions}
398
399The next task is to specify a number of quantities that we wish to
400set for each mesh point. The class \class{Domain} has a method
401\method{set\_quantity}, used to specify these quantities. It is a
402flexible method that allows the user to set quantities in a variety
403of ways---using constants, functions, numeric arrays, expressions
404involving other quantities, or arbitrary data points with associated
405values, all of which can be passed as arguments. All quantities can
406be initialised using \method{set\_quantity}. For a conserved
407quantity (such as \code{stage, xmomentum, ymomentum}) this is called
408an \emph{initial condition}. However, other quantities that aren't
409updated by the equation are also assigned values using the same
410interface. The code in the present example demonstrates a number of
411forms in which we can invoke \method{set\_quantity}.
412
413
414\subsubsection{Elevation}
415
416The elevation, or height of the bed, is set using a function,
417defined through the statements below, which is specific to this
418example and specifies a particularly simple initial configuration
419for demonstration purposes:
420
421{\small \begin{verbatim}
422    def f(x,y):
423        return -x/2
424\end{verbatim}}
425
426This simply associates an elevation with each point \code{(x, y)} of
427the plane.  It specifies that the bed slopes linearly in the
428\code{x} direction, with slope $-\frac{1}{2}$,  and is constant in
429the \code{y} direction.
430
431Once the function \function{f} is specified, the quantity
432\code{elevation} is assigned through the simple statement:
433
434{\small \begin{verbatim}
435    domain.set_quantity('elevation', f)
436\end{verbatim}}
437
438NOTE: If using function to set \code{elevation} it must be vector
439compatible. For example square root will not work.
440
441\subsubsection{Friction}
442
443The assignment of the friction quantity (a forcing term)
444demonstrates another way we can use \method{set\_quantity} to set
445quantities---namely, assign them to a constant numerical value:
446
447{\small \begin{verbatim}
448    domain.set_quantity('friction', 0.1)
449\end{verbatim}}
450
451This specifies that the Manning friction coefficient is set to 0.1
452at every mesh point.
453
454\subsubsection{Stage}
455
456The stage (the height of the water surface) is related to the
457elevation and the depth at any time by the equation
458
459{\small \begin{verbatim}
460    stage = elevation + depth
461\end{verbatim}}
462
463
464For this example, we simply assign a constant value to \code{stage},
465using the statement
466
467{\small \begin{verbatim}
468    domain.set_quantity('stage', -.4)
469\end{verbatim}}
470
471which specifies that the surface level is set to a height of $-0.4$,
472i.e. 0.4 units (m) below the zero level.
473
474Although it is not necessary for this example, it may be useful to
475digress here and mention a variant to this requirement, which allows
476us to illustrate another way to use \method{set\_quantity}---namely,
477incorporating an expression involving other quantities. Suppose,
478instead of setting a constant value for the stage, we wished to
479specify a constant value for the \emph{depth}. For such a case we
480need to specify that \code{stage} is everywhere obtained by adding
481that value to the value already specified for \code{elevation}. We
482would do this by means of the statements:
483
484{\small \begin{verbatim}
485    h = 0.05 # Constant depth
486    domain.set_quantity('stage', expression = 'elevation + %f' %h)
487\end{verbatim}}
488
489That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus
490the value of \code{elevation} already defined.
491
492The reader will probably appreciate that this capability to
493incorporate expressions into statements using \method{set\_quantity}
494greatly expands its power.) See Section \ref{sec:initial conditions} for more
495details.
496
497\subsection{Boundary Conditions}\index{boundary conditions}
498
499The boundary conditions are specified as follows:
500
501{\small \begin{verbatim}
502    Br = Reflective_boundary(domain)
503
504    Bt = Transmissive_boundary(domain)
505
506    Bd = Dirichlet_boundary([0.2,0.,0.])
507
508    Bw = Time_boundary(domain=domain,
509                f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
510\end{verbatim}}
511
512The effect of these statements is to set up a selection of different
513alternative boundary conditions and store them in variables that can be
514assigned as needed. Each boundary condition specifies the
515behaviour at a boundary in terms of the behaviour in neighbouring
516elements. The boundary conditions introduced here may be briefly described as
517follows:
518
519\begin{itemize}
520    \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as
521      as present in its neighbour volume but momentum vector
522      reversed 180 degrees (reflected).
523      Specific to the shallow water equation as it works with the
524      momentum quantities assumed to be the second and third conserved
525      quantities. A reflective boundary condition models a solid wall.
526    \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as
527      those present in its neighbour volume. This is one way of modelling
528      outflow from a domain, but it should be used with caution if flow is
529      not steady state as replication of momentum at the boundary
530      may cause occasional spurious effects. If this occurs,
531      consider using e.g. a Dirichlet boundary condition.
532    \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies
533      constant values for stage, $x$-momentum and $y$-momentum at the boundary.
534    \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet
535      boundary but with behaviour varying with time.
536\end{itemize}
537
538\label{ref:tagdescription}Before describing how these boundary
539conditions are assigned, we recall that a mesh is specified using
540three variables \code{points}, \code{vertices} and \code{boundary}.
541In the code we are discussing, these three variables are returned by
542the function \code{rectangular}; however, the example given in
543Section \ref{sec:realdataexample} illustrates another way of
544assigning the values, by means of the function
545\code{create\_mesh\_from\_regions}.
546
547These variables store the data determining the mesh as follows. (You
548may find that the example given in Section \ref{sec:meshexample}
549helps to clarify the following discussion, even though that example
550is a \emph{non-rectangular} mesh.)
551
552\begin{itemize}
553\item The variable \code{points} stores a list of 2-tuples giving the
554coordinates of the mesh points.
555
556\item The variable \code{vertices} stores a list of 3-tuples of
557numbers, representing vertices of triangles in the mesh. In this
558list, the triangle whose vertices are \code{points[i]},
559\code{points[j]}, \code{points[k]} is represented by the 3-tuple
560\code{(i, j, k)}.
561
562\item The variable \code{boundary} is a Python dictionary that
563not only stores the edges that make up the boundary but also assigns
564symbolic tags to these edges to distinguish different parts of the
565boundary. An edge with endpoints \code{points[i]} and
566\code{points[j]} is represented by the 2-tuple \code{(i, j)}. The
567keys for the dictionary are the 2-tuples \code{(i, j)} corresponding
568to boundary edges in the mesh, and the values are the tags are used
569to label them. In the present example, the value \code{boundary[(i,
570j)]} assigned to \code{(i, j)]} is one of the four tags
571\code{`left'}, \code{`right'}, \code{`top'} or \code{`bottom'},
572depending on whether the boundary edge represented by \code{(i, j)}
573occurs at the left, right, top or bottom of the rectangle bounding
574the mesh. The function \code{rectangular} automatically assigns
575these tags to the boundary edges when it generates the mesh.
576\end{itemize}
577
578The tags provide the means to assign different boundary conditions
579to an edge depending on which part of the boundary it belongs to.
580(In Section \ref{sec:realdataexample} we describe an example that
581uses different boundary tags --- in general, the possible tags are entirely selectable by the user when generating the mesh and not
582limited to `left', `right', `top' and `bottom' as in this example.)
583All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by ANUGA.
584
585
586Using the boundary objects described above, we assign a boundary
587condition to each part of the boundary by means of a statement like
588
589{\small \begin{verbatim}
590    domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br})
591\end{verbatim}}
592
593It is critical that all tags are assoctiated with a boundary conditing in this statement. If not the program will halt with a statement like
594
595\begin{verbatim}
596
597Traceback (most recent call last):
598  File "mesh_test.py", line 114, in ?
599    domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br})
600  File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary
601    raise msg
602ERROR (domain.py): Tag "exterior" has not been bound to a boundary object.
603All boundary tags defined in domain must appear in the supplied dictionary.
604The tags are: ['ocean', 'east', 'north', 'exterior', 'south']
605\end{verbatim}
606
607
608The command \code{set\_boundary} stipulates that, in the current example, the right
609boundary varies with time, as defined by the lambda function, while the other
610boundaries are all reflective.
611
612The reader may wish to experiment by varying the choice of boundary
613types for one or more of the boundaries. (In the case of \code{Bd}
614and \code{Bw}, the three arguments in each case represent the
615\code{stage}, $x$-momentum and $y$-momentum, respectively.)
616
617{\small \begin{verbatim}
618    Bw = Time_boundary(domain=domain,
619                       f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
620\end{verbatim}}
621
622
623
624\subsection{Evolution}\index{evolution}
625
626The final statement \nopagebreak[3]
627{\small \begin{verbatim}
628    for t in domain.evolve(yieldstep = 0.1, duration = 4.0):
629        print domain.timestepping_statistics()
630\end{verbatim}}
631
632causes the configuration of the domain to `evolve', over a series of
633steps indicated by the values of \code{yieldstep} and
634\code{duration}, which can be altered as required.  The value of
635\code{yieldstep} controls the time interval between successive model
636outputs.  Behind the scenes more time steps are generally taken.
637
638
639\subsection{Output}
640
641The output is a NetCDF file with the extension \code{.sww}. It
642contains stage and momentum information and can be used with the
643ANUGA viewer \code{animate} (see Section \ref{sec:animate})
644visualisation package
645to generate a visual display. See Section \ref{sec:file formats}
646(page \pageref{sec:file formats}) for more on NetCDF and other file
647formats.
648
649The following is a listing of the screen output seen by the user
650when this example is run:
651
652\verbatiminput{examples/runupoutput.txt}
653
654
655\section{How to Run the Code}
656
657The code can be run in various ways:
658
659\begin{itemize}
660  \item{from a Windows or Unix command line} as in\ \code{python runup.py}
661  \item{within the Python IDLE environment}
662  \item{within emacs}
663  \item{within Windows, by double-clicking the \code{runup.py}
664  file.}
665\end{itemize}
666
667
668\section{Exploring the Model Output}
669
670The following figures are screenshots from the \anuga visualisation
671tool \code{animate}. Figure \ref{fig:runupstart} shows the domain
672with water surface as specified by the initial condition, $t=0$.
673Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and
674$t=4$ where the system has been evolved and the wave is encroaching
675on the previously dry bed.  All figures are screenshots from an
676interactive animation tool called animate which is part of \anuga and
677distributed as in the package anuga\_viewer.
678Animate is described in more detail is Section \ref{sec:animate}.
679
680\begin{figure}[hbt]
681
682  \centerline{\includegraphics[width=75mm, height=75mm]
683    {graphics/bedslopestart.jpg}}
684
685  \caption{Runup example viewed with the ANUGA viewer}
686  \label{fig:runupstart}
687\end{figure}
688
689
690\begin{figure}[hbt]
691
692  \centerline{
693   \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg}
694    \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg}
695   }
696
697  \caption{Runup example viewed with ANGUA viewer}
698  \label{fig:runup2}
699\end{figure}
700
701
702
703\clearpage
704
705%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
706
707\section{A slightly more complex example}
708\label{sec:channelexample}
709
710\subsection{Overview}
711
712The next example is about waterflow in a channel with varying boundary conditions and
713more complex topograhies. These examples build on the
714concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
715The example will be built up through three progressively more complex scripts.
716
717\subsection{Overview}
718As in the case of \file{runup.py}, the actions carried
719out by the program can be organised according to this outline:
720
721\begin{enumerate}
722
723   \item Set up a triangular mesh.
724
725   \item Set certain parameters governing the mode of
726operation of the model---specifying, for instance, where to store the
727model output.
728
729   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
730
731   \item Set up the boundary conditions.
732
733   \item Carry out the evolution of the model through a series of time
734steps and output the results, providing a results file that can be
735visualised.
736
737\end{enumerate}
738
739
740\subsection{The Code}
741
742Here is the code for the first version of the channel flow \file{channel1.py}:
743
744\verbatiminput{demos/channel1.py}
745
746In discussing the details of this example, we follow the outline
747given above, discussing each major step of the code in turn.
748
749\subsection{Establishing the Mesh}\index{mesh, establishing}
750
751In this example we use a similar simple structured triangular mesh as in \code{runup.py}
752for simplicity, but this time we will use a symmetric one and also
753change the physical extent of the domain. The assignment
754
755{\small \begin{verbatim}
756    points, vertices, boundary = rectangular_cross(m, n,
757                                                   len1=length, len2=width)
758\end{verbatim}}
759returns a m x n mesh similar to the one used in the previous example, except that now the
760extent in the x and y directions are given by the value of \code{length} and \code{width}
761respectively.
762
763Defining m and n in terms of the extent as in this example provides a convenient way of
764controlling the resolution: By defining dx and dy to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows:
765
766{\small \begin{verbatim}
767length = 10.
768width = 5.
769dx = dy = 1           # Resolution: Length of subdivisions on both axes
770
771points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
772                                               len1=length, len2=width)
773\end{verbatim}}
774which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decrease the values of dx and dy.
775
776The rest of this script is as in the previous example.
777% except for an application of the 'expression' form of \code{set\_quantity} where we use the value of \code{elevation} to define the (dry) initial condition for \code{stage}:
778%{\small \begin{verbatim}
779%  domain.set_quantity('stage', expression='elevation')
780%\end{verbatim}}
781
782\section{Model Output}
783
784The following figure is a screenshot from the \anuga visualisation
785tool \code{animate} of output from this example.
786\begin{figure}[hbt]
787  \centerline{\includegraphics[height=75mm]
788    {graphics/channel1.png}}%
789
790  \caption{Simple channel example viewed with the ANUGA viewer.}
791  \label{fig:channel1}
792\end{figure}
793
794
795\subsection{Changing boundary conditions on the fly}
796\label{sec:change boundary}
797
798Here is the code for the second version of the channel flow \file{channel2.py}:
799\verbatiminput{demos/channel2.py}
800This example differs from the first version in that a constant outflow boundary condition has
801been defined
802{\small \begin{verbatim}
803    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
804\end{verbatim}}
805and that it is applied to the right hand side boundary when the water level there exceeds 0m.
806{\small \begin{verbatim}
807for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
808    domain.write_time()
809
810    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:
811        print 'Stage > 0: Changing to outflow boundary'
812        domain.set_boundary({'right': Bo})
813\end{verbatim}}
814\label{sec:change boundary code}
815
816The if statement in the timestepping loop (evolve) gets the quantity
817\code{stage} and obtain the interpolated value at the point (10m,
8182.5m) which is on the right boundary. If the stage exceeds 0m a
819message is printed and the old boundary condition at tag 'right' is
820replaced by the outflow boundary using the method
821{\small \begin{verbatim}
822    domain.set_boundary({'right': Bo})
823\end{verbatim}}
824This type of dynamically varying boundary could for example be
825used to model the
826breakdown of a sluice door when water exceeds a certain level.
827
828\subsection{Output}
829
830The text output from this example looks like this
831{\small \begin{verbatim}
832...
833Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
834Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
835Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
836Stage > 0: Changing to outflow boundary
837Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
838Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
839...
840\end{verbatim}}
841
842
843\subsection{Flow through more complex topograhies}
844
845Here is the code for the third version of the channel flow \file{channel3.py}:
846\verbatiminput{demos/channel3.py}
847
848This example differs from the first two versions in that the topography
849contains obstacles.
850
851This is accomplished here by defining the function \code{topography} as follows
852{\small \begin{verbatim}
853def topography(x,y):
854    """Complex topography defined by a function of vectors x and y
855    """
856
857    z = -x/10
858
859    N = len(x)
860    for i in range(N):
861
862        # Step
863        if 10 < x[i] < 12:
864            z[i] += 0.4 - 0.05*y[i]
865
866        # Constriction
867        if 27 < x[i] < 29 and y[i] > 3:
868            z[i] += 2
869
870        # Pole
871        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
872            z[i] += 2
873
874    return z
875\end{verbatim}}
876
877In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
878
879A screenshot of this model at time == 15s is
880\begin{figure}[hbt]
881
882  \centerline{\includegraphics[height=75mm]
883    {graphics/channel3.png}}
884
885  \caption{More complex flow in a channel}
886  \label{fig:channel3}
887\end{figure}
888
889
890
891
892\clearpage
893
894%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
895
896\section{An Example with Real Data}
897\label{sec:realdataexample} The following discussion builds on the
898concepts introduced through the \file{runup.py} example and
899introduces a second example, \file{runcairns.py}.  This refers to
900a {\bf hypothetical} scenario using real-life data,
901in which the domain of interest surrounds the
902Cairns region. Two scenarios are given; firstly, a
903hypothetical tsunami wave is generated by a submarine mass failure
904situated on the edge of the continental shelf, and secondly, a fixed wave
905of given amplitude and period is introduced through the boundary.
906
907{\bf
908Each scenario has been designed to generate a tsunami which will
909inundate the Cairns region. To achieve this, suitably large
910parameters were chosen and were not based on any known tsunami sources
911or realistic amplitudes.
912}
913
914\subsection{Overview}
915As in the case of \file{runup.py}, the actions carried
916out by the program can be organised according to this outline:
917
918\begin{enumerate}
919
920   \item Set up a triangular mesh.
921
922   \item Set certain parameters governing the mode of
923operation of the model---specifying, for instance, where to store the
924model output.
925
926   \item Input various quantities describing physical measurements, such
927as the elevation, to be specified at each mesh point (vertex).
928
929   \item Set up the boundary conditions.
930
931   \item Carry out the evolution of the model through a series of time
932steps and output the results, providing a results file that can be
933visualised.
934
935\end{enumerate}
936
937
938
939\subsection{The Code}
940
941Here is the code for \file{runcairns.py}:
942
943\verbatiminput{demos/cairns/runcairns.py}
944
945In discussing the details of this example, we follow the outline
946given above, discussing each major step of the code in turn.
947
948\subsection{Establishing the Mesh}\index{mesh, establishing}
949
950One obvious way that the present example differs from
951\file{runup.py} is in the use of a more complex method to
952create the mesh. Instead of imposing a mesh structure on a
953rectangular grid, the technique used for this example involves
954building mesh structures inside polygons specified by the user,
955using a mesh-generator.
956
957In its simplest form, the mesh-generator creates the mesh within a single
958polygon whose vertices are at geographical locations specified by
959the user. The user specifies the \emph{resolution}---that is, the
960maximal area of a triangle used for triangulation---and a triangular
961mesh is created inside the polygon using a mesh generation engine.
962On any given platform, the same mesh will be returned.
963%Figure
964%\ref{fig:pentagon} shows a simple example of this, in which the
965%triangulation is carried out within a pentagon.
966
967
968%\begin{figure}[hbt]
969
970%  \caption{Mesh points are created inside the polygon}
971  %\label{fig:pentagon}
972%\end{figure}
973
974Boundary tags are not restricted to \code{`left'}, \code{`bottom'},
975\code{`right'} and \code{`top'}, as in the case of
976\file{runup.py}. Instead the user specifies a list of
977tags appropriate to the configuration being modelled.
978
979In addition, the mesh-generator provides a way to adapt to geographic or
980other features in the landscape, whose presence may require an
981increase in resolution. This is done by allowing the user to specify
982a number of \emph{interior polygons}, each with a specified
983resolution. It is also
984possible to specify one or more `holes'---that is, areas bounded by
985polygons in which no triangulation is required.
986
987%\begin{figure}[hbt]
988%  \caption{Interior meshes with individual resolution}
989%  \label{fig:interior meshes}
990%\end{figure}
991
992In its general form, the mesh-generator takes for its input a bounding
993polygon and (optionally) a list of interior polygons. The user
994specifies resolutions, both for the bounding polygon and for each of
995the interior polygons. Given this data, the mesh-generator first creates a
996triangular mesh with varying resolution.
997
998The function used to implement this process is
999\function{create\_mesh\_from\_regions}. Its arguments include the
1000bounding polygon and its resolution, a list of boundary tags, and a
1001list of pairs \code{[polygon, resolution]}, specifying the interior
1002polygons and their resolutions.
1003
1004The resulting mesh is output to a \emph{mesh file}\index{mesh
1005file}\label{def:mesh file}. This term is used to describe a file of
1006a specific format used to store the data specifying a mesh. (There
1007are in fact two possible formats for such a file: it can either be a
1008binary file, with extension \code{.msh}, or an ASCII file, with
1009extension \code{.tsh}. In the present case, the binary file format
1010\code{.msh} is used. See Section \ref{sec:file formats} (page
1011\pageref{sec:file formats}) for more on file formats.)
