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2% documentation is available in ``Documenting Python'', which is part
3% of the standard documentation for Python.  It may be found online
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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
42% doesn't cause a new date to be used.  Setting
43% the date to \today can be used during draft
44% stages to make it easier to handle versions.
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46
47\longdate       % Make date format long using datetime.sty
48%\settimeformat{xxivtime} % 24 hour Format
49\settimeformat{oclock} % Verbose
50\date{\today, \ \currenttime}
51%\hyphenation{set\_datadir}
52
53\ifhtml
54\date{\today} % latex2html does not know about datetime
55\fi
56
57
58
59
60\input{version} % Get version info - this file may be modified by
61                % update_anuga_user_manual.py - if not a dummy
62                % will be used.
63               
64%\release{1.0}   % release version; this is used to define the
65%                % \version macro
66
67\makeindex          % tell \index to actually write the .idx file
68\makemodindex       % If this contains a lot of module sections.
69
70\setcounter{tocdepth}{3}
71\setcounter{secnumdepth}{3}
72
73
74\begin{document}
75\maketitle
76
77
78% This makes the contents more accessible from the front page of the HTML.
79\ifhtml
80\chapter*{Front Matter\label{front}}
81\fi
82
83%Subversion keywords:
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85%$LastChangedDate: 2008-07-16 02:28:52 +0000 (Wed, 16 Jul 2008) $
86%$LastChangedRevision: 5507 $
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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 geometries.
97Examples include dam breaks or the effects of natural hazards such
98as riverine flooding, storm surges and tsunami.
99
100The user must specify a study area represented by a mesh of triangular
101cells, the topography and bathymetry, frictional resistance, initial
102values for water level (called \emph{stage}\index{stage} within \anuga),
103boundary
104conditions and forces such as windstress or pressure gradients if
105applicable.
106
107\anuga tracks the evolution of water depth and horizontal momentum
108within each cell over time by solving the shallow water wave equation
109governing equation using a finite-volume method.
110
111\anuga also incorporates a mesh generator %, called \code{graphical
112                                %mesh generator},
113that
114allows the user to set up the geometry of the problem interactively as
115well as tools for interpolation and surface fitting, and a number of
116auxiliary tools for visualising and interrogating the model output.
117
118Most \anuga components are written in the object-oriented programming
119language Python and most users will interact with \anuga by writing
120small Python programs based on the \anuga library
121functions. Computationally intensive components are written for
122efficiency in C routines working directly with the Numerical Python
123structures.
124
125
126\end{abstract}
127
128\tableofcontents
129
130
131\chapter{Introduction}
132
133
134\section{Purpose}
135
136The purpose of this user manual is to introduce the new user to the
137inundation software, describe what it can do and give step-by-step
138instructions for setting up and running hydrodynamic simulations.
139
140\section{Scope}
141
142This manual covers only what is needed to operate the software after
143installation and configuration. It does not includes instructions
144for installing the software or detailed API documentation, both of
145which will be covered in separate publications and by documentation
146in the source code.
147
148\section{Audience}
149
150Readers are assumed to be familiar with the Python Programming language and
151its object oriented approach.
152Python tutorials include
153\url{http://docs.python.org/tut},
154\url{http://www.sthurlow.com/python}, and
155%\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}.
156\url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}.
157
158
159Readers also need to have a general understanding of scientific modelling,
160as well as
161enough programming experience to adapt the code to different
162requirements.
163
164
165
166\pagebreak
167\chapter{Background}
168
169
170Modelling the effects on the built environment of natural hazards such
171as riverine flooding, storm surges and tsunami is critical for
172understanding their economic and social impact on our urban
173communities.  Geoscience Australia and the Australian National
174University are developing a hydrodynamic inundation modelling tool
175called \anuga to help simulate the impact of these hazards.
176
177The core of \anuga is the fluid dynamics module, called \code{shallow\_water},
178which is based on a finite-volume method for solving the Shallow Water
179Wave Equation.  The study area is represented by a mesh of triangular
180cells.  By solving the governing equation within each cell, water
181depth and horizontal momentum are tracked over time.