1012
1013In practice, the details of the polygons used are read from a
1014separate file \file{project.py}. Here is a complete listing of
1015\file{project.py}:
1016
1017\verbatiminput{demos/cairns/project.py}
1018
1019Figure \ref{fig:cairns3d} illustrates the landscape of the region
1020for the Cairns example. Understanding the landscape is important in
1021determining the location and resolution of interior polygons. The
1022supporting data is found in the ASCII grid, \code{cairns.asc}, which
1023has been sourced from the publically available Australian Bathymetry
1024and Topography Grid 2005, \cite{grid250}. The required resolution
1025for inundation modelling will depend on the underlying topography and
1026bathymetry; as the terrain becomes more complex, the desired resolution
1027would decrease to the order of tens of metres.
1028
1029\begin{figure}[hbt]
1030\centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}}
1031\caption{Landscape of the Cairns scenario.}
1032\label{fig:cairns3d}
1033
1034\end{figure}
1035The following statements are used to read in the specific polygons
1036from \code{project.cairns} and assign a defined resolution to
1037each polygon.
1038
1039{\small \begin{verbatim}
1040    islands_res = 100000
1041    cairns_res = 100000
1042    shallow_res = 500000
1043    interior_regions = [[project.poly_cairns, cairns_res],
1044                        [project.poly_island0, islands_res],
1045                        [project.poly_island1, islands_res],
1046                        [project.poly_island2, islands_res],
1047                        [project.poly_island3, islands_res],
1048                        [project.poly_shallow, shallow_res]]
1049\end{verbatim}}
1050
1051Figure \ref{fig:cairnspolys}
1052illustrates the polygons used for the Cairns scenario.
1053
1054\begin{figure}[hbt]
1055
1056  \centerline{\includegraphics[scale=0.5]
1057      {graphics/cairnsmodel.jpg}}
1058  \caption{Interior and bounding polygons for the Cairns example.}
1059  \label{fig:cairnspolys}
1060\end{figure}
1061
1062The statement
1063
1064
1065{\small \begin{verbatim}
1066remainder_res = 10000000
1067create_mesh_from_regions(project.bounding_polygon,
1068                         boundary_tags={'top': [0],
1069                                        'ocean_east': [1],
1070                                        'bottom': [2],
1071                                        'onshore': [3]},
1072                         maximum_triangle_area=remainder_res,
1073                         filename=meshname,
1074                         interior_regions=interior_regions,
1075                         use_cache=True,
1076                         verbose=True)
1077\end{verbatim}}
1078is then used to create the mesh, taking the bounding polygon to be
1079the polygon \code{bounding\_polygon} specified in \file{project.py}.
1080The argument \code{boundary\_tags} assigns a dictionary, whose keys
1081are the names of the boundary tags used for the bounding
1082polygon---\code{`top'}, \code{`ocean\_east'}, \code{`bottom'}, and
1083\code{`onshore'}--- and whose values identify the indices of the
1084segments associated with each of these tags.
1085The polygon may be arranged either clock-wise or counter clock-wise and the
1086indices refer to edges in the order they appear: Edge 0 connects vertex 0 and vertex 1, edge 1 connects vertex 1 and 2; and so forth.
1087(Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges)
1088If polygons intersect, or edges coincide the resolution may be undefined in some regions.
1089Use the underlying mesh interface for such cases. See Section
1090\ref{sec:mesh interface}.
1091
1092Note that every point on each polygon defining the mesh will be used as vertices in triangles.
1093Consequently, polygons with points very close together will cause triangles with very small
1094areas to be generated irrespective of the requested resolution.
1095Make sure points on polygons are spaced to be no closer than the smallest resolution requested.
1096
1097
1098\subsection{Initialising the Domain}
1099
1100As with \file{runup.py}, once we have created the mesh, the next
1101step is to create the data structure \code{domain}. We did this for
1102\file{runup.py} by inputting lists of points and triangles and
1103specifying the boundary tags directly. However, in the present case,
1104we use a method that works directly with the mesh file
1105\code{meshname}, as follows:
1106
1107
1108{\small \begin{verbatim}
1109    domain = Domain(meshname, use_cache=True, verbose=True)
1110\end{verbatim}}
1111
1112Providing a filename instead of the lists used in \file{runup.py}
1113above causes \code{Domain} to convert a mesh file \code{meshname}
1114into an instance of \code{Domain}, allowing us to use methods like
1115\method{set\_quantity} to set quantities and to apply other
1116operations.
1117
1118%(In principle, the
1119%second argument of \function{pmesh\_to\_domain\_instance} can be any
1120%subclass of \class{Domain}, but for applications involving the
1121%shallow-water wave equation, the second argument of
1122%\function{pmesh\_to\_domain\_instance} can always be set simply to
1123%\class{Domain}.)
1124
1125The following statements specify a basename and data directory, and
1126identify quantities to be stored. For the first two, values are
1127taken from \file{project.py}.
1128
1129{\small \begin{verbatim}
1130    domain.set_name(project.basename)
1131    domain.set_datadir(project.outputdir)
1132    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
1133        'ymomentum'])
1134\end{verbatim}}
1135
1136
1137\subsection{Initial Conditions}
1138Quantities for \file{runcairns.py} are set
1139using similar methods to those in \file{runup.py}. However,
1140in this case, many of the values are read from the auxiliary file
1141\file{project.py} or, in the case of \code{elevation}, from an
1142ancillary points file.
1143
1144
1145
1146\subsubsection{Stage}
1147
1148For the scenario we are modelling in this case, we use a callable
1149object \code{tsunami\_source}, assigned by means of a function
1150\function{slide\_tsunami}. This is similar to how we set elevation in
1151\file{runup.py} using a function---however, in this case the
1152function is both more complex and more interesting.
1153
1154The function returns the water displacement for all \code{x} and
1155\code{y} in the domain. The water displacement is a double Gaussian
1156function that depends on the characteristics of the slide (length,
1157width, thickness, slope, etc), its location (origin) and the depth at that
1158location. For this example, we choose to apply the slide function
1159at a specified time into the simulation. {\bf Note, the parameters used
1160in this example have been deliberately chosen to generate a suitably
1161large amplitude tsunami which would inundate the Cairns region.}
1162
1163\subsubsection{Friction}
1164
1165We assign the friction exactly as we did for \file{runup.py}:
1166
1167{\small \begin{verbatim}
1168    domain.set_quantity('friction', 0.0)
1169\end{verbatim}}
1170
1171
1172\subsubsection{Elevation}
1173
1174The elevation is specified by reading data from a file:
1175
1176{\small \begin{verbatim}
1177    domain.set_quantity('elevation',
1178                        filename = project.dem_name + '.pts',
1179                        use_cache = True,
1180                        verbose = True)
1181\end{verbatim}}
1182
1183%However, before this step can be executed, some preliminary steps
1184%are needed to prepare the file from which the data is taken. Two
1185%source files are used for this data---their names are specified in
1186%the file \file{project.py}, in the variables \code{coarsedemname}
1187%and \code{finedemname}. They contain `coarse' and `fine' data,
1188%respectively---that is, data sampled at widely spaced points over a
1189%large region and data sampled at closely spaced points over a
1190%smaller subregion. The data in these files is combined through the
1191%statement
1192
1193%{\small \begin{verbatim}
1194%combine_rectangular_points_files(project.finedemname + '.pts',
1195%                                 project.coarsedemname + '.pts',
1196%                                 project.combineddemname + '.pts')
1197%\end{verbatim}}
1198%The effect of this is simply to combine the datasets by eliminating
1199%any coarse data associated with points inside the smaller region
1200%common to both datasets. The name to be assigned to the resulting
1201%dataset is also derived from the name stored in the variable
1202%\code{combinedname} in the file \file{project.py}.
1203
1204\subsection{Boundary Conditions}\index{boundary conditions}
1205
1206Setting boundaries follows a similar pattern to the one used for
1207\file{runup.py}, except that in this case we need to associate a
1208boundary type with each of the
1209boundary tag names introduced when we established the mesh. In place of the four
1210boundary types introduced for \file{runup.py}, we use the reflective
1211boundary for each of the
1212eight tagged segments defined by \code{create_mesh_from_regions}:
1213
1214{\small \begin{verbatim}
1215Bd = Dirichlet_boundary([0.0,0.0,0.0])
1216domain.set_boundary( {'ocean_east': Bd, 'bottom': Bd, 'onshore': Bd,
1217                          'top': Bd} )
1218\end{verbatim}}
1219
1220\subsection{Evolution}
1221
1222With the basics established, the running of the `evolve' step is
1223very similar to the corresponding step in \file{runup.py}. For the slide
1224scenario,
1225the simulation is run for 5000 seconds with the output stored every ten seconds.
1226For this example, we choose to apply the slide at 60 seconds into the simulation.
1227
1228{\small \begin{verbatim}
1229    import time t0 = time.time()
1230
1231
1232    for t in domain.evolve(yieldstep = 10, finaltime = 60):
1233            domain.write_time()
1234            domain.write_boundary_statistics(tags = 'ocean_east')
1235
1236        # add slide
1237        thisstagestep = domain.get_quantity('stage')
1238        if allclose(t, 60):
1239            slide = Quantity(domain)
1240            slide.set_values(tsunami_source)
1241            domain.set_quantity('stage', slide + thisstagestep)
1242
1243        for t in domain.evolve(yieldstep = 10, finaltime = 5000,
1244                               skip_initial_step = True):
1245            domain.write_time()
1246        domain.write_boundary_statistics(tags = 'ocean_east')
1247\end{verbatim}}
1248
1249For the fixed wave scenario, the simulation is run to 10000 seconds,
1250with the first half of the simulation stored at two minute intervals,
1251and the second half of the simulation stored at ten second intervals.
1252This functionality is especially convenient as it allows the detailed
1253parts of the simulation to be viewed at higher time resolution.
1254
1255
1256{\small \begin{verbatim}
1257
1258# save every two mins leading up to wave approaching land
1259    for t in domain.evolve(yieldstep = 120, finaltime = 5000):
1260        domain.write_time()
1261        domain.write_boundary_statistics(tags = 'ocean_east')
1262
1263    # save every 30 secs as wave starts inundating ashore
1264    for t in domain.evolve(yieldstep = 10, finaltime = 10000,
1265                           skip_initial_step = True):
1266        domain.write_time()
1267        domain.write_boundary_statistics(tags = 'ocean_east')
1268
1269\end{verbatim}}
1270
1271\section{Exploring the Model Output}
1272
1273Now that the scenario has been run, the user can view the output in a number of ways.
1274As described earlier, the user may run animate to view a three-dimensional representation
1275of the simulation.
1276
1277The user may also be interested in a maximum inundation map. This simply shows the
1278maximum water depth over the domain and is achieved with the function sww2dem (described in
1279Section \ref{sec:basicfileconversions}).
1280\file{ExportResults.py} demonstrates how this function can be used:
1281
1282\verbatiminput{demos/cairns/ExportResults.py}
1283
1284The script generates an maximum water depth ASCII grid at a defined
1285resolution (here 100 m$^2$) which can then be viewed in a GIS environment, for
1286example. The parameters used in the function are defined in \file{project.py}.
1287Figures \ref{fig:maxdepthcairnsslide} and \ref{fig:maxdepthcairnsfixedwave} show
1288the maximum water depth within the defined region for the slide and fixed wave scenario
1289respectively. {\bf Note, these inundation maps have been based on purely hypothetical
1290scenarios and were designed explicitly for demonstration purposes only.}
1291The user could develop a maximum absolute momentum or other expressions which can be
1292derived from the quantities.
1293It must be noted here that depth is more meaningful when the elevation is positive
1294(\code{depth} = \code{stage} $-$ \code{elevation}) as it describes the water height
1295above the available elevation. When the elevation is negative, depth is meauring the
1296water height from the sea floor. With this in mind, maximum inundation maps are
1297typically "clipped" to the coastline. However, the data input here did not contain a
1298coastline.
1299
1300\begin{figure}[hbt]
1301\centerline{\includegraphics[scale=0.5]{graphics/slidedepth.jpg}}
1302\caption{Maximum inundation map for the Cairns slide scenario. \bf Note, this
1303inundaiton map has been based on a purely hypothetical scenario which was
1304designed explictiy for demonstration purposes only.}
1305\label{fig:maxdepthcairnsslide}
1306\end{figure}
1307
1308\begin{figure}[hbt]
1309\centerline{\includegraphics[scale=0.5]{graphics/fixedwavedepth.jpg}}
1310\caption{Maximum inundation map for the Cairns fixed wave scenario.
1311\bf Note, this
1312inundaiton map has been based on a purely hypothetical scenario which was
1313designed explictiy for demonstration purposes only.}
1314\label{fig:maxdepthcairnsfixedwave}
1315\end{figure}
1316
1317The user may also be interested in interrogating the solution at a particular spatial
1318location to understand the behaviour of the system through time. To do this, the user
1319must first define the locations of interest. A number of locations have been
1320identified for the Cairns scenario, as shown in Figure \ref{fig:cairnsgauges}.
1321
1322\begin{figure}[hbt]
1323\centerline{\includegraphics[scale=0.5]{graphics/cairnsgauges.jpg}}
1324\caption{Point locations to show time series information for the Cairns scenario.}
1325\label{fig:cairnsgauges}
1326\end{figure}
1327
1328These locations
1329must be stored in either a .csv or .txt file. The corresponding .csv file for
1330the gauges shown in Figure \ref{fig:cairnsgauges} is \file{gauges.csv}
1331
1332\verbatiminput{demos/cairns/gauges.csv}
1333
1334Header information has been included to identify the location in terms of eastings and
1335northings, and each gauge is given a name. The elevation column can be zero here.
1336This information is then passed to the function \code{sww2csv_gauges} (shown in
1337\file{GetTimeseries.py} which generates the csv files for each point location. The csv files
1338can then be used in \code{csv2timeseries_graphs} to create the timeseries plot for each desired
1339quantity. \code{csv2timeseries_graphs} relies on \code{pylab} to be installed which is not part
1340of the standard \code{anuga} release, however it can be downloaded and installed from \code{http://matplotlib.sourceforge.net/}
1341
1342\verbatiminput{demos/cairns/GetTimeseries.py}
1343
1344Here, the time series for the quantities stage, depth and speed will be generated for
1345each gauge defined in the gauge file. As described earlier, depth is more meaningful
1346for onshore gauges, and stage is more appropriate for offshore gauges.
1347
1348As an example output,
1349Figure \ref{fig:reef} shows the time series for the quantity stage for the
1350Elford Reef location for each scenario (the elevation at this location is negative,
1351therefore stage is the more appropriate quantity to plot). Note the large negative stage value when the slide was
1352introduced. This is due to the double gaussian form of the initial surface
1353displacement of the slide. By contrast, the time series for depth is shown for the onshore location of the Cairns
1354Airport in Figure \ref{fig:airportboth}.
1355
1356\begin{figure}[hbt]
1357\centerline{\includegraphics[scale=0.5]{graphics/gaugeElfordReefstage.png}}
1358\caption{Time series information of the quantity stage for the Elford Reef location for the
1359fixed wave and slide scenario.}
1360\label{fig:reef}
1361\end{figure}
1362
1363\begin{figure}[hbt]
1364\centerline{\includegraphics[scale=0.5]{graphics/gaugeCairnsAirportdepth.png}}
1365\caption{Time series information of the quantity depth for the Cairns Airport
1366location for the slide and fixed wave scenario.}
1367\label{fig:airportboth}
1368\end{figure}
1369
1370
1371%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1372%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1373
1374\chapter{\anuga Public Interface}
1375\label{ch:interface}
1376
1377This chapter gives an overview of the features of \anuga available
1378to the user at the public interface. These are grouped under the
1379following headings, which correspond to the outline of the examples
1380described in Chapter \ref{ch:getstarted}:
1381
1382\begin{itemize}
1383    \item Establishing the Mesh: Section \ref{sec:establishing the mesh}
1384    \item Initialising the Domain: Section \ref{sec:initialising the domain}
1385    \item Specifying the Quantities: Section \ref{sec:quantitis}
1386    \item Initial Conditions: Section \ref{sec:initial conditions}
1387    \item Boundary Conditions: Section \ref{sec:boundary conditions}
1388    \item Forcing Terms: Section \ref{sec:forcing terms}
1389    \item Evolution: Section \ref{sec:evolution}
1390\end{itemize}
1391
1392The listings are intended merely to give the reader an idea of what
1393each feature is, where to find it and how it can be used---they do
1394not give full specifications; for these the reader
1395may consult the code. The code for every function or class contains
1396a documentation string, or `docstring', that specifies the precise
1397syntax for its use. This appears immediately after the line
1398introducing the code, between two sets of triple quotes.
1399
1400Each listing also describes the location of the module in which
1401the code for the feature being described can be found. All modules
1402are in the folder \file{inundation} or one of its subfolders, and the
1403location of each module is described relative to \file{inundation}. Rather
1404than using pathnames, whose syntax depends on the operating system,
1405we use the format adopted for importing the function or class for
1406use in Python code. For example, suppose we wish to specify that the
1407function \function{create\_mesh\_from\_regions} is in a module called
1408\module{mesh\_interface} in a subfolder of \module{inundation} called
1409\code{pmesh}. In Linux or Unix syntax, the pathname of the file
1410containing the function, relative to \file{inundation}, would be
1411
1412\begin{center}
1413%    \code{pmesh/mesh\_interface.py}
1414    \code{pmesh}$\slash$\code{mesh\_interface.py}
1415\end{center}
1416\label{sec:mesh interface}
1417
1418while in Windows syntax it would be
1419
1420\begin{center}
1421    \code{pmesh}$\backslash$\code{mesh\_interface.py}
1422\end{center}
1423
1424Rather than using either of these forms, in this chapter we specify
1425the location simply as \code{pmesh.mesh\_interface}, in keeping with
1426the usage in the Python statement for importing the function,
1427namely:
1428\begin{center}
1429    \code{from pmesh.mesh\_interface import create\_mesh\_from\_regions}
1430\end{center}
1431
1432Each listing details the full set of parameters for the class or
1433function; however, the description is generally limited to the most
1434important parameters and the reader is again referred to the code
1435for more details.
1436
1437The following parameters are common to many functions and classes
1438and are omitted from the descriptions given below:
1439
1440%\begin{center}
1441\begin{tabular}{ll}  %\hline
1442%\textbf{Name } & \textbf{Description}\\
1443%\hline
1444\emph{use\_cache} & Specifies whether caching is to be used for improved performance. See Section \ref{sec:caching} for details on the underlying caching functionality\\
1445\emph{verbose} & If \code{True}, provides detailed terminal output
1446to the user\\  % \hline
1447\end{tabular}
1448%\end{center}
1449
1450\section{Mesh Generation}\index{Mesh!generation}
1451\label{sec:establishing the mesh}
1452Before discussing the part of the interface relating to mesh
1453generation, we begin with a description of a simple example of a
1454mesh and use it to describe how mesh data is stored.
1455
1456\label{sec:meshexample} Figure \ref{fig:simplemesh} represents a
1457very simple mesh comprising just 11 points and 10 triangles.
1458
1459
1460\begin{figure}[h]
1461  \begin{center}
1462    \includegraphics[width=90mm, height=90mm]{triangularmesh.jpg}
1463  \end{center}
1464
1465  \caption{A simple mesh}
1466  \label{fig:simplemesh}
1467\end{figure}
1468
1469
1470The variables \code{points}, \code{vertices} and \code{boundary}
1471represent the data displayed in Figure \ref{fig:simplemesh} as
1472follows. The list \code{points} stores the coordinates of the
1473points, and may be displayed schematically as in Table
1474\ref{tab:points}.
1475
1476
1477\begin{table}
1478  \begin{center}
1479    \begin{tabular}[t]{|c|cc|} \hline
1480      index & \code{x} & \code{y}\\  \hline
1481      0 & 1 & 1\\
1482      1 & 4 & 2\\
1483      2 & 8 & 1\\
1484      3 & 1 & 3\\
1485      4 & 5 & 5\\
1486      5 & 8 & 6\\
1487      6 & 11 & 5\\
1488      7 & 3 & 6\\
1489      8 & 1 & 8\\
1490      9 & 4 & 9\\
1491      10 & 10 & 7\\  \hline
1492    \end{tabular}
1493  \end{center}
1494
1495  \caption{Point coordinates for mesh in
1496    Figure \protect \ref{fig:simplemesh}}
1497  \label{tab:points}
1498\end{table}
1499
1500The list \code{vertices} specifies the triangles that make up the
1501mesh. It does this by specifying, for each triangle, the indices
1502(the numbers shown in the first column above) that correspond to the
1503three points at its vertices, taken in an anti-clockwise order
1504around the triangle. Thus, in the example shown in Figure
1505\ref{fig:simplemesh}, the variable \code{vertices} contains the
1506entries shown in Table \ref{tab:vertices}. The starting point is
1507arbitrary so triangle $(0,1,3)$ is considered the same as $(1,3,0)$
1508and $(3,0,1)$.
1509
1510
1511\begin{table}
1512  \begin{center}
1513    \begin{tabular}{|c|ccc|} \hline
1514      index & \multicolumn{3}{c|}{\code{vertices}}\\ \hline
1515      0 & 0 & 1 & 3\\
1516      1 & 1 & 2 & 4\\
1517      2 & 2 & 5 & 4\\
1518      3 & 2 & 6 & 5\\
1519      4 & 4 & 5 & 9\\
1520      5 & 4 & 9 & 7\\
1521      6 & 3 & 4 & 7\\
1522      7 & 7 & 9 & 8\\
1523      8 & 1 & 4 & 3\\
1524      9 & 5 & 10 & 9\\  \hline
1525    \end{tabular}
1526  \end{center}
1527
1528  \caption{Vertices for mesh in Figure \protect \ref{fig:simplemesh}}
1529  \label{tab:vertices}
1530\end{table}
1531
1532Finally, the variable \code{boundary} identifies the boundary
1533triangles and associates a tag with each.
1534
1535\refmodindex[pmesh.meshinterface]{pmesh.mesh\_interface}\label{sec:meshgeneration}
1536
1537\begin{funcdesc}  {create\_mesh\_from\_regions}{bounding_polygon,
1538                             boundary_tags,
1539                             maximum_triangle_area,
1540                             filename=None,
1541                             interior_regions=None,
1542                             poly_geo_reference=None,
1543                             mesh_geo_reference=None,
1544                             minimum_triangle_angle=28.0}
1545Module: \module{pmesh.mesh\_interface}
1546
1547This function allows a user to initiate the automatic creation of a
1548mesh inside a specified polygon (input \code{bounding_polygon}).
1549Among the parameters that can be set are the \emph{resolution}
1550(maximal area for any triangle in the mesh) and the minimal angle
1551allowable in any triangle. The user can specify a number of internal
1552polygons within each of which the resolution of the mesh can be
1553specified. \code{interior_regions} is a paired list containing the
1554interior polygon and its resolution.  Additionally, the user specifies
1555a list of boundary tags, one for each edge of the bounding polygon.
1556
1557\textbf{WARNING}. Note that the dictionary structure used for the
1558parameter \code{boundary\_tags} is different from that used for the
1559variable \code{boundary} that occurs in the specification of a mesh.
1560In the case of \code{boundary}, the tags are the \emph{values} of
1561the dictionary, whereas in the case of \code{boundary_tags}, the
1562tags are the \emph{keys} and the \emph{value} corresponding to a
1563particular tag is a list of numbers identifying boundary edges
1564labelled with that tag. Because of this, it is theoretically
1565possible to assign the same edge to more than one tag. However, an
1566attempt to do this will cause an error.
1567
1568\textbf{WARNING}. Do not have polygon lines cross or be on-top of each
1569    other. This can result in regions of unspecified resolutions. Do
1570    not have polygon close to each other. This can result in the area
1571    between the polygons having small triangles.  For more control
1572    over the mesh outline use the methods described below.
1573
1574\end{funcdesc}
1575
1576
1577
1578\subsection{Advanced mesh generation}
1579
1580For more control over the creation of the mesh outline, use the
1581methods of the class \class{Mesh}.
1582
1583
1584\begin{classdesc}  {Mesh}{userSegments=None,
1585                 userVertices=None,
1586                 holes=None,
1587                 regions=None}
1588Module: \module{pmesh.mesh}
1589
1590A class used to build a mesh outline and generate a two-dimensional
1591triangular mesh. The mesh outline is used to describe features on the
1592mesh, such as the mesh boundary. Many of this classes methods are used
1593to build a mesh outline, such as \code{add\_vertices} and
1594\code{add\_region\_from\_polygon}.
1595
1596\end{classdesc}
1597
1598
1599\subsubsection{Key Methods of Class Mesh}
1600
1601
1602\begin{methoddesc} {add\_hole}{x,y}
1603Module: \module{pmesh.mesh},  Class: \class{Mesh}
1604
1605This method is used to build the mesh outline.  It defines a hole,
1606when the boundary of the hole has already been defined, by selecting a
1607point within the boundary.
1608
1609\end{methoddesc}
1610
1611
1612\begin{methoddesc}  {add\_hole\_from\_polygon}{self, polygon, tags=None}
1613Module: \module{pmesh.mesh},  Class: \class{Mesh}
1614
1615This method is used to add a `hole' within a region ---that is, to
1616define a interior region where the triangular mesh will not be
1617generated---to a \class{Mesh} instance. The region boundary is described by
1618the polygon passed in.  Additionally, the user specifies a list of
1619boundary tags, one for each edge of the bounding polygon.
1620\end{methoddesc}
1621
1622
1623\begin{methoddesc}  {add\_points_and_segments}{self, points, segments,
1624    segment\_tags=None}
1625Module: \module{pmesh.mesh},  Class: \class{Mesh}
1626
1627This method is used to build the mesh outline. It adds points and
1628segments connecting the points.  A tag for each segment can optionally
1629be added.
1630
1631\end{methoddesc}
1632
1633\begin{methoddesc} {add\_region}{x,y}
1634Module: \module{pmesh.mesh},  Class: \class{Mesh}
1635
1636This method is used to build the mesh outline.  It defines a region,
1637when the boundary of the region has already been defined, by selecting
1638a point within the boundary.  A region instance is returned.  This can
1639be used to set the resolution.
1640
1641\end{methoddesc}
1642
1643\begin{methoddesc}  {add\_region\_from\_polygon}{self, polygon,
1644segment_tags=None, region_tag=None
1645                                max_triangle_area=None}
1646Module: \module{pmesh.mesh},  Class: \class{Mesh}
1647
1648This method is used to build the mesh outline.  It adds a region to a
1649\class{Mesh} instance.  Regions are commonly used to describe an area
1650with an increased density of triangles, by setting
1651\code{max_triangle_area}.  The
1652region boundary is described by the input \code{polygon}.  Additionally, the
1653user specifies a list of segment tags, one for each edge of the
1654bounding polygon.  The regional tag is set using  \code{region}.
1655
1656\end{methoddesc}
1657
1658
1659
1660
1661
1662\begin{methoddesc} {add\_vertices}{point_data}
1663Module: \module{pmesh.mesh},  Class: \class{Mesh}
1664
1665Add user vertices. The point_data can be a list of (x,y) values, a numeric
1666array or a geospatial_data instance.
1667\end{methoddesc}
1668
1669\begin{methoddesc} {auto\_segment}{raw_boundary=raw_boundary,
1670                    remove_holes=remove_holes,
1671                    smooth_indents=smooth_indents,
1672                    expand_pinch=expand_pinch}
1673Module: \module{pmesh.mesh},  Class: \class{Mesh}
1674
1675Add segments between some of the user vertices to give the vertices an
1676outline.  The outline is an alpha shape. This method is
1677useful since a set of user vertices need to be outlined by segments
1678before generate_mesh is called.
1679
1680\end{methoddesc}
1681
1682\begin{methoddesc}  {export\_mesh_file}{self,ofile}
1683Module: \module{pmesh.mesh},  Class: \class{Mesh}
1684
1685This method is used to save the mesh to a file. \code{ofile} is the
1686name of the mesh file to be written, including the extension.  Use
1687the extension \code{.msh} for the file to be in NetCDF format and
1688\code{.tsh} for the file to be ASCII format.
1689\end{methoddesc}
1690
1691\begin{methoddesc}  {generate\_mesh}{self,
1692                      maximum_triangle_area=None,
1693                      minimum_triangle_angle=28.0,
1694                      verbose=False}
1695Module: \module{pmesh.mesh},  Class: \class{Mesh}
1696
1697This method is used to generate the triangular mesh.  The  maximal
1698area of any triangle in the mesh can be specified, which is used to
1699control the triangle density, along with the
1700minimum angle in any triangle.
1701\end{methoddesc}
1702
1703
1704
1705\begin{methoddesc}  {import_ungenerate_file}{self,ofile, tag=None,
1706region_tag=None}
1707Module: \module{pmesh.mesh},  Class: \class{Mesh}
1708
1709This method is used to import a polygon file in the ungenerate format,
1710which is used by arcGIS. The polygons from the file are converted to
1711vertices and segments. \code{ofile} is the name of the polygon file.
1712\code{tag} is the tag given to all the polygon's segments.
1713\code{region_tag} is the tag given to all the polygon's segments.  If
1714it is a string the one value will be assigned to all regions.  If it
1715is a list the first value in the list will be applied to the first
1716polygon etc.  If \code{tag} is not given a value it defaults to None,
1717which means the segement will not effect the water flow, it will only
1718effect the mesh generation.
1719
1720This function can be used to import building footprints.
1721\end{methoddesc}
1722
1723%%%%%%
1724\section{Initialising the Domain}\index{Initialising the Domain}
1725\label{sec:initialising the domain}
1726
1727%Include description of the class Domain and the module domain.
1728
1729%FIXME (Ole): This is also defined in a later chapter
1730%\declaremodule{standard}{...domain}
1731
1732\begin{classdesc} {Domain} {source=None,
1733                 triangles=None,
1734                 boundary=None,
1735                 conserved_quantities=None,
1736                 other_quantities=None,
1737                 tagged_elements=None,
1738                 use_inscribed_circle=False,
1739                 mesh_filename=None,
1740                 use_cache=False,
1741                 verbose=False,
1742                 full_send_dict=None,
1743                 ghost_recv_dict=None,
1744                 processor=0,
1745                 numproc=1}
1746Module: \refmodule{abstract_2d_finite_volumes.domain}
1747
1748This class is used to create an instance of a data structure used to
1749store and manipulate data associated with a mesh. The mesh is
1750specified either by assigning the name of a mesh file to
1751\code{source} or by specifying the points, triangle and boundary of the
1752mesh.
1753\end{classdesc}
1754
1755\subsection{Key Methods of Domain}
1756
1757\begin{methoddesc} {set\_name}{name}
1758    Module: \refmodule{abstract\_2d\_finite\_volumes.domain},
1759    page \pageref{mod:domain}
1760
1761    Assigns the name \code{name} to the domain.
1762\end{methoddesc}
1763
1764\begin{methoddesc} {get\_name}{}
1765    Module: \module{abstract\_2d\_finite\_volumes.domain}
1766
1767    Returns the name assigned to the domain by \code{set\_name}. If no name has been
1768    assigned, returns \code{`domain'}.
1769\end{methoddesc}
1770
1771\begin{methoddesc} {set\_datadir}{name}
1772    Module: \module{abstract\_2d\_finite\_volumes.domain}
1773
1774    Specifies the directory used for SWW files, assigning it to the
1775    pathname \code{name}. The default value, before
1776    \code{set\_datadir} has been run, is the value \code{default\_datadir}
1777    specified in \code{config.py}.
1778
1779    Since different operating systems use different formats for specifying pathnames,
1780    it is necessary to specify path separators using the Python code \code{os.sep}, rather than
1781    the operating-specific ones such as `$\slash$' or `$\backslash$'.
1782    For this to work you will need to include the statement \code{import os}
1783    in your code, before the first appearance of \code{set\_datadir}.
1784
1785    For example, to set the data directory to a subdirectory
1786    \code{data} of the directory \code{project}, you could use
1787    the statements:
1788
1789    {\small \begin{verbatim}
1790        import os
1791        domain.set_datadir{'project' + os.sep + 'data'}
1792    \end{verbatim}}
1793\end{methoddesc}
1794
1795\begin{methoddesc} {get\_datadir}{}
1796    Module: \module{abstract\_2d\_finite\_volumes.domain}
1797
1798    Returns the data directory set by \code{set\_datadir} or,
1799    if \code{set\_datadir} has not
1800    been run, returns the value \code{default\_datadir} specified in
1801    \code{config.py}.
1802\end{methoddesc}
1803
1804
1805\begin{methoddesc} {set\_minimum_allowed_height}{}
1806    Module: \module{shallow\_water.shallow\_water\_domain}
1807
1808    Set the minimum depth (in meters) that will be recognised in
1809    the numerical scheme (including limiters and flux computations)
1810
1811    Default value is $10^{-3}$ m, but by setting this to a greater value,
1812    e.g.\ for large scale simulations, the computation time can be
1813    significantly reduced.
1814\end{methoddesc}
1815
1816
1817\begin{methoddesc} {set\_minimum_storable_height}{}
1818    Module: \module{shallow\_water.shallow\_water\_domain}
1819
1820    Sets the minimum depth that will be recognised when writing
1821    to an sww file. This is useful for removing thin water layers
1822    that seems to be caused by friction creep.
1823\end{methoddesc}
1824
1825
1826\begin{methoddesc} {set\_maximum_allowed_speed}{}
1827    Module: \module{shallow\_water.shallow\_water\_domain}
1828
1829    Set the maximum particle speed that is allowed in water
1830    shallower than minimum_allowed_height. This is useful for
1831    controlling speeds in very thin layers of water and at the same time
1832    allow some movement avoiding pooling of water.
1833\end{methoddesc}
1834
1835
1836\begin{methoddesc} {set\_time}{time=0.0}
1837    Module: \module{abstract\_2d\_finite\_volumes.domain}
1838
1839    Sets the initial time, in seconds, for the simulation. The
1840    default is 0.0.
1841\end{methoddesc}
1842
1843\begin{methoddesc} {set\_default\_order}{n}
1844    Sets the default (spatial) order to the value specified by
1845    \code{n}, which must be either 1 or 2. (Assigning any other value
1846    to \code{n} will cause an error.)
1847\end{methoddesc}
1848
1849
1850\begin{methoddesc} {set\_store\_vertices\_uniquely}{flag}
1851Decide whether vertex values should be stored uniquely as
1852computed in the model or whether they should be reduced to one
1853value per vertex using averaging.
1854
1855Triangles stored in the sww file can be discontinuous reflecting
1856the internal representation of the finite-volume scheme
1857(this is a feature allowing for arbitrary steepness).
1858However, for visual purposes and also for use with \code{Field\_boundary}
1859(and \code{File\_boundary}) it is often desirable to store triangles
1860with values at each vertex point as the average of the potentially
1861discontinuous numbers found at vertices of different triangles sharing the
1862same vertex location.
1863
1864Storing one way or the other is controlled in ANUGA through the method
1865\code{domain.store\_vertices\_uniquely}. Options are
1866\begin{itemize}
1867  \item \code{domain.store\_vertices\_uniquely(True)}: Allow discontinuities in the sww file
1868  \item \code{domain.store\_vertices\_uniquely(False)}: (Default).
1869  Average values
1870  to ensure continuity in sww file. The latter also makes for smaller
1871  sww files.
1872\end{itemize}
1873
1874\end{methoddesc}
1875
1876
1877% Structural methods
1878\begin{methoddesc}{get\_nodes}{absolute=False}
1879    Return x,y coordinates of all nodes in mesh.
1880
1881    The nodes are ordered in an Nx2 array where N is the number of nodes.
1882    This is the same format they were provided in the constructor
1883    i.e. without any duplication.
1884
1885    Boolean keyword argument absolute determines whether coordinates
1886    are to be made absolute by taking georeference into account
1887    Default is False as many parts of ANUGA expects relative coordinates.
1888\end{methoddesc}
1889
1890
1891\begin{methoddesc}{get\_vertex_coordinates}{absolute=False}
1892
1893    Return vertex coordinates for all triangles.
1894
1895    Return all vertex coordinates for all triangles as a 3*M x 2 array
1896    where the jth vertex of the ith triangle is located in row 3*i+j and
1897    M the number of triangles in the mesh.
1898
1899    Boolean keyword argument absolute determines whether coordinates
1900    are to be made absolute by taking georeference into account
1901    Default is False as many parts of ANUGA expects relative coordinates.
1902\end{methoddesc}
1903
1904
1905\begin{methoddesc}{get\_triangles}{indices=None}
1906
1907        Return Mx3 integer array where M is the number of triangles.
1908        Each row corresponds to one triangle and the three entries are
1909        indices into the mesh nodes which can be obtained using the method
1910        get\_nodes()
1911
1912        Optional argument, indices is the set of triangle ids of interest.
1913\end{methoddesc}
1914
1915\begin{methoddesc}{get\_disconnected\_triangles}{}
1916
1917Get mesh based on nodes obtained from get_vertex_coordinates.
1918
1919        Return array Mx3 array of integers where each row corresponds to
1920        a triangle. A triangle is a triplet of indices into
1921        point coordinates obtained from get_vertex_coordinates and each
1922        index appears only once.\\
1923
1924        This provides a mesh where no triangles share nodes
1925        (hence the name disconnected triangles) and different
1926        nodes may have the same coordinates.\\
1927
1928        This version of the mesh is useful for storing meshes with
1929        discontinuities at each node and is e.g. used for storing
1930        data in sww files.\\
1931
1932        The triangles created will have the format
1933
1934    {\small \begin{verbatim}
1935        [[0,1,2],
1936         [3,4,5],
1937         [6,7,8],
1938         ...
1939         [3*M-3 3*M-2 3*M-1]]
1940     \end{verbatim}}
1941\end{methoddesc}
1942
1943
1944
1945%%%%%%
1946\section{Initial Conditions}\index{Initial Conditions}
1947\label{sec:initial conditions}
1948In standard usage of partial differential equations, initial conditions
1949refers to the values associated to the system variables (the conserved
1950quantities here) for \code{time = 0}. In setting up a scenario script
1951as described in Sections \ref{sec:simpleexample} and \ref{sec:realdataexample},
1952\code{set_quantity} is used to define the initial conditions of variables
1953other than the conserved quantities, such as friction. Here, we use the terminology
1954of initial conditions to refer to initial values for variables which need
1955prescription to solve the shallow water wave equation. Further, it must be noted
1956that \code{set_quantity} does not necessarily have to be used in the initial
1957condition setting; it can be used at any time throughout the simulation.
1958
1959\begin{methoddesc}{set\_quantity}{name,
1960    numeric = None,
1961    quantity = None,
1962    function = None,
1963    geospatial_data = None,
1964    filename = None,
1965    attribute_name = None,
1966    alpha = None,
1967    location = 'vertices',
1968    indices = None,
1969    verbose = False,
1970    use_cache = False}
1971  Module: \module{abstract\_2d\_finite\_volumes.domain}
1972  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
1973
1974This function is used to assign values to individual quantities for a
1975domain. It is very flexible and can be used with many data types: a
1976statement of the form \code{domain.set\_quantity(name, x)} can be used
1977to define a quantity having the name \code{name}, where the other
1978argument \code{x} can be any of the following:
1979
1980\begin{itemize}
1981\item a number, in which case all vertices in the mesh gets that for
1982the quantity in question.
1983\item a list of numbers or a Numeric array ordered the same way as the mesh vertices.
1984\item a function (e.g.\ see the samples introduced in Chapter 2)
1985\item an expression composed of other quantities and numbers, arrays, lists (for
1986example, a linear combination of quantities, such as
1987\code{domain.set\_quantity('stage','elevation'+x))}
1988\item the name of a file from which the data can be read. In this case, the optional argument attribute\_name will select which attribute to use from the file. If left out, set\_quantity will pick one. This is useful in cases where there is only one attribute.
1989\item a geospatial dataset (See Section \ref{sec:geospatial}).
1990Optional argument attribute\_name applies here as with files.
1991\end{itemize}
1992
1993
1994Exactly one of the arguments
1995  numeric, quantity, function, points, filename
1996must be present.
1997
1998
1999Set quantity will look at the type of the second argument (\code{numeric}) and
2000determine what action to take.