182
183A major capability of \anuga is that it can model the process of
184wetting and drying as water enters and leaves an area.  This means
185that it is suitable for simulating water flow onto a beach or dry land
186and around structures such as buildings.  \anuga is also capable
187of modelling hydraulic jumps due to the ability of the finite-volume
188method to accommodate discontinuities in the solution.
189
190To set up a particular scenario the user specifies the geometry
191(bathymetry and topography), the initial water level (stage),
192boundary conditions such as tide, and any forcing terms that may
193drive the system such as rain_fall, abstraction of water, wind stress or atmospheric pressure
194gradients. Gravity and frictional resistance from the different
195terrains in the model are represented by predefined forcing terms.
196See section \ref{sec:forcing terms} for details on forcing terms available in ANUGA.
197
198The built-in mesh generator, called \code{graphical\_mesh\_generator},
199allows the user to set up the geometry
200of the problem interactively and to identify boundary segments and
201regions using symbolic tags.  These tags may then be used to set the
202actual boundary conditions and attributes for different regions
203(e.g.\ the Manning friction coefficient) for each simulation.
204
205Most \anuga components are written in the object-oriented programming
206language Python.  Software written in Python can be produced quickly
207and can be readily adapted to changing requirements throughout its
208lifetime.  Computationally intensive components are written for
209efficiency in C routines working directly with the Numerical Python
210structures.  The animation tool developed for \anuga is based on
211OpenSceneGraph, an Open Source Software (OSS) component allowing high
212level interaction with sophisticated graphics primitives.
213See \cite{nielsen2005} for more background on \anuga.
214
215\chapter{Restrictions and limitations on \anuga}
216\label{ch:limitations}
217
218Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a
219number of limitations that any potential user need to be aware of. They are
220
221\begin{itemize}
222  \item The mathematical model is the 2D shallow water wave equation.
223  As such it cannot resolve vertical convection and consequently not breaking
224  waves or 3D turbulence (e.g.\ vorticity).
225  \item The surface is assumed to be open, e.g. \anuga cannot model
226  flow under ceilings or in pipes
227  \item All spatial coordinates are assumed to be UTM (meters). As such,
228  ANUGA is unsuitable for modelling flows in areas larger than one UTM zone
229  (6 degrees wide).
230  \item Fluid is assumed to be inviscid
231  \item The finite volume is a very robust and flexible numerical technique,
232  but it is not the fastest method around. If the geometry is sufficiently
233  simple and if there is no need for wetting or drying, a finite-difference
234  method may be able to solve the problem faster than \anuga.
235  %\item Mesh resolutions near coastlines with steep gradients need to be...
236  \item Frictional resistance is implemented using Manning's formula, but
237  \anuga has not yet been fully validated in regard to bottom roughness
238  \item ANUGA contains no tsunami-genic functionality relating to
239  earthquakes.
240\end{itemize}
241
242
243
244\chapter{Getting Started}
245\label{ch:getstarted}
246
247This section is designed to assist the reader to get started with
248\anuga by working through some examples. Two examples are discussed;
249the first is a simple example to illustrate many of the ideas, and
250the second is a more realistic example.
251
252\section{A Simple Example}
253\label{sec:simpleexample}
254
255\subsection{Overview}
256
257What follows is a discussion of the structure and operation of a
258script called \file{runup.py}.
259
260This example carries out the solution of the shallow-water wave
261equation in the simple case of a configuration comprising a flat
262bed, sloping at a fixed angle in one direction and having a
263constant depth across each line in the perpendicular direction.
264
265The example demonstrates the basic ideas involved in setting up a
266complex scenario. In general the user specifies the geometry
267(bathymetry and topography), the initial water level, boundary
268conditions such as tide, and any forcing terms that may drive the
269system such as rain_fall, abstraction of water, wind stress or atmospheric pressure gradients.