2001
2002Values can also be set using the appropriate keyword arguments.
2003If x is a function, for example, \code{domain.set\_quantity(name, x)}, \code{domain.set\_quantity(name, numeric=x)}, and \code{domain.set\_quantity(name, function=x)}
2004are all equivalent.
2005
2006
2007Other optional arguments are
2008\begin{itemize}
2009\item \code{indices} which is a list of ids of triangles to which set\_quantity should apply its assignment of values.
2010\item \code{location} determines which part of the triangles to assign
2011  to. Options are 'vertices' (default), 'edges', 'unique vertices', and 'centroids'.
2012\end{itemize}
2013
2014%%%
2015\anuga provides a number of predefined initial conditions to be used
2016with \code{set\_quantity}. See for example callable object
2017\code{slump\_tsunami} below.
2018
2019\end{methoddesc}
2020
2021
2022
2023
2024\begin{funcdesc}{set_region}{tag, quantity, X, location='vertices'}
2025  Module: \module{abstract\_2d\_finite\_volumes.domain}
2026
2027  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
2028
2029This function is used to assign values to individual quantities given
2030a regional tag.   It is similar to \code{set\_quantity}.
2031For example, if in the mesh-generator a regional tag of 'ditch' was
2032used, set\_region can be used to set elevation of this region to
2033-10m. X is the constant or function to be applied to the quantity,
2034over the tagged region.  Location describes how the values will be
2035applied.  Options are 'vertices' (default), 'edges', 'unique
2036vertices', and 'centroids'.
2037
2038This method can also be called with a list of region objects.  This is
2039useful for adding quantities in regions, and having one quantity
2040value based on another quantity. See  \module{abstract\_2d\_finite\_volumes.region} for
2041more details.
2042\end{funcdesc}
2043
2044
2045
2046
2047\begin{funcdesc}{slump_tsunami}{length, depth, slope, width=None, thickness=None,
2048                x0=0.0, y0=0.0, alpha=0.0,
2049                gravity=9.8, gamma=1.85,
2050                massco=1, dragco=1, frictionco=0, psi=0,
2051                dx=None, kappa=3.0, kappad=0.8, zsmall=0.01,
2052                domain=None,
2053                verbose=False}
2054Module: \module{shallow\_water.smf}
2055
2056This function returns a callable object representing an initial water
2057displacement generated by a submarine sediment failure. These failures can take the form of
2058a submarine slump or slide. In the case of a slide, use \code{slide_tsunami} instead.
2059
2060The arguments include as a minimum, the slump or slide length, the water depth to the centre of sediment
2061mass, and the bathymetric slope. Other slump or slide parameters can be included if they are known.
2062\end{funcdesc}
2063
2064
2065%%%
2066\begin{funcdesc}{file\_function}{filename,
2067    domain = None,
2068    quantities = None,
2069    interpolation_points = None,
2070    verbose = False,
2071    use_cache = False}
2072Module: \module{abstract\_2d\_finite\_volumes.util}
2073
2074Reads the time history of spatial data for
2075specified interpolation points from a NetCDF file (\code{filename})
2076and returns
2077a callable object. \code{filename} could be a \code{sww} or \code{sts} file.
2078Returns interpolated values based on the input
2079file using the underlying \code{interpolation\_function}.
2080
2081\code{quantities} is either the name of a single quantity to be
2082interpolated or a list of such quantity names. In the second case, the resulting
2083function will return a tuple of values---one for each quantity.
2084
2085\code{interpolation\_points} is a list of absolute coordinates or a
2086geospatial object
2087for points at which values are sought.
2088
2089\code{boundary_polygon} is a list of coordinates specifying the vertices of the boundary. This must be the same polygon as used when calling \code{create_mesh_from_regions}. This argument can only be used when reading boundary data from the STS format.
2090
2091The model time stored within the file function can be accessed using
2092the method \code{f.get\_time()}
2093
2094
2095The underlying algorithm used is as follows:\\
2096Given a time series (i.e.\ a series of values associated with
2097different times), whose values are either just numbers, a set of
2098 numbers defined at the vertices of a triangular mesh (such as those
2099 stored in SWW files) or a set of
2100 numbers defined at a number of points on the boundary (such as those
2101 stored in STS files), \code{Interpolation\_function} is used to
2102 create a callable object that interpolates a value for an arbitrary
2103 time \code{t} within the model limits and possibly a point \code{(x,
2104 y)} within a mesh region.
2105
2106 The actual time series at which data is available is specified by
2107 means of an array \code{time} of monotonically increasing times. The
2108 quantities containing the values to be interpolated are specified in
2109 an array---or dictionary of arrays (used in conjunction with the
2110 optional argument \code{quantity\_names}) --- called
2111 \code{quantities}. The optional arguments \code{vertex\_coordinates}
2112 and \code{triangles} represent the spatial mesh associated with the
2113 quantity arrays. If omitted the function must be created using an STS file
2114 or a TMS file.
2115
2116 Since, in practice, values need to be computed at specified points,
2117 the syntax allows the user to specify, once and for all, a list
2118 \code{interpolation\_points} of points at which values are required.
2119 In this case, the function may be called using the form \code{f(t,
2120 id)}, where \code{id} is an index for the list
2121 \code{interpolation\_points}.
2122
2123
2124\end{funcdesc}
2125
2126%%%
2127%% \begin{classdesc}{Interpolation\_function}{self,
2128%%     time,
2129%%     quantities,
2130%%     quantity_names = None,
2131%%     vertex_coordinates = None,
2132%%     triangles = None,
2133%%     interpolation_points = None,
2134%%     verbose = False}
2135%% Module: \module{abstract\_2d\_finite\_volumes.least\_squares}
2136
2137%% Given a time series (i.e.\ a series of values associated with
2138%% different times), whose values are either just numbers or a set of
2139%% numbers defined at the vertices of a triangular mesh (such as those
2140%% stored in SWW files), \code{Interpolation\_function} is used to
2141%% create a callable object that interpolates a value for an arbitrary
2142%% time \code{t} within the model limits and possibly a point \code{(x,
2143%% y)} within a mesh region.
2144
2145%% The actual time series at which data is available is specified by
2146%% means of an array \code{time} of monotonically increasing times. The
2147%% quantities containing the values to be interpolated are specified in
2148%% an array---or dictionary of arrays (used in conjunction with the
2149%% optional argument \code{quantity\_names}) --- called
2150%% \code{quantities}. The optional arguments \code{vertex\_coordinates}
2151%% and \code{triangles} represent the spatial mesh associated with the
2152%% quantity arrays. If omitted the function created by
2153%% \code{Interpolation\_function} will be a function of \code{t} only.
2154
2155%% Since, in practice, values need to be computed at specified points,
2156%% the syntax allows the user to specify, once and for all, a list
2157%% \code{interpolation\_points} of points at which values are required.
2158%% In this case, the function may be called using the form \code{f(t,
2159%% id)}, where \code{id} is an index for the list
2160%% \code{interpolation\_points}.
2161
2162%% \end{classdesc}
2163
2164%%%
2165%\begin{funcdesc}{set\_region}{functions}
2166%[Low priority. Will be merged into set\_quantity]
2167
2168%Module:\module{abstract\_2d\_finite\_volumes.domain}
2169%\end{funcdesc}
2170
2171
2172
2173%%%%%%
2174\section{Boundary Conditions}\index{boundary conditions}
2175\label{sec:boundary conditions}
2176
2177\anuga provides a large number of predefined boundary conditions,
2178represented by objects such as \code{Reflective\_boundary(domain)} and
2179\code{Dirichlet\_boundary([0.2, 0.0, 0.0])}, described in the examples
2180in Chapter 2. Alternatively, you may prefer to ``roll your own'',
2181following the method explained in Section \ref{sec:roll your own}.
2182
2183These boundary objects may be used with the function \code{set\_boundary} described below
2184to assign boundary conditions according to the tags used to label boundary segments.
2185
2186\begin{methoddesc}{set\_boundary}{boundary_map}
2187Module: \module{abstract\_2d\_finite\_volumes.domain}
2188
2189This function allows you to assign a boundary object (corresponding to a
2190pre-defined or user-specified boundary condition) to every boundary segment that
2191has been assigned a particular tag.
2192
2193This is done by specifying a dictionary \code{boundary\_map}, whose values are the boundary objects
2194and whose keys are the symbolic tags.
2195
2196\end{methoddesc}
2197
2198\begin{methoddesc} {get\_boundary\_tags}{}
2199Module: \module{abstract\_2d\_finite\_volumes.domain}
2200
2201Returns a list of the available boundary tags.
2202\end{methoddesc}
2203
2204%%%
2205\subsection{Predefined boundary conditions}
2206
2207\begin{classdesc}{Reflective\_boundary}{Boundary}
2208Module: \module{shallow\_water}
2209
2210Reflective boundary returns same conserved quantities as those present in
2211the neighbouring volume but reflected.
2212
2213This class is specific to the shallow water equation as it works with the
2214momentum quantities assumed to be the second and third conserved quantities.
2215\end{classdesc}
2216
2217%%%
2218\begin{classdesc}{Transmissive\_boundary}{domain = None}
2219Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2220
2221A transmissive boundary returns the same conserved quantities as
2222those present in the neighbouring volume.
2223
2224The underlying domain must be specified when the boundary is instantiated.
2225\end{classdesc}
2226
2227%%%
2228\begin{classdesc}{Dirichlet\_boundary}{conserved_quantities=None}
2229Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2230
2231A Dirichlet boundary returns constant values for each of conserved
2232quantities. In the example of \code{Dirichlet\_boundary([0.2, 0.0, 0.0])},
2233the \code{stage} value at the boundary is 0.2 and the \code{xmomentum} and
2234\code{ymomentum} at the boundary are set to 0.0. The list must contain
2235a value for each conserved quantity.
2236\end{classdesc}
2237
2238%%%
2239\begin{classdesc}{Time\_boundary}{domain = None, f = None}
2240Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2241
2242A time-dependent boundary returns values for the conserved
2243quantities as a function \code{f(t)} of time. The user must specify
2244the domain to get access to the model time.
2245\end{classdesc}
2246
2247%%%
2248\begin{classdesc}{File\_boundary}{Boundary}
2249Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2250
2251This method may be used if the user wishes to apply a SWW file, STS file or
2252a time series file (TMS) to a boundary segment or segments.
2253The boundary values are obtained from a file and interpolated to the
2254appropriate segments for each conserved quantity.
2255\end{classdesc}
2256
2257
2258
2259%%%
2260\begin{classdesc}{Transmissive\_Momentum\_Set\_Stage\_boundary}{Boundary}
2261Module: \module{shallow\_water}
2262
2263This boundary returns same momentum conserved quantities as
2264those present in its neighbour volume but sets stage as in a Time\_boundary.
2265The underlying domain must be specified when boundary is instantiated
2266
2267This type of boundary is useful when stage is known at the boundary as a
2268function of time, but momenta (or speeds) aren't.
2269
2270This class is specific to the shallow water equation as it works with the
2271momentum quantities assumed to be the second and third conserved quantities.
2272\end{classdesc}
2273
2274
2275\begin{classdesc}{Dirichlet\_Discharge\_boundary}{Boundary}
2276Module: \module{shallow\_water}
2277
2278Sets stage (stage0)
2279Sets momentum (wh0) in the inward normal direction.
2280\end{classdesc}
2281
2282
2283
2284\subsection{User-defined boundary conditions}
2285\label{sec:roll your own}
2286
2287All boundary classes must inherit from the generic boundary class
2288\code{Boundary} and have a method called \code{evaluate} which must
2289take as inputs \code{self, vol\_id, edge\_id} where self refers to the
2290object itself and vol\_id and edge\_id are integers referring to
2291particular edges. The method must return a list of three floating point
2292numbers representing values for \code{stage},
2293\code{xmomentum} and \code{ymomentum}, respectively.
2294
2295The constructor of a particular boundary class may be used to specify
2296particular values or flags to be used by the \code{evaluate} method.
2297Please refer to the source code for the existing boundary conditions
2298for examples of how to implement boundary conditions.
2299
2300
2301
2302\section{Forcing Terms}\index{Forcing terms}
2303\label{sec:forcing terms}
2304
2305\anuga provides a number of predefined forcing functions to be used with simulations.
2306Gravity and friction are always calculated using the elevation and friction quantities, but the user may additionally add forcing terms to the list
2307\code{domain.forcing\_terms} and have them affect the model.
2308 
2309Currently, predefined forcing terms are
2310
2311\begin{funcdesc}{General\_forcing}{}
2312  Module: \module{shallow\_water.shallow\_water\_domain}
2313
2314  This is a general class to modify any quantity according to a given rate of change.
2315  Other specific forcing terms are based on this class but it can be used by itself as well (e.g.\ to modify momentum).
2316 
2317  The General\_forcing class takes as input:
2318  \begin{itemize} 
2319    \item \code{domain}: a reference to the domain being evolved
2320    \item \code{quantity\_name}: The name of the quantity that will be affected by this forcing term
2321    \item \code{rate}: The rate at which the quantity should change. The parameter \code{rate} can be eithe a constant or a
2322                function of time. Positive values indicate increases,
2323                negative values indicate decreases.
2324                The parametr \code{rate} can be \code{None} at initialisation but must be specified
2325                before forcing term is applied (i.e. simulation has started).
2326                The default value is 0.0 - i.e.\ no forcing.
2327    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2328    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2329  \end{itemize}
2330  Note specifying both center, radius and polygon will cause an exception to be thrown.
2331  Moreover, if the specified polygon or circle does not lie fully within the mesh boundary an Exception will be thrown.
2332
2333  \bigskip 
2334  Example:
2335  {\scriptsize \begin{verbatim} 
2336    P = [[x0, y0], [x1, y0], [x1, y1], [x0, y1]] # Square polygon
2337 
2338    xmom = General_forcing(domain, 'xmomentum', polygon=P)
2339    ymom = General_forcing(domain, 'ymomentum', polygon=P)
2340
2341    xmom.rate = f
2342    ymom.rate = g
2343 
2344    domain.forcing_terms.append(xmom)
2345    domain.forcing_terms.append(ymom)   
2346  \end{verbatim}}
2347  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.
2348  P is assumed to be polygon, specified as a list of points.
2349 
2350\end{funcdesc} 
2351
2352
2353\begin{funcdesc}{Inflow}{}
2354  Module: \module{shallow\_water.shallow\_water\_domain}
2355
2356  This is a general class for inflow and abstraction of water according to a given rate of change.
2357  This class will always modify the \code{stage} quantity.
2358 
2359  Inflow is based on the General_forcing class so the functionality is similar.
2360 
2361  The Inflow class takes as input:
2362  \begin{itemize} 
2363    \item \code{domain}: a reference to the domain being evolved
2364    \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
2365                function of time. Positive values indicate inflow,
2366                negative values indicate outflow.
2367               
2368                Note: The specified flow will be divided by the area of
2369                the inflow region and then applied to update the
2370                stage quantity.     
2371    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2372    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2373  \end{itemize}
2374
2375  \bigskip     
2376  Example:
2377  {\scriptsize \begin{verbatim} 
2378    hydrograph = Inflow(center=(320, 300), radius=10,
2379                        rate=file_function('QPMF_Rot_Sub13.tms'))
2380
2381    domain.forcing_terms.append(hydrograph)
2382  \end{verbatim}}
2383  Here, \code{'QPMF_Rot_Sub13.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for a hydrograph.
2384\end{funcdesc} 
2385
2386
2387\begin{funcdesc}{Rainfall}{}
2388  Module: \module{shallow\_water.shallow\_water\_domain}
2389
2390  This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon.
2391  This class will always modify the \code{stage} quantity.
2392 
2393  Rainfall is based on the General_forcing class so the functionality is similar.
2394 
2395  The Rainfall class takes as input:
2396  \begin{itemize} 
2397    \item \code{domain}: a reference to the domain being evolved
2398    \item \code{rate}: Total rain rate over the specified domain. 
2399                  Note: Raingauge Data needs to reflect the time step.
2400                  For example: if rain gauge is mm read every \code{dt} seconds, then the input
2401                  here is as \code{mm/dt} so 10 mm in 5 minutes becomes
2402                  10/(5x60) = 0.0333mm/s.
2403       
2404                  This parameter can be either a constant or a
2405                  function of time. Positive values indicate rain being added (or be used for general infiltration),
2406                  negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction).
2407    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2408    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2409  \end{itemize}
2410 
2411  \bigskip   
2412  Example:
2413  {\scriptsize \begin{verbatim} 
2414 
2415    catchmentrainfall = Rainfall(rain=file_function('Q100_2hr_Rain.tms')) 
2416    domain.forcing_terms.append(catchmentrainfall)
2417
2418  \end{verbatim}}
2419  Here, \code{'Q100_2hr_Rain.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for the rainfall.
2420\end{funcdesc} 
2421
2422
2423
2424\begin{funcdesc}{Culvert\_flow}{}
2425  Module: \module{culver\_flows.culvert\_class}
2426
2427  This is a general class for implementing flow through a culvert.
2428  This class modifies the quantities \code{stage, xmomentum, ymomentum} in areas at both ends of the culvert.
2429 
2430  The Culvert\_flow forcing term uses \code{Inflow} and {General\_forcing} to update the quantities. The flow drection is determined on-the-fly so
2431  openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow and Outflow.
2432 
2433  The Culvert\_flow class takes as input:
2434  \begin{itemize} 
2435    \item \code{domain}: a reference to the domain being evolved
2436    \item \code{label}: Short text naming the culvert
2437    \item \code{description}: Text describing it
2438    \item \code{end_point0}: Coordinates of one opening
2439    \item \code{end_point1}: Coordinates of other opening
2440    \item \code{width}:
2441    \item \code{height}:
2442    \item \code{diameter}:
2443    \item \code{manning}: Mannings Roughness for Culvert
2444    \item \code{invert_level0}: Invert level if not the same as the Elevation on the Domain
2445    \item \code{invert_level1}: Invert level if not the same as the Elevation on the Domain
2446    \item \code{culvert_routine}: Function specifying the calculation of flow based on energy difference between the two openings (see below)
2447  \end{itemize}
2448
2449  The user can specify different culvert routines. Hower ANUGA currently provides only one, namely the \code{boyd\_generalised\_culvert\_model} as used in the example below.
2450     
2451  \bigskip       
2452  Example:
2453  {\scriptsize \begin{verbatim} 
2454    from anuga.culvert_flows.culvert_class import Culvert_flow
2455    from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model 
2456
2457    culvert1 = Culvert_flow(domain,
2458                           label='Culvert No. 1',
2459                           description='This culvert is a test unit 1.2m Wide by 0.75m High',   
2460                           end_point0=[9.0, 2.5],
2461                           end_point1=[13.0, 2.5],
2462                           width=1.20,height=0.75,
2463                           culvert_routine=boyd_generalised_culvert_model,       
2464                           verbose=True)
2465
2466    culvert2 = Culvert_flow(domain,
2467                           label='Culvert No. 2',
2468                           description='This culvert is a circular test with d=1.2m',   
2469                           end_point0=[9.0, 1.5],
2470                           end_point1=[30.0, 3.5],
2471                           diameter=1.20,
2472                           invert_level0=7,
2473                           culvert_routine=boyd_generalised_culvert_model,       
2474                           verbose=True)
2475                           
2476    domain.forcing_terms.append(culvert1)
2477    domain.forcing_terms.append(culvert2)
2478
2479   
2480  \end{verbatim}}
2481\end{funcdesc} 
2482
2483
2484
2485
2486
2487
2488\section{Evolution}\index{evolution}
2489\label{sec:evolution}
2490
2491  \begin{methoddesc}{evolve}{yieldstep = None, finaltime = None, duration = None, skip_initial_step = False}
2492
2493  Module: \module{abstract\_2d\_finite\_volumes.domain}
2494
2495  This function (a method of \class{domain}) is invoked once all the
2496  preliminaries have been completed, and causes the model to progress
2497  through successive steps in its evolution, storing results and
2498  outputting statistics whenever a user-specified period
2499  \code{yieldstep} is completed (generally during this period the
2500  model will evolve through several steps internally
2501  as the method forces the water speed to be calculated
2502  on successive new cells). The user
2503  specifies the total time period over which the evolution is to take
2504  place, by specifying values (in seconds) for either \code{duration}
2505  or \code{finaltime}, as well as the interval in seconds after which
2506  results are to be stored and statistics output.