270Frictional resistance from the different terrains in the model is
271represented by predefined forcing terms. In this example, the
272boundary is reflective on three sides and a time dependent wave on
273one side.
274
275The present example represents a simple scenario and does not
276include any forcing terms, nor is the data taken from a file as it
277would typically be.
278
279The conserved quantities involved in the
280problem are stage (absolute height of water surface),
281$x$-momentum and $y$-momentum. Other quantities
282involved in the computation are the friction and elevation.
283
284Water depth can be obtained through the equation
285
286\begin{tabular}{rcrcl}
287  \code{depth} &=& \code{stage} &$-$& \code{elevation}
288\end{tabular}
289
290
291\subsection{Outline of the Program}
292
293In outline, \file{runup.py} performs the following steps:
294
295\begin{enumerate}
296
297   \item Sets up a triangular mesh.
298
299   \item Sets certain parameters governing the mode of
300operation of the model-specifying, for instance, where to store the model output.
301
302   \item Inputs various quantities describing physical measurements, such
303as the elevation, to be specified at each mesh point (vertex).
304
305   \item Sets up the boundary conditions.
306
307   \item Carries out the evolution of the model through a series of time
308steps and outputs the results, providing a results file that can
309be visualised.
310
311\end{enumerate}
312
313\subsection{The Code}
314
315%FIXME: we are using the \code function here.
316%This should be used wherever possible
317For reference we include below the complete code listing for
318\file{runup.py}. Subsequent paragraphs provide a
319`commentary' that describes each step of the program and explains it
320significance.
321
322\verbatiminput{demos/runup.py}
323
324\subsection{Establishing the Mesh}\index{mesh, establishing}
325
326The first task is to set up the triangular mesh to be used for the
327scenario. This is carried out through the statement:
328
329{\small \begin{verbatim}
330    points, vertices, boundary = rectangular_cross(10, 10)
331\end{verbatim}}
332
333The function \function{rectangular_cross} is imported from a module
334\module{mesh\_factory} defined elsewhere. (\anuga also contains
335several other schemes that can be used for setting up meshes, but we
336shall not discuss these.) The above assignment sets up a $10 \times
33710$ rectangular mesh, triangulated in a regular way. The assignment
338
339{\small \begin{verbatim}
340    points, vertices, boundary = rectangular_cross(m, n)
341\end{verbatim}}
342
343returns:
344
345\begin{itemize}
346
347   \item a list \code{points} giving the coordinates of each mesh point,
348
349   \item a list \code{vertices} specifying the three vertices of each triangle, and
350
351   \item a dictionary \code{boundary} that stores the edges on
352   the boundary and associates each with one of the symbolic tags \code{`left'}, \code{`right'},
353   \code{`top'} or \code{`bottom'}.
354
355\end{itemize}
356
357(For more details on symbolic tags, see page
358\pageref{ref:tagdescription}.)
359
360An example of a general unstructured mesh and the associated data
361structures \code{points}, \code{vertices} and \code{boundary} is
362given in Section \ref{sec:meshexample}.
363
364
365
366
367\subsection{Initialising the Domain}
368
369These variables are then used to set up a data structure
370\code{domain}, through the assignment:
371
372{\small \begin{verbatim}
373    domain = Domain(points, vertices, boundary)
374\end{verbatim}}
375
376This creates an instance of the \class{Domain} class, which
377represents the domain of the simulation. Specific options are set at
378this point, including the basename for the output file and the
379directory to be used for data:
380
381{\small \begin{verbatim}
382    domain.set_name('runup')
383\end{verbatim}}
384
385{\small \begin{verbatim}
386    domain.set_datadir('.')