2507
2508  You can include \method{evolve} in a statement of the type:
2509
2510  {\small \begin{verbatim}
2511      for t in domain.evolve(yieldstep, finaltime):
2512          <Do something with domain and t>
2513  \end{verbatim}}
2514
2515  \end{methoddesc}
2516
2517
2518
2519\subsection{Diagnostics}
2520\label{sec:diagnostics}
2521
2522
2523  \begin{funcdesc}{statistics}{}
2524  Module: \module{abstract\_2d\_finite\_volumes.domain}
2525
2526  \end{funcdesc}
2527
2528  \begin{funcdesc}{timestepping\_statistics}{}
2529  Module: \module{abstract\_2d\_finite\_volumes.domain}
2530
2531  Returns a string of the following type for each
2532  timestep:
2533
2534  \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12
2535  (12)}
2536
2537  Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and
2538  the number of first-order steps, respectively.\\
2539
2540  The optional keyword argument \code{track_speeds=True} will
2541  generate a histogram of speeds generated by each triangle. The
2542  speeds relate to the size of the timesteps used by ANUGA and
2543  this diagnostics may help pinpoint problem areas where excessive speeds
2544  are generated.
2545
2546  \end{funcdesc}
2547
2548
2549  \begin{funcdesc}{boundary\_statistics}{quantities = None, tags = None}
2550  Module: \module{abstract\_2d\_finite\_volumes.domain}
2551
2552  Returns a string of the following type when \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']}:
2553
2554  {\small \begin{verbatim}
2555 Boundary values at time 0.5000:
2556    top:
2557        stage in [ -0.25821218,  -0.02499998]
2558    bottom:
2559        stage in [ -0.27098821,  -0.02499974]
2560  \end{verbatim}}
2561
2562  \end{funcdesc}
2563
2564
2565  \begin{funcdesc}{get\_quantity}{name, location='vertices', indices = None}
2566  Module: \module{abstract\_2d\_finite\_volumes.domain}
2567
2568  Allow access to individual quantities and their methods
2569
2570  \end{funcdesc}
2571
2572
2573  \begin{funcdesc}{set\_quantities\_to\_be\_monitored}{}
2574  Module: \module{abstract\_2d\_finite\_volumes.domain}
2575
2576  Selects quantities and derived quantities for which extrema attained at internal timesteps
2577  will be collected.
2578
2579  Information can be tracked in the evolve loop by printing \code{quantity\_statistics} and
2580  collected data will be stored in the sww file.
2581
2582  Optional parameters \code{polygon} and \code{time\_interval} may be specified to restrict the
2583  extremum computation.
2584  \end{funcdesc}
2585
2586  \begin{funcdesc}{quantity\_statistics}{}
2587  Module: \module{abstract\_2d\_finite\_volumes.domain}
2588
2589  Reports on extrema attained by selected quantities.
2590
2591  Returns a string of the following type for each
2592  timestep:
2593
2594  \begin{verbatim}
2595  Monitored quantities at time 1.0000:
2596    stage-elevation:
2597      values since time = 0.00 in [0.00000000, 0.30000000]
2598      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2599      maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667)
2600    ymomentum:
2601      values since time = 0.00 in [0.00000000, 0.06241221]
2602      minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667)
2603      maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667)
2604    xmomentum:
2605      values since time = 0.00 in [-0.06062178, 0.47886313]
2606      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2607      maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667)
2608  \end{verbatim}
2609
2610  The quantities (and derived quantities) listed here must be selected at model
2611  initialisation using the method \code{domain.set_quantities_to_be_monitored}.\\
2612
2613  The optional keyword argument \code{precision='\%.4f'} will
2614  determine the precision used for floating point values in the output.
2615  This diagnostics helps track extrema attained by the selected quantities
2616  at every internal timestep.
2617
2618  These values are also stored in the sww file for post processing.
2619
2620  \end{funcdesc}
2621
2622
2623
2624  \begin{funcdesc}{get\_values}{location='vertices', indices = None}
2625  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2626
2627  Extract values for quantity as an array
2628
2629  \end{funcdesc}
2630
2631
2632  \begin{funcdesc}{get\_integral}{}
2633  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2634
2635  Return computed integral over entire domain for this quantity
2636
2637  \end{funcdesc}
2638
2639
2640
2641
2642  \begin{funcdesc}{get\_maximum\_value}{indices = None}
2643  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2644
2645  Return maximum value of quantity (on centroids)
2646
2647  Optional argument indices is the set of element ids that
2648  the operation applies to. If omitted all elements are considered.
2649
2650  We do not seek the maximum at vertices as each vertex can
2651  have multiple values - one for each triangle sharing it.
2652  \end{funcdesc}
2653
2654
2655
2656  \begin{funcdesc}{get\_maximum\_location}{indices = None}
2657  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2658
2659  Return location of maximum value of quantity (on centroids)
2660
2661  Optional argument indices is the set of element ids that
2662  the operation applies to.
2663
2664  We do not seek the maximum at vertices as each vertex can
2665  have multiple values - one for each triangle sharing it.
2666
2667  If there are multiple cells with same maximum value, the
2668  first cell encountered in the triangle array is returned.
2669  \end{funcdesc}
2670
2671
2672
2673  \begin{funcdesc}{get\_wet\_elements}{indices=None}
2674  Module: \module{shallow\_water.shallow\_water\_domain}
2675
2676  Return indices for elements where h $>$ minimum_allowed_height
2677  Optional argument indices is the set of element ids that the operation applies to.
2678  \end{funcdesc}
2679
2680
2681  \begin{funcdesc}{get\_maximum\_inundation\_elevation}{indices=None}
2682  Module: \module{shallow\_water.shallow\_water\_domain}
2683
2684  Return highest elevation where h $>$ 0.\\
2685  Optional argument indices is the set of element ids that the operation applies to.\\
2686
2687  Example to find maximum runup elevation:\\
2688     z = domain.get_maximum_inundation_elevation()
2689  \end{funcdesc}
2690
2691
2692  \begin{funcdesc}{get\_maximum\_inundation\_location}{indices=None}
2693  Module: \module{shallow\_water.shallow\_water\_domain}
2694
2695  Return location (x,y) of highest elevation where h $>$ 0.\\
2696  Optional argument indices is the set of element ids that the operation applies to.\\
2697
2698  Example to find maximum runup location:\\
2699     x, y = domain.get_maximum_inundation_location()
2700  \end{funcdesc}
2701
2702
2703\section{Queries of SWW model output files}
2704After a model has been run, it is often useful to extract various information from the sww
2705output file (see Section \ref{sec:sww format}). This is typically more convenient than using the
2706diagnostics described in Section \ref{sec:diagnostics} which rely on the model running - something
2707that can be very time consuming. The sww files are easy and quick to read and offer much information
2708about the model results such as runup heights, time histories of selected quantities,
2709flow through cross sections and much more.
2710
2711\begin{funcdesc}{get\_maximum\_inundation\_elevation}{filename, polygon=None,
2712    time_interval=None, verbose=False}
2713  Module: \module{shallow\_water.data\_manager}
2714
2715  Return highest elevation where depth is positive ($h > 0$)
2716
2717  Example to find maximum runup elevation:\\
2718  max_runup = get_maximum_inundation_elevation(filename,
2719  polygon=None,
2720  time_interval=None,
2721  verbose=False)
2722
2723
2724  filename is a NetCDF sww file containing ANUGA model output.
2725  Optional arguments polygon and time_interval restricts the maximum runup calculation
2726  to a points that lie within the specified polygon and time interval.
2727
2728  If no inundation is found within polygon and time_interval the return value
2729  is None signifying "No Runup" or "Everything is dry".
2730
2731  See doc string for general function get_maximum_inundation_data for details.
2732\end{funcdesc}
2733
2734
2735\begin{funcdesc}{get\_maximum\_inundation\_location}{filename, polygon=None,
2736    time_interval=None, verbose=False}
2737  Module: \module{shallow\_water.data\_manager}
2738
2739  Return location (x,y) of highest elevation where depth is positive ($h > 0$)
2740
2741  Example to find maximum runup location:\\
2742  max_runup_location = get_maximum_inundation_location(filename,
2743  polygon=None,
2744  time_interval=None,
2745  verbose=False)
2746
2747
2748  filename is a NetCDF sww file containing ANUGA model output.
2749  Optional arguments polygon and time_interval restricts the maximum runup calculation
2750  to a points that lie within the specified polygon and time interval.
2751
2752  If no inundation is found within polygon and time_interval the return value
2753  is None signifying "No Runup" or "Everything is dry".
2754
2755  See doc string for general function get_maximum_inundation_data for details.
2756\end{funcdesc}
2757
2758
2759\begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report = None, reportname = None,
2760plot_quantity = None, generate_fig = False, surface = None, time_min = None, time_max = None, time_thinning = 1,
2761time_unit = None, title_on = None, use_cache = False, verbose = False}
2762
2763  Module: \module{anuga.abstract\_2d\_finite\_volumes.util}
2764
2765  Return csv files for the location in the \code{gauge_filename} and can also return plots of them
2766
2767  See doc string for general function sww2timeseries for details.
2768
2769\end{funcdesc}
2770
2771
2772\begin{funcdesc}{get\_flow\_through\_cross\_section}{filename, cross\_section, verbose=False}
2773  Module: \module{shallow\_water.data\_manager}
2774
2775  Obtain flow $[m^3/s]$ perpendicular to specified cross section.
2776
2777  Inputs:
2778  \begin{itemize} 
2779        \item filename: Name of sww file containing ANUGA model output.
2780        \item polyline: Representation of desired cross section - it may contain multiple
2781          sections allowing for complex shapes. Assume absolute UTM coordinates.
2782  \end{itemize} 
2783
2784  Output:
2785  \begin{itemize}
2786    \item time: All stored times in sww file
2787    \item Q: Hydrograph of total flow across given segments for all stored times.
2788  \end{itemize} 
2789 
2790  The normal flow is computed for each triangle intersected by the polyline and
2791  added up.  Multiple segments at different angles are specified the normal flows
2792  may partially cancel each other.
2793 
2794  Example to find flow through cross section:
2795 
2796  \begin{verbatim} 
2797  cross_section = [[x, 0], [x, width]]
2798  time, Q = get_flow_through_cross_section(filename,
2799                                           cross_section,
2800                                           verbose=False)
2801  \end{verbatim} 
2802
2803
2804  See doc string for general function get_maximum_inundation_data for details.
2805 
2806\end{funcdesc}
2807
2808
2809
2810\section{Other}
2811
2812  \begin{funcdesc}{domain.create\_quantity\_from\_expression}{string}
2813
2814  Handy for creating derived quantities on-the-fly as for example
2815  \begin{verbatim}
2816  Depth = domain.create_quantity_from_expression('stage-elevation')
2817
2818  exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5')
2819  Absolute_momentum = domain.create_quantity_from_expression(exp)
2820  \end{verbatim}
2821
2822  %See also \file{Analytical\_solution\_circular\_hydraulic\_jump.py} for an example of use.
2823  \end{funcdesc}
2824
2825
2826
2827
2828
2829%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2830%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2831
2832\chapter{\anuga System Architecture}
2833
2834
2835\section{File Formats}
2836\label{sec:file formats}
2837
2838\anuga makes use of a number of different file formats. The
2839following table lists all these formats, which are described in more
2840detail in the paragraphs below.
2841
2842\bigskip
2843
2844\begin{center}
2845
2846\begin{tabular}{|ll|}  \hline
2847
2848\textbf{Extension} & \textbf{Description} \\
2849\hline\hline
2850
2851\code{.sww} & NetCDF format for storing model output with mesh information
2852\code{f(t,x,y)}\\
2853
2854\code{.sts} & NetCDF format for storing model ouput \code{f(t,x,y)} without any mesh information\\
2855
2856\code{.tms} & NetCDF format for storing time series \code{f(t)}\\
2857
2858\code{.csv/.txt} & ASCII format called points csv for storing
2859arbitrary points and associated attributes\\
2860
2861\code{.pts} & NetCDF format for storing arbitrary points and
2862associated attributes\\
2863
2864\code{.asc} & ASCII format of regular DEMs as output from ArcView\\
2865
2866\code{.prj} & Associated ArcView file giving more metadata for
2867\code{.asc} format\\
2868
2869\code{.ers} & ERMapper header format of regular DEMs for ArcView\\
2870
2871\code{.dem} & NetCDF representation of regular DEM data\\
2872
2873\code{.tsh} & ASCII format for storing meshes and associated
2874boundary and region info\\
2875
2876\code{.msh} & NetCDF format for storing meshes and associated
2877boundary and region info\\
2878
2879\code{.nc} & Native ferret NetCDF format\\
2880
2881\code{.geo} & Houdinis ASCII geometry format (?) \\  \par \hline
2882%\caption{File formats used by \anuga}
2883\end{tabular}
2884
2885
2886\end{center}
2887
2888The above table shows the file extensions used to identify the
2889formats of files. However, typically, in referring to a format we
2890capitalise the extension and omit the initial full stop---thus, we
2891refer, for example, to `SWW files' or `PRJ files'.
2892
2893\bigskip
2894
2895A typical dataflow can be described as follows:
2896
2897\subsection{Manually Created Files}
2898
2899\begin{tabular}{ll}
2900ASC, PRJ & Digital elevation models (gridded)\\
2901NC & Model outputs for use as boundary conditions (e.g. from MOST)
2902\end{tabular}
2903
2904\subsection{Automatically Created Files}
2905
2906\begin{tabular}{ll}
2907ASC, PRJ  $\rightarrow$  DEM  $\rightarrow$  PTS & Convert
2908DEMs to native \code{.pts} file\\
2909
2910NC $\rightarrow$ SWW & Convert MOST boundary files to
2911boundary \code{.sww}\\
2912
2913PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\
2914
2915TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using
2916\code{animate}\\
2917
2918TSH + Boundary SWW $\rightarrow$ SWW & Simulation using
2919\code{\anuga}\\
2920
2921Polygonal mesh outline $\rightarrow$ & TSH or MSH
2922\end{tabular}
2923
2924
2925
2926
2927\bigskip
2928
2929\subsection{SWW, STS and TMS Formats}
2930\label{sec:sww format}
2931
2932The SWW, STS and TMS formats are all NetCDF formats, and are of key
2933importance for \anuga.
2934
2935An SWW file is used for storing \anuga output and therefore pertains
2936to a set of points and a set of times at which a model is evaluated.
2937It contains, in addition to dimension information, the following
2938variables:
2939
2940\begin{itemize}
2941    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2942    \item \code{elevation}, a Numeric array storing bed-elevations
2943    \item \code{volumes}, a list specifying the points at the vertices of each of the
2944    triangles
2945    % Refer here to the example to be provided in describing the simple example
2946    \item \code{time}, a Numeric array containing times for model
2947    evaluation
2948\end{itemize}
2949
2950
2951The contents of an SWW file may be viewed using the anuga viewer
2952\code{animate}, which creates an on-screen geometric
2953representation. See section \ref{sec:animate} (page
2954\pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more
2955on \code{animate}.
2956
2957Alternatively, there are tools, such as \code{ncdump}, that allow
2958you to convert an NetCDF file into a readable format such as the
2959Class Definition Language (CDL). The following is an excerpt from a
2960CDL representation of the output file \file{runup.sww} generated
2961from running the simple example \file{runup.py} of
2962Chapter \ref{ch:getstarted}:
2963
2964\verbatiminput{examples/bedslopeexcerpt.cdl}
2965
2966The SWW format is used not only for output but also serves as input
2967for functions such as \function{file\_boundary} and
2968\function{file\_function}, described in Chapter \ref{ch:interface}.
2969
2970An STS file is used for storing a set of points and and associated set of times.
2971It contains, in addition to dimension information, the following
2972variables:
2973\begin{itemize}
2974    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2975    \item \code{elevation}, a Numeric array storing bed-elevations
2976    % Refer here to the example to be provided in describing the simple example
2977    \item \code{time}, a Numeric array containing times for model
2978    evaluation
2979\end{itemize}
2980The only difference between the STS format and the SWW format is the former does not contain a list specifying the points at the vertices of each of the triangles (\code{volumes}). Consequenlty information (arrays) stored within an STS file such as \code{elevation} can be accessed in exactly the same way as it would be extraced from an SWW file.
2981
2982A TMS file is used to store time series data that is independent of
2983position.
2984
2985
2986\subsection{Mesh File Formats}
2987
2988A mesh file is a file that has a specific format suited to
2989triangular meshes and their outlines. A mesh file can have one of
2990two formats: it can be either a TSH file, which is an ASCII file, or
2991an MSH file, which is a NetCDF file. A mesh file can be generated
2992from the function \function{create\_mesh\_from\_regions} (see
2993Section \ref{sec:meshgeneration}) and used to initialise a domain.
2994
2995A mesh file can define the outline of the mesh---the vertices and
2996line segments that enclose the region in which the mesh is
2997created---and the triangular mesh itself, which is specified by
2998listing the triangles and their vertices, and the segments, which
2999are those sides of the triangles that are associated with boundary
3000conditions.
3001
3002In addition, a mesh file may contain `holes' and/or `regions'. A
3003hole represents an area where no mesh is to be created, while a
3004region is a labelled area used for defining properties of a mesh,
3005such as friction values.  A hole or region is specified by a point
3006and bounded by a number of segments that enclose that point.
3007
3008A mesh file can also contain a georeference, which describes an
3009offset to be applied to $x$ and $y$ values---eg to the vertices.
3010
3011
3012\subsection{Formats for Storing Arbitrary Points and Attributes}
3013
3014
3015A CSV/TXT file is used to store data representing
3016arbitrary numerical attributes associated with a set of points.
3017
3018The format for an CSV/TXT file is:\\
3019%\begin{verbatim}
3020
3021            first line:     \code{[column names]}\\
3022            other lines:  \code{[x value], [y value], [attributes]}\\
3023
3024            for example:\\
3025            \code{x, y, elevation, friction}\\
3026            \code{0.6, 0.7, 4.9, 0.3}\\
3027            \code{1.9, 2.8, 5, 0.3}\\
3028            \code{2.7, 2.4, 5.2, 0.3}
3029
3030        The delimiter is a comma. The first two columns are assumed to
3031        be x, y coordinates.
3032       
3033
3034A PTS file is a NetCDF representation of the data held in an points CSV
3035file. If the data is associated with a set of $N$ points, then the
3036data is stored using an $N \times 2$ Numeric array of float
3037variables for the points and an $N \times 1$ Numeric array for each
3038attribute.
3039
3040%\end{verbatim}
3041
3042\subsection{ArcView Formats}
3043
3044Files of the three formats ASC, PRJ and ERS are all associated with
3045data from ArcView.
3046
3047An ASC file is an ASCII representation of DEM output from ArcView.
3048It contains a header with the following format:
3049
3050\begin{tabular}{l l}
3051\code{ncols}      &   \code{753}\\
3052\code{nrows}      &   \code{766}\\
3053\code{xllcorner}  &   \code{314036.58727982}\\
3054\code{yllcorner}  & \code{6224951.2960092}\\
3055\code{cellsize}   & \code{100}\\
3056\code{NODATA_value} & \code{-9999}
3057\end{tabular}
3058
3059The remainder of the file contains the elevation data for each grid point
3060in the grid defined by the above information.
3061
3062A PRJ file is an ArcView file used in conjunction with an ASC file
3063to represent metadata for a DEM.
3064
3065
3066\subsection{DEM Format}
3067
3068A DEM file in \anuga is a NetCDF representation of regular DEM data.
3069
3070
3071\subsection{Other Formats}
3072
3073
3074
3075
3076\subsection{Basic File Conversions}
3077\label{sec:basicfileconversions}
3078
3079  \begin{funcdesc}{sww2dem}{basename_in, basename_out = None,
3080            quantity = None,
3081            timestep = None,
3082            reduction = None,
3083            cellsize = 10,
3084            number_of_decimal_places = None,
3085            NODATA_value = -9999,
3086            easting_min = None,
3087            easting_max = None,
3088            northing_min = None,
3089            northing_max = None,
3090            expand_search = False,
3091            verbose = False,
3092            origin = None,
3093            datum = 'WGS84',
3094            format = 'ers'}
3095  Module: \module{shallow\_water.data\_manager}
3096
3097  Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or
3098  ERS) of a desired grid size \code{cellsize} in metres. The user can select how
3099  many the decimal places the output data can be written to using \code{number_of_decimal_places},
3100  with the default being 3.
3101  The easting and northing values are used if the user wished to determine the output
3102  within a specified rectangular area. The \code{reduction} input refers to a function
3103  to reduce the quantities over all time step of the SWW file, example, maximum.
3104  \end{funcdesc}
3105
3106
3107  \begin{funcdesc}{dem2pts}{basename_in, basename_out=None,
3108            easting_min=None, easting_max=None,
3109            northing_min=None, northing_max=None,
3110            use_cache=False, verbose=False}
3111  Module: \module{shallow\_water.data\_manager}
3112
3113  Takes DEM data (a NetCDF file representation of data from a regular Digital
3114  Elevation Model) and converts it to PTS format.
3115  \end{funcdesc}
3116
3117  \begin{funcdesc}{urs2sts}{basename_in, basename_out=None,
3118            weights=None, verbose=False,
3119            origin=None,mean_stage=0.0,
3120            zscale=1.0, ordering_filename=None}
3121  Module: \module{shallow\_water.data\_manager}
3122
3123  Takes urs data in (timeseries data in mux2 format) and converts it to STS format.
3124  \end{funcdesc}
3125
3126
3127
3128%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3129%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3130
3131\chapter{\anuga mathematical background}
3132\label{cd:mathematical background}
3133
3134\section{Introduction}
3135
3136This chapter outlines the mathematics underpinning \anuga.
3137
3138
3139
3140\section{Model}
3141\label{sec:model}
3142
3143The shallow water wave equations are a system of differential
3144conservation equations which describe the flow of a thin layer of
3145fluid over terrain. The form of the equations are:
3146\[
3147\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
3148x}+\frac{\partial \GG}{\partial y}=\SSS
3149\]
3150where $\UU=\left[ {{\begin{array}{*{20}c}
3151 h & {uh} & {vh} \\
3152\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
3153$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
3154entering the system are bed elevation $z$ and stage (absolute water
3155level) $w$, where the relation $w = z + h$ holds true at all times.
3156The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
3157by
3158\[
3159\EE=\left[ {{\begin{array}{*{20}c}
3160 {uh} \hfill \\
3161 {u^2h+gh^2/2} \hfill \\
3162 {uvh} \hfill \\
3163\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
3164 {vh} \hfill \\
3165 {vuh} \hfill \\
3166 {v^2h+gh^2/2} \hfill \\
3167\end{array} }} \right]
3168\]
3169and the source term (which includes gravity and friction) is given
3170by
3171\[
3172\SSS=\left[ {{\begin{array}{*{20}c}
3173 0 \hfill \\
3174 -{gh(z_{x} + S_{fx} )} \hfill \\
3175 -{gh(z_{y} + S_{fy} )} \hfill \\
3176\end{array} }} \right]
3177\]
3178where $S_f$ is the bed friction. The friction term is modelled using
3179Manning's resistance law
3180\[
3181S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
3182=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
3183\]
3184in which $\eta$ is the Manning resistance coefficient.
3185The model does not currently include consideration of kinematic viscosity.
3186
3187As demonstrated in our papers, \cite{ZR1999,nielsen2005} these
3188equations and their implementation in \anuga provide a reliable
3189model of general flows associated with inundation such as dam breaks
3190and tsunamis.
3191
3192\section{Finite Volume Method}
3193\label{sec:fvm}
3194
3195We use a finite-volume method for solving the shallow water wave
3196equations \cite{ZR1999}. The study area is represented by a mesh of
3197triangular cells as in Figure~\ref{fig:mesh} in which the conserved
3198quantities of  water depth $h$, and horizontal momentum $(uh, vh)$,
3199in each volume are to be determined. The size of the triangles may
3200be varied within the mesh to allow greater resolution in regions of
3201particular interest.
3202
3203\begin{figure}
3204\begin{center}
3205\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five}
3206\caption{Triangular mesh used in our finite volume method. Conserved
3207quantities $h$, $uh$ and $vh$ are associated with the centroid of
3208each triangular cell.} \label{fig:mesh}
3209\end{center}
3210\end{figure}
3211
3212The equations constituting the finite-volume method are obtained by
3213integrating the differential conservation equations over each
3214triangular cell of the mesh. Introducing some notation we use $i$ to
3215refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the
3216set of indices referring to the cells neighbouring the $i$th cell.
3217Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is
3218the length of the edge between the $i$th and $j$th cells.
3219
3220By applying the divergence theorem we obtain for each volume an
3221equation which describes the rate of change of the average of the
3222conserved quantities within each cell, in terms of the fluxes across
3223the edges of the cells and the effect of the source terms. In
3224particular, rate equations associated with each cell have the form
3225$$
3226 \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i
3227$$
3228where
3229\begin{itemize}
3230\item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell,
3231\item $\SSS_i$ is the source term associated with the $i$th cell,
3232and
3233\item $\HH_{ij}$ is the outward normal flux of
3234material across the \textit{ij}th edge.
3235\end{itemize}
3236
3237
3238%\item $l_{ij}$ is the length of the edge between the $i$th and $j$th
3239%cells
3240%\item $m_{ij}$ is the midpoint of
3241%the \textit{ij}th edge,
3242%\item
3243%$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing
3244%normal along the \textit{ij}th edge, and The
3245
3246The flux $\HH_{ij}$ is evaluated using a numerical flux function
3247$\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow
3248water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$
3249$$
3250H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 .
3251$$
3252
3253Then
3254$$
3255\HH_{ij}  = \HH(\UU_i(m_{ij}),
3256\UU_j(m_{ij}); \mathbf{n}_{ij})
3257$$
3258where $m_{ij}$ is the midpoint of the \textit{ij}th edge and
3259$\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the
3260\textit{ij}th edge. The function $\UU_i(x)$ for $x \in
3261T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and
3262neighbouring  cells.
3263
3264We use a second order reconstruction to produce a piece-wise linear
3265function construction of the conserved quantities for  all $x \in
3266T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This
3267function is allowed to be discontinuous across the edges of the
3268cells, but the slope of this function is limited to avoid
3269artificially introduced oscillations.
3270
3271Godunov's method (see \cite{Toro1992}) involves calculating the
3272numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly
3273solving the corresponding one dimensional Riemann problem normal to
3274the edge. We use the central-upwind scheme of \cite{KurNP2001} to
3275calculate an approximation of the flux across each edge.
3276
3277\begin{figure}
3278\begin{center}
3279\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct}
3280\caption{From the values of the conserved quantities at the centroid
3281of the cell and its neighbouring cells, a discontinuous piecewise
3282linear reconstruction of the conserved quantities is obtained.}
3283\label{fig:mesh:reconstruct}
3284\end{center}
3285\end{figure}
3286
3287In the computations presented in this paper we use an explicit Euler
3288time stepping method with variable timestepping adapted to the
3289observed CFL condition:
3290
3291\begin{equation} 
3292  \Delta t = \min_{k,i=[0,1,2]}  \min \left( \frac{r_k}{v_{k,i}}, \frac{r_{n_{k,i}}}{v_{k,i}} \right )
3293  \label{eq:CFL condition}
3294\end{equation} 
3295where $r_k$ is the radius of the $k$'th triangle and $v_{k,i}$ is the maximal velocity across
3296edge joining triangle $k$ and it's $i$'th neighbour, triangle $n_{k,i}$, as calculated by the
3297numerical flux function
3298using the central upwind scheme of \cite{KurNP2001}. The symbol $r_{n_{k,i}}$  denotes the radius
3299of the $i$'th neighbour of triangle $k$. The radii are calculated as radii of the inscribed circles
3300of each triangle.
3301
3302\section{Flux limiting}
3303
3304The shallow water equations are solved numerically using a
3305finite volume method on unstructured triangular grid.
3306The upwind central scheme due to Kurganov and Petrova is used as an
3307approximate Riemann solver for the computation of inviscid flux functions.
3308This makes it possible to handle discontinuous solutions.
3309
3310To alleviate the problems associated with numerical instabilities due to
3311small water depths near a wet/dry boundary we employ a new flux limiter that
3312ensures that unphysical fluxes are never encounted.
3313
3314
3315Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction,
3316$w$ the absolute water level (stage) and
3317$z$ the bed elevation. The latter are assumed to be relative to the
3318same height datum.
3319The conserved quantities tracked by ANUGA are momentum in the
3320$x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$)
3321and depth ($h = w-z$).
3322
3323The flux calculation requires access to the velocity vector $(u, v)$
3324where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively.
3325In the presence of very small water depths, these calculations become
3326numerically unreliable and will typically cause unphysical speeds.
3327
3328We have employed a flux limiter which replaces the calculations above with
3329the limited approximations.
3330\begin{equation}
3331  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
3332\end{equation}
3333where $h_0$ is a regularisation parameter that controls the minimal
3334magnitude of the denominator. Taking the limits we have for $\hat{u}$
3335\[
3336  \lim_{h \rightarrow 0} \hat{u} =
3337  \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0
3338\]
3339and
3340\[
3341  \lim_{h \rightarrow \infty} \hat{u} =
3342  \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u
3343\]
3344with similar results for $\hat{v}$.
3345
3346The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator)
3347\[
3348  1 - h_0/h^2 = 0
3349\]
3350or
3351\[
3352  h_0 = h^2
3353\]
3354
3355
3356ANUGA has a global parameter $H_0$ that controls the minimal depth which
3357is considered in the various equations. This parameter is typically set to
3358$10^{-3}$. Setting
3359\[
3360  h_0 = H_0^2
3361\]
3362provides a reasonable balance between accurracy and stability. In fact,
3363setting $h=H_0$ will scale the predicted speed by a factor of $0.5$:
3364\[
3365  \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \frac{\mu}{2 H_0}
3366\]
3367In general, for multiples of the minimal depth $N H_0$ one obtains
3368\[
3369  \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
3370  \frac{\mu}{H_0 (1 + 1/N^2)}
3371\]
3372which converges quadratically to the true value with the multiple N.
3373
3374
3375%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.
3376
3377
3378
3379
3380
3381\section{Slope limiting}
3382A 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.
3383
3384However 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.
3385
3386
3387Let $w, z, h$  be the stage, bed elevation and depth at the centroid and
3388let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$.
3389Define the minimal depth across all vertices as $\hmin$ as
3390\[
3391  \hmin = \min_i h_i
3392\]
3393
3394Let $\tilde{w_i}$ be the stage obtained from a gradient limiter
3395limiting on stage only. The corresponding depth is then defined as
3396\[
3397  \tilde{h_i} = \tilde{w_i} - z_i
3398\]
3399We would use this limiter in deep water which we will define (somewhat boldly)
3400as
3401\[
3402  \hmin \ge \epsilon
3403\]
3404
3405
3406Similarly, let $\bar{w_i}$ be the stage obtained from a gradient
3407limiter limiting on depth respecting the bed slope.
3408The corresponding depth is defined as
3409\[
3410  \bar{h_i} = \bar{w_i} - z_i
3411\]
3412
3413
3414We introduce the concept of a balanced stage $w_i$ which is obtained as
3415the linear combination
3416
3417\[
3418  w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i}
3419\]
3420or
3421\[
3422  w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i}
3423\]
3424where $\alpha \in [0, 1]$.
3425
3426Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope
3427is ignored we have immediately that
3428\[
3429  \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0
3430\]
3431%where the maximal bed elevation range $dz$ is defined as
3432%\[
3433%  dz = \max_i |z_i - z|
3434%\]
3435
3436If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that
3437no negative depths occur. Formally, we will require that
3438\[
3439  \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i
3440\]
3441or
3442\begin{equation}
3443  \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i
3444  \label{eq:limiter bound}
3445\end{equation}
3446
3447There are two cases:
3448\begin{enumerate}
3449  \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage)
3450  vertex is at least as far away from the bed than the shallow water
3451  (limited using depth). In this case we won't need any contribution from
3452  $\bar{h_i}$ and can accept any $\alpha$.
3453
3454  E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to
3455  \[
3456    \tilde{h_i} > \epsilon
3457  \]
3458  whereas $\alpha=0$ yields
3459  \[
3460    \bar{h_i} > \epsilon
3461  \]
3462  all well and good.
3463  \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is
3464  closer to the bed than the shallow water vertex or even below the bed.
3465  In this case we need to find an $\alpha$ that will ensure a positive depth.
3466  Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one
3467  obtains the bound
3468  \[
3469    \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i
3470  \]
3471\end{enumerate}
3472
3473Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one
3474arrives at the definition
3475\[
3476  \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}}
3477\]
3478which will guarantee that no vertex 'cuts' through the bed. Finally, should
3479$\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting
3480$\alpha=0$ and similarly capping $\alpha$ at 1 just in case.
3481
3482%Furthermore,
3483%dropping the $\epsilon$ ensures that alpha is always positive and also
3484%provides a numerical safety {??)
3485
3486
3487
3488
3489
3490%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3491%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3492
3493\chapter{Basic \anuga Assumptions}
3494
3495
3496Physical model time cannot be earlier than 1 Jan 1970 00:00:00.
3497If one wished to recreate scenarios prior to that date it must be done
3498using some relative time (e.g. 0).
3499
3500
3501All spatial data relates to the WGS84 datum (or GDA94) and has been
3502projected into UTM with false easting of 500000 and false northing of
35031000000 on the southern hemisphere (0 on the northern).
3504
3505It is assumed that all computations take place within one UTM zone and
3506all locations must consequently be specified in Cartesian coordinates
3507(eastings, northings) or (x,y) where the unit is metres.
3508
3509DEMs, meshes and boundary conditions can have different origins within
3510one UTM zone. However, the computation will use that of the mesh for
3511numerical stability.
3512
3513When generating a mesh it is assumed that polygons do not cross.
3514Having polygons tht cross can cause the mesh generation to fail or bad
3515meshes being produced.
3516
3517
3518%OLD
3519%The dataflow is: (See data_manager.py and from scenarios)
3520%
3521%
3522%Simulation scenarios
3523%--------------------%
3524%%
3525%
3526%Sub directories contain scrips and derived files for each simulation.
3527%The directory ../source_data contains large source files such as
3528%DEMs provided externally as well as MOST tsunami simulations to be used
3529%as boundary conditions.
3530%
3531%Manual steps are:
3532%  Creation of DEMs from argcview (.asc + .prj)
3533%  Creation of mesh from pmesh (.tsh)
3534%  Creation of tsunami simulations from MOST (.nc)
3535%%
3536%
3537%Typical scripted steps are%
3538%
3539%  prepare_dem.py:  Convert asc and prj files supplied by arcview to
3540%                   native dem and pts formats%
3541%
3542%  prepare_pts.py: Convert netcdf output from MOST to an sww file suitable
3543%                  as boundary condition%
3544%
3545%  prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares
3546%                   smoothing. The outputs are tsh files with elevation data.%
3547%
3548%  run_simulation.py: Use the above together with various parameters to
3549%                     run inundation simulation.
3550
3551
3552%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3553%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3554
3555\appendix
3556
3557\chapter{Supporting Tools}
3558\label{ch:supportingtools}
3559
3560This section describes a number of supporting tools, supplied with \anuga, that offer a
3561variety of types of functionality and enhance the basic capabilities of \anuga.
3562
3563\section{caching}
3564\label{sec:caching}
3565
3566The \code{cache} function is used to provide supervised caching of function
3567results. A Python function call of the form
3568
3569      {\small \begin{verbatim}
3570      result = func(arg1,...,argn)
3571      \end{verbatim}}
3572
3573  can be replaced by
3574
3575      {\small \begin{verbatim}
3576      from caching import cache
3577      result = cache(func,(arg1,...,argn))
3578      \end{verbatim}}
3579
3580  which returns the same output but reuses cached
3581  results if the function has been computed previously in the same context.
3582  \code{result} and the arguments can be simple types, tuples, list, dictionaries or
3583  objects, but not unhashable types such as functions or open file objects.
3584  The function \code{func} may be a member function of an object or a module.
3585
3586  This type of caching is particularly useful for computationally intensive
3587  functions with few frequently used combinations of input arguments. Note that
3588  if the inputs or output are very large caching may not save time because
3589  disc access may dominate the execution time.
3590
3591  If the function definition changes after a result has been cached, this will be
3592  detected by examining the functions \code{bytecode (co\_code, co\_consts,
3593  func\_defaults, co\_argcount)} and the function will be recomputed.
3594  However, caching will not detect changes in modules used by \code{func}.
3595  In this case cache must be cleared manually.
3596
3597  Options are set by means of the function \code{set\_option(key, value)},
3598  where \code{key} is a key associated with a
3599  Python dictionary \code{options}. This dictionary stores settings such as the name of
3600  the directory used, the maximum
3601  number of cached files allowed, and so on.
3602
3603  The \code{cache} function allows the user also to specify a list of dependent files. If any of these
3604  have been changed, the function is recomputed and the results stored again.
3605
3606  %Other features include support for compression and a capability to \ldots
3607
3608
3609   \textbf{USAGE:} \nopagebreak
3610
3611    {\small \begin{verbatim}
3612    result = cache(func, args, kwargs, dependencies, cachedir, verbose,
3613                   compression, evaluate, test, return_filename)
3614    \end{verbatim}}
3615
3616
3617\section{ANUGA viewer - animate}
3618\label{sec:animate}
3619 The output generated by \anuga may be viewed by
3620means of the visualisation tool \code{animate}, which takes the
3621\code{SWW} file output by \anuga and creates a visual representation
3622of the data. Examples may be seen in Figures \ref{fig:runupstart}
3623and \ref{fig:runup2}. To view an \code{SWW} file with
3624\code{animate} in the Windows environment, you can simply drag the
3625icon representing the file over an icon on the desktop for the
3626\code{animate} executable file (or a shortcut to it), or set up a
3627file association to make files with the extension \code{.sww} open
3628with \code{animate}. Alternatively, you can operate \code{animate}
3629from the command line, in both Windows and Linux environments.
3630
3631On successful operation, you will see an interactive moving-picture
3632display. You can use keys and the mouse to slow down, speed up or
3633stop the display, change the viewing position or carry out a number
3634of other simple operations. Help is also displayed when you press
3635the \code{h} key.
3636
3637The main keys operating the interactive screen are:\\
3638
3639\begin{center}
3640\begin{tabular}{|ll|}   \hline
3641
3642\code{w} & toggle wireframe \\
3643
3644space bar & start/stop\\
3645
3646up/down arrows & increase/decrease speed\\
3647
3648left/right arrows & direction in time \emph{(when running)}\\
3649& step through simulation \emph{(when stopped)}\\
3650
3651left mouse button & rotate\\
3652
3653middle mouse button & pan\\
3654
3655right mouse button & zoom\\  \hline
3656
3657\end{tabular}
3658\end{center}
3659
3660\vfill
3661
3662The following table describes how to operate animate from the command line:
3663
3664Usage: \code{animate [options] swwfile \ldots}\\  \nopagebreak
3665Options:\\  \nopagebreak
3666\begin{tabular}{ll}
3667  \code{--display <type>} & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\
3668                                    & \code{HEAD\_MOUNTED\_DISPLAY}\\
3669  \code{--rgba} & Request a RGBA colour buffer visual\\
3670  \code{--stencil} & Request a stencil buffer visual\\
3671  \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\
3672                                    & overridden by environmental variable\\
3673  \code{--stereo <mode>} & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\
3674                                    & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\
3675                                     & \code{ON | OFF} \\
3676  \code{-alphamax <float 0-1>} & Maximum transparency clamp value\\
3677  \code{-alphamin <float 0-1>} & Transparency value at \code{hmin}\\
3678\end{tabular}
3679
3680\begin{tabular}{ll}
3681  \code{-cullangle <float angle 0-90>} & Cull triangles steeper than this value\\
3682  \code{-help} & Display this information\\
3683  \code{-hmax <float>} & Height above which transparency is set to
3684                                     \code{alphamax}\\
3685\end{tabular}
3686
3687\begin{tabular}{ll}
3688
3689  \code{-hmin <float>} & Height below which transparency is set to
3690                                     zero\\
3691\end{tabular}
3692
3693\begin{tabular}{ll}
3694  \code{-lightpos <float>,<float>,<float>} & $x,y,z$ of bedslope directional light ($z$ is
3695                                     up, default is overhead)\\
3696\end{tabular}
3697
3698\begin{tabular}{ll}
3699  \code{-loop}  & Repeated (looped) playback of \code{.swm} files\\
3700
3701\end{tabular}
3702
3703\begin{tabular}{ll}
3704  \code{-movie <dirname>} & Save numbered images to named directory and
3705                                     quit\\
3706
3707  \code{-nosky} & Omit background sky\\
3708
3709
3710  \code{-scale <float>} & Vertical scale factor\\
3711  \code{-texture <file>} & Image to use for bedslope topography\\
3712  \code{-tps <rate>} & Timesteps per second\\
3713  \code{-version} & Revision number and creation (not compile)
3714                                     date\\
3715\end{tabular}
3716
3717\section{utilities/polygons}
3718
3719  \declaremodule{standard}{utilities.polygon}
3720  \refmodindex{utilities.polygon}
3721
3722  \begin{classdesc}{Polygon\_function}{regions, default=0.0, geo_reference=None}
3723  Module: \code{utilities.polygon}
3724
3725  Creates a callable object that returns one of a specified list of values when
3726  evaluated at a point \code{x, y}, depending on which polygon, from a specified list of polygons, the
3727  point belongs to. The parameter \code{regions} is a list of pairs
3728  \code{(P, v)}, where each \code{P} is a polygon and each \code{v}
3729  is either a constant value or a function of coordinates \code{x}
3730  and \code{y}, specifying the return value for a point inside \code{P}. The
3731  optional parameter \code{default} may be used to specify a value
3732  (or a function)
3733  for a point not lying inside any of the specified polygons. When a
3734  point lies in more than one polygon, the return value is taken to
3735  be the value for whichever of these polygon appears later in the
3736  list.
3737  %FIXME (Howard): CAN x, y BE VECTORS?
3738  The optional parameter geo\_reference refers to the status of points
3739  that are passed into the function. Typically they will be relative to
3740  some origin. In ANUGA, a typical call will take the form:
3741  {\small \begin{verbatim}
3742     set_quantity('elevation',
3743                  Polygon_function([(P1, v1), (P2, v2)],
3744                                   default=v3,
3745                                   geo_reference=domain.geo_reference))
3746  \end{verbatim}}
3747 
3748
3749  \end{classdesc}
3750
3751  \begin{funcdesc}{read\_polygon}{filename}
3752  Module: \code{utilities.polygon}
3753
3754  Reads the specified file and returns a polygon. Each
3755  line of the file must contain exactly two numbers, separated by a comma, which are interpreted
3756  as coordinates of one vertex of the polygon.
3757  \end{funcdesc}
3758
3759  \begin{funcdesc}{populate\_polygon}{polygon, number_of_points, seed = None, exclude = None}
3760  Module: \code{utilities.polygon}
3761
3762  Populates the interior of the specified polygon with the specified number of points,
3763  selected by means of a uniform distribution function.
3764  \end{funcdesc}
3765
3766  \begin{funcdesc}{point\_in\_polygon}{polygon, delta=1e-8}
3767  Module: \code{utilities.polygon}
3768
3769  Returns a point inside the specified polygon and close to the edge. The distance between
3770  the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the
3771  second argument \code{delta}, which is taken as $10^{-8}$ by default.
3772  \end{funcdesc}
3773
3774  \begin{funcdesc}{inside\_polygon}{points, polygon, closed = True, verbose = False}
3775  Module: \code{utilities.polygon}
3776
3777  Used to test whether the members of a list of points
3778  are inside the specified polygon. Returns a Numeric
3779  array comprising the indices of the points in the list that lie inside the polygon.
3780  (If none of the points are inside, returns \code{zeros((0,), 'l')}.)
3781  Points on the edges of the polygon are regarded as inside if
3782  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3783  \end{funcdesc}
3784
3785  \begin{funcdesc}{outside\_polygon}{points, polygon, closed = True, verbose = False}
3786  Module: \code{utilities.polygon}
3787
3788  Exactly like \code{inside\_polygon}, but with the words `inside' and `outside' interchanged.
3789  \end{funcdesc}
3790
3791  \begin{funcdesc}{is\_inside\_polygon}{point, polygon, closed=True, verbose=False}
3792  Module: \code{utilities.polygon}
3793
3794  Returns \code{True} if \code{point} is inside \code{polygon} or
3795  \code{False} otherwise. Points on the edges of the polygon are regarded as inside if
3796  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3797  \end{funcdesc}
3798
3799  \begin{funcdesc}{is\_outside\_polygon}{point, polygon, closed=True, verbose=False}
3800  Module: \code{utilities.polygon}
3801
3802  Exactly like \code{is\_outside\_polygon}, but with the words `inside' and `outside' interchanged.
3803  \end{funcdesc}
3804
3805  \begin{funcdesc}{point\_on\_line}{x, y, x0, y0, x1, y1}
3806  Module: \code{utilities.polygon}
3807
3808  Returns \code{True} or \code{False}, depending on whether the point with coordinates
3809  \code{x, y} is on the line passing through the points with coordinates \code{x0, y0}
3810  and \code{x1, y1} (extended if necessary at either end).
3811  \end{funcdesc}
3812
3813  \begin{funcdesc}{separate\_points\_by\_polygon}{points, polygon, closed = True, verbose = False}
3814    \indexedcode{separate\_points\_by\_polygon}
3815  Module: \code{utilities.polygon}
3816
3817  \end{funcdesc}
3818
3819  \begin{funcdesc}{polygon\_area}{polygon}
3820  Module: \code{utilities.polygon}
3821
3822  Returns area of arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html)
3823  \end{funcdesc}
3824
3825  \begin{funcdesc}{plot\_polygons}{polygons, style, figname, verbose = False}
3826    Module: \code{utilities.polygon}
3827 
3828    Plots each polygon contained in input polygon list, e.g.
3829   \code{polygons = [poly1, poly2, poly3]} where \code{poly1 = [[x11,y11],[x12,y12],[x13,y13]]}
3830   etc.  Each polygon can be closed for plotting purposes by assigning the style type to each
3831   polygon in the list, e.g. \code{style = ['line','line','line']}. The default will be a line
3832   type when \code{style = None}.
3833   The subsequent plot will be saved to \code{figname} or defaulted to \code{test_image.png}.
3834    The function returns a list containing the minimum and maximum of \code{x} and \code{y},
3835    i.e. \code{[x_{min}, x_{max}, y_{min}, y_{max}]}.
3836  \end{funcdesc}
3837
3838\section{coordinate\_transforms}
3839
3840\section{geospatial\_data}
3841\label{sec:geospatial}
3842
3843This describes a class that represents arbitrary point data in UTM
3844coordinates along with named attribute values.
3845
3846%FIXME (Ole): This gives a LaTeX error
3847%\declaremodule{standard}{geospatial_data}
3848%\refmodindex{geospatial_data}
3849
3850
3851
3852\begin{classdesc}{Geospatial\_data}
3853  {data_points = None,
3854    attributes = None,
3855    geo_reference = None,
3856    default_attribute_name = None,
3857    file_name = None}
3858Module: \code{geospatial\_data}
3859
3860This class is used to store a set of data points and associated
3861attributes, allowing these to be manipulated by methods defined for
3862the class.
3863
3864The data points are specified either by reading them from a NetCDF
3865or CSV file, identified through the parameter \code{file\_name}, or
3866by providing their \code{x}- and \code{y}-coordinates in metres,
3867either as a sequence of 2-tuples of floats or as an $M \times 2$
3868Numeric array of floats, where $M$ is the number of points.
3869Coordinates are interpreted relative to the origin specified by the
3870object \code{geo\_reference}, which contains data indicating the UTM
3871zone, easting and northing. If \code{geo\_reference} is not
3872specified, a default is used.
3873
3874Attributes are specified through the parameter \code{attributes},
3875set either to a list or array of length $M$ or to a dictionary whose
3876keys are the attribute names and whose values are lists or arrays of
3877length $M$. One of the attributes may be specified as the default
3878attribute, by assigning its name to \code{default\_attribute\_name}.
3879If no value is specified, the default attribute is taken to be the
3880first one.
3881
3882Note that the Geospatial\_data object currently reads entire datasets
3883into memory i.e.\ no memomry blocking takes place. 
3884For this we refer to the set\_quantity method which will read .pts and .csv files into \anuga using memory blocking allowing large files to be used.
3885\end{classdesc}
3886
3887
3888\begin{methoddesc}{import\_points\_file}{delimiter = None, verbose = False}
3889
3890\end{methoddesc}
3891
3892
3893\begin{methoddesc}{export\_points\_file}{ofile, absolute=False}
3894
3895\end{methoddesc}
3896
3897
3898\begin{methoddesc}{get\_data\_points}{absolute = True, as\_lat\_long =
3899    False}
3900    If \code{as\_lat\_long} is\code{True} the point information
3901    returned will be in Latitudes and Longitudes.
3902
3903\end{methoddesc}
3904
3905
3906\begin{methoddesc}{set\_attributes}{attributes}
3907
3908\end{methoddesc}
3909
3910
3911\begin{methoddesc}{get\_attributes}{attribute_name = None}
3912
3913\end{methoddesc}
3914
3915
3916\begin{methoddesc}{get\_all\_attributes}{}
3917
3918\end{methoddesc}
3919
3920
3921\begin{methoddesc}{set\_default\_attribute\_name}{default_attribute_name}
3922
3923\end{methoddesc}
3924
3925
3926\begin{methoddesc}{set\_geo\_reference}{geo_reference}
3927
3928\end{methoddesc}
3929
3930
3931\begin{methoddesc}{add}{}
3932
3933\end{methoddesc}
3934
3935
3936\begin{methoddesc}{clip}{}
3937Clip geospatial data by a polygon
3938
3939Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3940a Geospatial data object and \code{closed}(optional) which determines
3941whether points on boundary should be regarded as belonging to the polygon
3942(\code{closed=True}) or not (\code{closed=False}).
3943Default is \code{closed=True}.
3944
3945Returns new Geospatial data object representing points
3946inside specified polygon.
3947\end{methoddesc}
3948
3949
3950\begin{methoddesc}{clip_outside}{}
3951Clip geospatial data by a polygon
3952
3953Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3954a Geospatial data object and \code{closed}(optional) which determines
3955whether points on boundary should be regarded as belonging to the polygon
3956(\code{closed=True}) or not (\code{closed=False}).
3957Default is \code{closed=True}.
3958
3959Returns new Geospatial data object representing points
3960\emph{out}side specified polygon.
3961\end{methoddesc}
3962
3963\begin{methoddesc}{split}{factor=0.5, seed_num=None, verbose=False}
3964Returns two geospatial_data object, first is the size of the 'factor'
3965smaller the original and the second is the remainder. The two
3966new object are disjoin set of each other.
3967       
3968Points of the two new geospatial_data object are selected RANDOMLY.
3969       
3970Input - the (\code{factor}) which to split the object, if 0.1 then 10% of the
3971together object will be returned
3972       
3973Output - two geospatial_data objects that are disjoint sets of the original
3974\end{methoddesc}
3975
3976\begin{methoddesc}{find_optimal_smoothing_parameter}{data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000,
3977north_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}
3978
3979Removes a small random sample of points from 'data_file'. Creates
3980models from resulting points in 'data_file' with different alpha values from 'alpha_list' and cross validates
3981the predicted value to the previously removed point data. Returns the
3982alpha value which has the smallest covariance.
3983
3984data_file: must not contain points outside the boundaries defined
3985and it either a pts, txt or csv file.
3986   
3987alpha_list: the alpha values to test in a single list
3988   
3989mesh_file: name of the created mesh file or if passed in will read it.
3990NOTE, if there is a mesh file mesh_resolution, north_boundary, south... etc will be ignored.
3991   
3992mesh_resolution: the maximum area size for a triangle
3993   
3994north_boundary... west_boundary: the value of the boundary
3995   
3996plot_name: the name for the plot contain the results
3997   
3998seed_num: the seed to the random number generator
3999   
4000USAGE:
4001convariance_value, alpha = find_optimal_smoothing_parameter(data_file=fileName,
4002                                             alpha_list=[0.0001, 0.01, 1],
4003                                             mesh_file=None,
4004                                             mesh_resolution=3,
4005                                             north_boundary=5,
4006                                             south_boundary=-5,
4007                                             east_boundary=5,
4008                                             west_boundary=-5,
4009                                             plot_name='all_alphas',
4010                                             seed_num=100000,
4011                                             verbose=False)
4012   
4013OUTPUT: returns the minumum normalised covalance calculate AND the
4014alpha that created it. PLUS writes a plot of the results
4015           
4016NOTE: code will not work if the data_file extent is greater than the
4017boundary_polygon or any of the boundaries, eg north_boundary...west_boundary
4018\end{methoddesc}
4019
4020
4021
4022\section{Graphical Mesh Generator GUI}
4023The program \code{graphical\_mesh\_generator.py} in the pmesh module
4024allows the user to set up the mesh of the problem interactively.
4025It can be used to build the outline of a mesh or to visualise a mesh
4026automatically generated.
4027
4028Graphical Mesh Generator will let the user select various modes. The
4029current allowable modes are vertex, segment, hole or region.  The mode
4030describes what sort of object is added or selected in response to
4031mouse clicks.  When changing modes any prior selected objects become
4032deselected.
4033
4034In general the left mouse button will add an object and the right
4035mouse button will select an object.  A selected object can de deleted
4036by pressing the the middle mouse button (scroll bar).
4037
4038\section{alpha\_shape}
4039\emph{Alpha shapes} are used to generate close-fitting boundaries
4040around sets of points. The alpha shape algorithm produces a shape
4041that approximates to the `shape formed by the points'---or the shape
4042that would be seen by viewing the points from a coarse enough
4043resolution. For the simplest types of point sets, the alpha shape
4044reduces to the more precise notion of the convex hull. However, for
4045many sets of points the convex hull does not provide a close fit and
4046the alpha shape usually fits more closely to the original point set,
4047offering a better approximation to the shape being sought.
4048
4049In \anuga, an alpha shape is used to generate a polygonal boundary
4050around a set of points before mesh generation. The algorithm uses a
4051parameter $\alpha$ that can be adjusted to make the resultant shape
4052resemble the shape suggested by intuition more closely. An alpha
4053shape can serve as an initial boundary approximation that the user
4054can adjust as needed.
4055
4056The following paragraphs describe the class used to model an alpha
4057shape and some of the important methods and attributes associated
4058with instances of this class.
4059
4060\begin{classdesc}{Alpha\_Shape}{points, alpha = None}
4061Module: \code{alpha\_shape}
4062
4063To instantiate this class the user supplies the points from which
4064the alpha shape is to be created (in the form of a list of 2-tuples
4065\code{[[x1, y1],[x2, y2]}\ldots\code{]}, assigned to the parameter
4066\code{points}) and, optionally, a value for the parameter
4067\code{alpha}. The alpha shape is then computed and the user can then
4068retrieve details of the boundary through the attributes defined for
4069the class.
4070\end{classdesc}
4071
4072
4073\begin{funcdesc}{alpha\_shape\_via\_files}{point_file, boundary_file, alpha= None}
4074Module: \code{alpha\_shape}
4075
4076This function reads points from the specified point file
4077\code{point\_file}, computes the associated alpha shape (either
4078using the specified value for \code{alpha} or, if no value is
4079specified, automatically setting it to an optimal value) and outputs
4080the boundary to a file named \code{boundary\_file}. This output file
4081lists the coordinates \code{x, y} of each point in the boundary,
4082using one line per point.
4083\end{funcdesc}
4084
4085
4086\begin{methoddesc}{set\_boundary\_type}{self,raw_boundary=True,
4087                          remove_holes=False,
4088                          smooth_indents=False,
4089                          expand_pinch=False,
4090                          boundary_points_fraction=0.2}
4091Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4092
4093This function sets flags that govern the operation of the algorithm
4094that computes the boundary, as follows:
4095
4096\code{raw\_boundary = True} returns raw boundary, i.e. the regular edges of the
4097                alpha shape.\\
4098\code{remove\_holes = True} removes small holes (`small' is defined by
4099\code{boundary\_points\_fraction})\\
4100\code{smooth\_indents = True} removes sharp triangular indents in
4101boundary\\
4102\code{expand\_pinch = True} tests for pinch-off and
4103corrects---preventing a boundary vertex from having more than two edges.
4104\end{methoddesc}
4105
4106
4107\begin{methoddesc}{get\_boundary}{}
4108Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4109
4110Returns a list of tuples representing the boundary of the alpha
4111shape. Each tuple represents a segment in the boundary by providing
4112the indices of its two endpoints.
4113\end{methoddesc}
4114
4115
4116\begin{methoddesc}{write\_boundary}{file_name}
4117Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4118
4119Writes the list of 2-tuples returned by \code{get\_boundary} to the
4120file \code{file\_name}, using one line per tuple.
4121\end{methoddesc}
4122
4123\section{Numerical Tools}
4124
4125The following table describes some useful numerical functions that
4126may be found in the module \module{utilities.numerical\_tools}:
4127
4128\begin{tabular}{|p{8cm} p{8cm}|}  \hline
4129\code{angle(v1, v2=None)} & Angle between two-dimensional vectors
4130\code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if
4131\code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\
4132
4133\code{normal\_vector(v)} & Normal vector to \code{v}.\\
4134
4135\code{mean(x)} & Mean value of a vector \code{x}.\\
4136
4137\code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}.
4138If \code{y} is \code{None}, returns \code{cov(x, x)}.\\
4139
4140\code{err(x, y=0, n=2, relative=True)} & Relative error of
4141$\parallel$\code{x}$-$\code{y}$\parallel$ to
4142$\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm
4143if \code{n} = \code{None}). If denominator evaluates to zero or if
4144\code{y}
4145is omitted or if \code{relative = False}, absolute error is returned.\\
4146
4147\code{norm(x)} & 2-norm of \code{x}.\\
4148
4149\code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If
4150\code{y} is \code{None} returns autocorrelation of \code{x}.\\
4151
4152\code{ensure\_numeric(A, typecode = None)} & Returns a Numeric array
4153for any sequence \code{A}. If \code{A} is already a Numeric array it
4154will be returned unaltered. Otherwise, an attempt is made to convert
4155it to a Numeric array. (Needed because \code{array(A)} can
4156cause memory overflow.)\\
4157
4158\code{histogram(a, bins, relative=False)} & Standard histogram. If
4159\code{relative} is \code{True}, values will be normalised against
4160the total and thus represent frequencies rather than counts.\\
4161
4162\code{create\_bins(data, number\_of\_bins = None)} & Safely create
4163bins for use with histogram. If \code{data} contains only one point
4164or is constant, one bin will be created. If \code{number\_of\_bins}
4165is omitted, 10 bins will be created.\\  \hline
4166
4167\section{Finding the Optimal Alpha Value}
4168
4169The function ????
4170more to come very soon
4171
4172\end{tabular}
4173
4174
4175\chapter{Modules available in \anuga}
4176
4177
4178\section{\module{abstract\_2d\_finite\_volumes.general\_mesh} }
4179\declaremodule[generalmesh]{}{general\_mesh}
4180\label{mod:generalmesh}
4181
4182\section{\module{abstract\_2d\_finite\_volumes.neighbour\_mesh} }
4183\declaremodule[neighbourmesh]{}{neighbour\_mesh}
4184\label{mod:neighbourmesh}
4185
4186\section{\module{abstract\_2d\_finite\_volumes.domain}}
4187Generic module for 2D triangular domains for finite-volume computations of conservation laws
4188\declaremodule{}{domain}
4189\label{mod:domain}
4190
4191
4192\section{\module{abstract\_2d\_finite\_volumes.quantity}}
4193\declaremodule{}{quantity}
4194\label{mod:quantity}
4195
4196\begin{verbatim}
4197Class Quantity - Implements values at each triangular element
4198
4199To create:
4200
4201   Quantity(domain, vertex_values)
4202
4203   domain: Associated domain structure. Required.
4204
4205   vertex_values: N x 3 array of values at each vertex for each element.
4206                  Default None
4207
4208   If vertex_values are None Create array of zeros compatible with domain.
4209   Otherwise check that it is compatible with dimenions of domain.
4210   Otherwise raise an exception
4211
4212\end{verbatim}
4213
4214
4215
4216
4217\section{\module{shallow\_water}}
42182D triangular domains for finite-volume
4219computations of the shallow water wave equation.
4220This module contains a specialisation of class Domain from module domain.py consisting of methods specific to the Shallow Water
4221Wave Equation
4222\declaremodule[shallowwater]{}{shallow\_water}
4223\label{mod:shallowwater}
4224
4225
4226
4227
4228%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4229
4230\chapter{Frequently Asked Questions}
4231
4232
4233\section{General Questions}
4234
4235\subsubsection{What is \anuga?}
4236It is a software package suitable for simulating 2D water flows in
4237complex geometries.
4238
4239\subsubsection{Why is it called \anuga?}
4240The software was developed in collaboration between the
4241Australian National University (ANU) and Geoscience Australia (GA).
4242
4243\subsubsection{How do I obtain a copy of \anuga?}
4244See \url{https://datamining.anu.edu.au/anuga} for all things ANUGA.
4245
4246%\subsubsection{What developments are expected for \anuga in the future?}
4247%This
4248
4249\subsubsection{Are there any published articles about \anuga that I can reference?}
4250See \url{https://datamining.anu.edu.au/anuga} for links.
4251
4252
4253\subsubsection{How do I find out what version of \anuga I am running?}
4254Use the following code snippet
4255\begin{verbatim}
4256from anuga.utilities.system_tools import get_revision_number
4257print get_revision_number()
4258\end{verbatim}
4259This should work both for installations from SourceForge as well as when working off the repository.
4260
4261
4262
4263
4264\section{Modelling Questions}
4265
4266\subsubsection{Which type of problems are \anuga good for?}
4267General 2D waterflows in complex geometries such as
4268dam breaks, flows amoung structurs, coastal inundation etc.
4269
4270\subsubsection{Which type of problems are beyond the scope of \anuga?}
4271See Chapter \ref{ch:limitations}.
4272
4273\subsubsection{Can I start the simulation at an arbitrary time?}
4274Yes, using \code{domain.set\_time()} you can specify an arbitrary
4275starting time. This is for example useful in conjunction with a
4276file\_boundary, which may start hours before anything hits the model
4277boundary. By assigning a later time for the model to start,
4278computational resources aren't wasted.
4279
4280\subsubsection{Can I change values for any quantity during the simulation?}
4281Yes, using \code{domain.set\_quantity()} inside the domain.evolve
4282loop you can change values of any quantity. This is for example
4283useful if you wish to let the system settle for a while before
4284assigning an initial condition. Another example would be changing
4285the values for elevation to model e.g. erosion.
4286
4287\subsubsection{Can I change boundary conditions during the simulation?}
4288Yes - see example on page \pageref{sec:change boundary code} in Section
4289\ref{sec:change boundary}.
4290
4291\subsubsection{How do I access model time during the simulation?}
4292The variable \code{t} in the evolve for loop is the model time.
4293For 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})
4294one would write something like
4295{\small \begin{verbatim}
4296    for t in domain.evolve(yieldstep = 0.2, duration = 40.0):
4297
4298        if Numeric.allclose(t, 15):
4299            print 'Changing boundary to outflow'
4300            domain.set_boundary({'right': Bo})
4301
4302\end{verbatim}}
4303The 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()}.
4304
4305
4306\subsubsection{Why does a file\_function return a list of numbers when evaluated?}
4307Currently, file\_function works by returning values for the conserved
4308quantities \code{stage}, \code{xmomentum} and \code{ymomentum} at a given point in time
4309and space as a triplet. To access e.g.\ \code{stage} one must specify element 0 of the
4310triplet returned by file\_function, to access \code{xmomentum} one must specify element 1 of the triplet etc.
4311
4312\subsubsection{Which diagnostics are available to troubleshoot a simulation?}
4313
4314\subsubsection{How do I use a DEM in my simulation?}
4315You use \code{dem2pts} to convert your DEM to the required .pts format. This .pts file is then called
4316when setting the elevation data to the mesh in \code{domain.set_quantity}
4317
4318\subsubsection{What sort of DEM resolution should I use?}
4319Try and work with the \emph{best} you have available. Onshore DEMs
4320are typically available in 25m, 100m and 250m grids. Note, offshore
4321data is often sparse, or non-existent.
4322
4323Note that onshore DEMS can be much finer as the underlying datasets from which they
4324are created often contain several datapoints per m$^2$.
4325It may be necessary to thin out the data so that it can be imported
4326without exceeding available memory. One tool available on the net is called 'decimate'. %FIXME: (Need reference?). 
4327
4328
4329\subsubsection{What sort of mesh resolution should I use?}
4330The 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,
4331if 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,
4332you need a fine mesh over regions where the DEM changes rapidly, and other areas of significant interest, such as the coast.
4333If meshes are too coarse, discretisation errors in both stage and momentum may lead to unrealistic results. All studies should include sensitivity and convergence studies based on different resolutions.
4334
4335
4336\subsubsection{How do I tag interior polygons?}
4337At the moment create_mesh_from_regions does not allow interior
4338polygons with symbolic tags. If tags are needed, the interior
4339polygons must be created subsequently. For example, given a filename
4340of polygons representing solid walls (in Arc Ungenerate format) can
4341be tagged as such using the code snippet:
4342\begin{verbatim}
4343  # Create mesh outline with tags
4344  mesh = create_mesh_from_regions(bounding_polygon,
4345                                  boundary_tags=boundary_tags)
4346  # Add buildings outlines with tags set to 'wall'. This would typically
4347  # bind to a Reflective boundary
4348  mesh.import_ungenerate_file(buildings_filename, tag='wall')
4349
4350  # Generate and write mesh to file
4351  mesh.generate_mesh(maximum_triangle_area=max_area)
4352  mesh.export_mesh_file(mesh_filename)
4353\end{verbatim}
4354
4355Note that a mesh object is returned from \code{create_mesh_from_regions}
4356when file name is omitted.
4357
4358\subsubsection{How often should I store the output?}
4359This 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
4360to look in detail at the evolution, then you will need to balance your storage requirements and the duration of the simulation.
4361If 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
4362quantities on a mesh with approximately 300000 triangles on a 2 min interval for 5 hours will result in approximately 350Mb SWW file
4363(as for the \file{run\_sydney\_smf.py} example).
4364
4365\subsubsection{How can I set the friction in different areas in the domain?}
4366The model area will typically be estimating the water height and momentum over varying
4367topographies which will have different friction values. One way of assigning
4368different friction values is to create polygons (say \code{poly1, poly2 and poly3}) describing each
4369area and then set the corresponding friction values in the following way
4370
4371\code{domain.set_quantity('friction',Polygon_function([(poly1,f1),(poly2,f2),
4372(poly3,f3))]))}
4373
4374The values of \code{f1,f2} and \code{f3} could be constant or functions
4375as determined by the user.
4376
4377\subsubsection{How can I combine data sets?}
4378
4379A user may have access to a range of different resolution DEMs and raw data points (such
4380as beach profiles, spot heights, single or multi-beam data etc) and will need
4381to combine them to create an overall elevation data set.
4382
4383If there are multiple DEMs, say of 10m and 25m resolution, then the technique is similar to
4384that defined in the Cairns example described earlier, that is
4385
4386{\small \begin{verbatim}
4387convert_dem_from_ascii2netcdf(10m_dem_name, use_cache=True, verbose=True)
4388convert_dem_from_ascii2netcdf(25m_dem_name, use_cache=True, verbose=True)
4389\end{verbatim}}
4390followed by
4391{\small \begin{verbatim}
4392dem2pts(10m_dem_name, use_cache=True, verbose=True)
4393dem2pts(25m_dem_name, use_cache=True, verbose=True)
4394\end{verbatim}}
4395These data sets can now be combined by
4396{\small \begin{verbatim}
4397from anuga.geospatial_data.geospatial_data import *
4398G1 = Geospatial_data(file_name = 10m_dem_name + '.pts')
4399G2 = Geospatial_data(file_name = 25m_dem_name + '.pts')
4400G = G1 + G2
4401G.export_points_file(combined_dem_name + ᅵ.ptsᅵ)
4402\end{verbatim}}
4403this is the basic way of combining data sets, however, the user will need to
4404assess the boundaries of each data set and whether they overlap. For example, consider
4405if the 10m DEM is describing by \code{poly1} and the 25m DEM is described by \code{poly2}
4406with \code{poly1} completely enclosed in \code{poly2} as shown in Figure \ref{fig:polydata}
4407\begin{figure}[hbt]
4408  \centerline{\includegraphics{graphics/polyanddata.jpg}}
4409  \caption{Polygons describing the extent of the 10m and 25m DEM.}
4410  \label{fig:polydata}
4411\end{figure}
4412To combine the data sets, the geospatial addition is updated to
4413{\small \begin{verbatim}
4414G = G1 + G2.clip_outside(Geospatial_data(poly1))
4415\end{verbatim}}
4416For this example, we assume that \code{poly2} is the domain, otherwise an additional dataset
4417would be required for the remainder of the domain.
4418
4419This technique can be expanded to handle point data sets as well. In the case
4420of a bathymetry data set available in text format in an \code{.csv} file, then
4421the geospatial addition is updated to
4422{\small \begin{verbatim}
4423G3 = Geospatial_data(file_name = bathy_data_name + '.csv')
4424G = G1 + G2.clip_outside(Geospatial_data(poly1)) + G3
4425\end{verbatim}}
4426The \code{.csv} file has the data stored as \code{x,y,elevation} with the text \code{elevation}
4427on the first line.
4428
4429The coastline could be included
4430as part of the clipping polygon to separate the offshore and onshore datasets if required.
4431Assume that \code{poly1} crosses the coastline
4432In this case, two new polygons could be created out of \code{poly1} which uses the coastline
4433as the divider. As shown in Figure \ref{fig:polycoast}, \code{poly3} describes the
4434onshore data and \code{poly4} describes the offshore data.
4435\begin{figure}[hbt]
4436  \centerline{\includegraphics{graphics/polyanddata2.jpg}}
4437  \caption{Inclusion of new polygons separating the 10m DEM area into an
4438  onshore (poly3) and offshore (poly4) data set.}
4439  \label{fig:polycoast}
4440\end{figure}
4441Let's include the bathymetry
4442data described above, so to combine the datasets in this case,
4443{\small \begin{verbatim}
4444G = G1.clip(Geospatial_data(poly3)) + G2.clip_outside(Geospatial_data(poly1)) + G3
4445\end{verbatim}}
4446
4447Finally, to fit the elevation data to the mesh, the script is adjusted in this way
4448{\small \begin{verbatim}
4449    domain.set_quantity('elevation',
4450                        filename = combined_dem_name + '.pts',
4451                        use_cache = True,
4452                        verbose = True)
4453\end{verbatim}}
4454\subsection{Boundary Conditions}
4455
4456\subsubsection{How do I create a Dirichlet boundary condition?}
4457
4458A Dirichlet boundary condition sets a constant value for the
4459conserved quantities at the boundaries. A list containing
4460the constant values for stage, xmomentum and ymomentum is constructed
4461and used in the function call, e.g. \code{Dirichlet_boundary([0.2,0.,0.])}
4462
4463\subsubsection{How do I know which boundary tags are available?}
4464The method \code{domain.get\_boundary\_tags()} will return a list of
4465available tags for use with
4466\code{domain.set\_boundary\_condition()}.
4467
4468\subsubsection{What is the difference between file_boundary and field_boundary?}
4469The only difference is field_boundary will allow you to change the level of the stage height when you read in the boundary condition.
4470This is very useful when running different tide heights in the same area as you need only to convert
4471one boundary condition to a SWW file, ideally for tide height of 0 m (saving disk space). Then you can
4472use field_boundary to read this SWW file and change the stage height (tide) on the fly depending on the scenario.
4473
4474
4475
4476
4477\subsection{Analysing Results}
4478
4479\subsubsection{How do I easily plot "tide gauges" timeseries graphs from a SWW file?}
4480
4481There is two ways to do this.
4482
44831) Create csv files from the sww file using \code{anuga.abstract_2d_finite_volumes.util sww2csv_gauges}
4484and then use \code{anuga.abstract_2d_finite_volumes.util csv2timeseries_graphs} to
4485create the plots. This code is newer, has unit tests and might be easier to use. Read doc strings for more information and
4486review section 4.7 of this manual.
4487
4488Or
4489
44902) Use \code{anuga.abstract_2d_finite_volumes.util sww2timeseries} to do the whole thing
4491however this doesn't have a much control on the file name and plots. Plus there is no unit tests yet.
4492
4493Read the doc string for more information.
4494
4495\subsubsection{How do I extract elevation and other quantities from a SWW file?}
4496
4497The function \code{sww2dem} can extract any quantity, or expression using
4498quantities, from a SWW file as used in
4499the Cairns example described earlier. This function is used in \code{ExportResults.py}
4500in the Cairns demo folder where stage, absolute momentum, depth, speed and elevation
4501can be exported from the input sww file. Note that depth, absolute momentum and speed
4502are expressions and stage and elevation are quantities. In addition to extracting a particular
4503quantity or expression, the user can define a region to extract these values by
4504defining the minimum and maximum of both the easting and northing coordinates. The function
4505also calls for a grid resolution, or cell size, to extract these values at. It is
4506recommended to align this resolution with the mesh resolution in the desired region and to not
4507generate a fine grid where the model output cannot support that resolution.
4508
4509 
4510
4511\chapter{Glossary}
4512
4513\begin{tabular}{|lp{10cm}|c|}  \hline
4514%\begin{tabular}{|llll|}  \hline
4515    \emph{Term} & \emph{Definition} & \emph{Page}\\  \hline
4516
4517    \indexedbold{\anuga} & Name of software (joint development between ANU and
4518    GA) & \pageref{def:anuga}\\
4519
4520    \indexedbold{bathymetry} & offshore elevation &\\
4521
4522    \indexedbold{conserved quantity} & conserved (stage, x and y
4523    momentum) & \\
4524
4525%    \indexedbold{domain} & The domain of a function is the set of all input values to the
4526%    function.&\\
4527
4528    \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations,
4529sampled systematically at equally spaced intervals.& \\
4530
4531    \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation
4532 that specifies the values the solution is to take on the boundary of the
4533 domain. & \pageref{def:dirichlet boundary}\\
4534
4535    \indexedbold{edge} & A triangular cell within the computational mesh can be depicted
4536    as a set of vertices joined by lines (the edges). & \\
4537
4538    \indexedbold{elevation} & refers to bathymetry and topography &\\
4539
4540    \indexedbold{evolution} & integration of the shallow water wave equations
4541    over time &\\
4542
4543    \indexedbold{finite volume method} & The method evaluates the terms in the shallow water
4544    wave equation as fluxes at the surfaces of each finite volume. Because the
4545    flux entering a given volume is identical to that leaving the adjacent volume,
4546    these methods are conservative. Another advantage of the finite volume method is
4547    that it is easily formulated to allow for unstructured meshes. The method is used
4548    in many computational fluid dynamics packages. & \\
4549
4550    \indexedbold{forcing term} & &\\
4551
4552    \indexedbold{flux} & the amount of flow through the volume per unit
4553    time & \\
4554
4555    \indexedbold{grid} & Evenly spaced mesh & \\
4556
4557    \indexedbold{latitude} & The angular distance on a mericlear north and south of the
4558    equator, expressed in degrees and minutes. & \\
4559
4560    \indexedbold{longitude} & The angular distance east or west, between the meridian
4561    of a particular place on Earth and that of the Prime Meridian (located in Greenwich,
4562    England) expressed in degrees or time.& \\
4563
4564    \indexedbold{Manning friction coefficient} & &\\
4565
4566    \indexedbold{mesh} & Triangulation of domain &\\
4567
4568    \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\
4569
4570    \indexedbold{NetCDF} & &\\
4571
4572    \indexedbold{node} & A point at which edges meet & \\
4573
4574    \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance
4575    north from a north-south reference line, usually a meridian used as the axis of
4576    origin within a map zone or projection. Northing is a UTM (Universal Transverse
4577    Mercator) coordinate. & \\
4578
4579
4580    \indexedbold{points file} & A PTS or CSV file & \\  \hline
4581
4582    \end{tabular}
4583
4584    \begin{tabular}{|lp{10cm}|c|}  \hline
4585
4586    \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon
4587    either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$
4588    Numeric array, where $N$ is the number of points.
4589
4590    The unit square, for example, would be represented either as
4591    \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1],
4592    [0,1] )}.
4593
4594    NOTE: For details refer to the module \module{utilities/polygon.py}. &
4595    \\     \indexedbold{resolution} &  The maximal area of a triangular cell in a
4596    mesh & \\
4597
4598
4599    \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved
4600    quantities as those present in the neighbouring volume but reflected. Specific to the
4601    shallow water equation as it works with the momentum quantities assumed to be the
4602    second and third conserved quantities. & \pageref{def:reflective boundary}\\
4603
4604    \indexedbold{stage} & &\\
4605
4606%    \indexedbold{try this}
4607
4608    \indexedbold{animate} & visualisation tool used with \anuga &
4609    \pageref{sec:animate}\\
4610
4611    \indexedbold{time boundary} & Returns values for the conserved
4612quantities as a function of time. The user must specify
4613the domain to get access to the model time. & \pageref{def:time boundary}\\
4614
4615    \indexedbold{topography} & onshore elevation &\\
4616
4617    \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\
4618
4619    \indexedbold{vertex} & A point at which edges meet. & \\
4620
4621    \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say
4622    only \code{x} and \code{y} and NOT \code{z}) &\\
4623
4624    \indexedbold{ymomentum}  & conserved quantity & \\  \hline
4625
4626    \end{tabular}
4627
4628
4629%The \code{\e appendix} markup need not be repeated for additional
4630%appendices.
4631
4632
4633%
4634%  The ugly "%begin{latexonly}" pseudo-environments are really just to
4635%  keep LaTeX2HTML quiet during the \renewcommand{} macros; they're
4636%  not really valuable.
4637%
4638%  If you don't want the Module Index, you can remove all of this up
4639%  until the second \input line.
4640%
4641
4642%begin{latexonly}
4643%\renewcommand{\indexname}{Module Index}
4644%end{latexonly}
4645\input{mod\jobname.ind}        % Module Index
4646%
4647%begin{latexonly}
4648%\renewcommand{\indexname}{Index}
4649%end{latexonly}
4650\input{\jobname.ind}            % Index
4651
4652
4653
4654\begin{thebibliography}{99}
4655\bibitem[nielsen2005]{nielsen2005}
4656{\it Hydrodynamic modelling of coastal inundation}.
4657Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman.
4658In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on
4659Modelling and Simulation. Modelling and Simulation Society of Australia and
4660New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\
4661http://www.mssanz.org.au/modsim05/papers/nielsen.pdf
4662
4663\bibitem[grid250]{grid250}
4664Australian Bathymetry and Topography Grid, June 2005.
4665Webster, M.A. and Petkovic, P.
4666Geoscience Australia Record 2005/12. ISBN: 1-920871-46-2.\\
4667http://www.ga.gov.au/meta/ANZCW0703008022.html
4668
4669\bibitem[ZR1999]{ZR1999}
4670\newblock {Catastrophic Collapse of Water Supply Reservoirs in Urban Areas}.
4671\newblock C.~Zoppou and S.~Roberts.
4672\newblock {\em ASCE J. Hydraulic Engineering}, 125(7):686--695, 1999.
4673
4674\bibitem[Toro1999]{Toro1992}
4675\newblock Riemann problems and the waf method for solving the two-dimensional
4676  shallow water equations.
4677\newblock E.~F. Toro.
4678\newblock {\em Philosophical Transactions of the Royal Society, Series A},
4679  338:43--68, 1992.
4680
4681\bibitem{KurNP2001}
4682\newblock Semidiscrete central-upwind schemes for hyperbolic conservation laws
4683  and hamilton-jacobi equations.
4684\newblock A.~Kurganov, S.~Noelle, and G.~Petrova.
4685\newblock {\em SIAM Journal of Scientific Computing}, 23(3):707--740, 2001.
4686\end{thebibliography}{99}
4687
4688\end{document}
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