387\end{verbatim}}
388
389In addition, the following statement now specifies that the
390quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are
391to be stored:
392
393{\small \begin{verbatim}
394    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
395    'ymomentum'])
396\end{verbatim}}
397
398
399\subsection{Initial Conditions}
400
401The next task is to specify a number of quantities that we wish to
402set for each mesh point. The class \class{Domain} has a method
403\method{set\_quantity}, used to specify these quantities. It is a
404flexible method that allows the user to set quantities in a variety
405of ways---using constants, functions, numeric arrays, expressions
406involving other quantities, or arbitrary data points with associated
407values, all of which can be passed as arguments. All quantities can
408be initialised using \method{set\_quantity}. For a conserved
409quantity (such as \code{stage, xmomentum, ymomentum}) this is called
410an \emph{initial condition}. However, other quantities that aren't
411updated by the equation are also assigned values using the same
412interface. The code in the present example demonstrates a number of
413forms in which we can invoke \method{set\_quantity}.
414
415
416\subsubsection{Elevation}
417
418The elevation, or height of the bed, is set using a function,
419defined through the statements below, which is specific to this
420example and specifies a particularly simple initial configuration
421for demonstration purposes:
422
423{\small \begin{verbatim}
424    def f(x,y):
425        return -x/2
426\end{verbatim}}
427
428This simply associates an elevation with each point \code{(x, y)} of
429the plane.  It specifies that the bed slopes linearly in the
430\code{x} direction, with slope $-\frac{1}{2}$,  and is constant in
431the \code{y} direction.
432
433Once the function \function{f} is specified, the quantity
434\code{elevation} is assigned through the simple statement:
435
436{\small \begin{verbatim}
437    domain.set_quantity('elevation', f)
438\end{verbatim}}
439
440NOTE: If using function to set \code{elevation} it must be vector
441compatible. For example square root will not work.
442
443\subsubsection{Friction}
444
445The assignment of the friction quantity (a forcing term)
446demonstrates another way we can use \method{set\_quantity} to set
447quantities---namely, assign them to a constant numerical value:
448
449{\small \begin{verbatim}
450    domain.set_quantity('friction', 0.1)
451\end{verbatim}}
452
453This specifies that the Manning friction coefficient is set to 0.1
454at every mesh point.
455
456\subsubsection{Stage}
457
458The stage (the height of the water surface) is related to the
459elevation and the depth at any time by the equation
460
461{\small \begin{verbatim}
462    stage = elevation + depth
463\end{verbatim}}
464
465
466For this example, we simply assign a constant value to \code{stage},
467using the statement
468
469{\small \begin{verbatim}
470    domain.set_quantity('stage', -.4)
471\end{verbatim}}
472
473which specifies that the surface level is set to a height of $-0.4$,
474i.e. 0.4 units (m) below the zero level.
475
476Although it is not necessary for this example, it may be useful to
477digress here and mention a variant to this requirement, which allows
478us to illustrate another way to use \method{set\_quantity}---namely,
479incorporating an expression involving other quantities. Suppose,
480instead of setting a constant value for the stage, we wished to
481specify a constant value for the \emph{depth}. For such a case we
482need to specify that \code{stage} is everywhere obtained by adding
483that value to the value already specified for \code{elevation}. We
484would do this by means of the statements:
485
486{\small \begin{verbatim}
487    h = 0.05 # Constant depth
488    domain.set_quantity('stage', expression = 'elevation + %f' %h)
489\end{verbatim}}
490
491That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus
492the value of \code{elevation} already defined.
493
494The reader will probably appreciate that this capability to
495incorporate expressions into statements using \method{set\_quantity}
496greatly expands its power.) See Section \ref{sec:Initial Conditions} for more
497details.
498
499\subsection{Boundary Conditions}\index{boundary conditions}
500
501The boundary conditions are specified as follows:
502
503{\small \begin{verbatim}
504    Br = Reflective_boundary(domain)
505
506    Bt = Transmissive_boundary(domain)
507
508    Bd = Dirichlet_boundary([0.2,0.,0.])
509
510    Bw = Time_boundary(domain=domain,
511                f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
512\end{verbatim}}
513
514The effect of these statements is to set up a selection of different
515alternative boundary conditions and store them in variables that can be
516assigned as needed. Each boundary condition specifies the
517behaviour at a boundary in terms of the behaviour in neighbouring
518elements. The boundary conditions introduced here may be briefly described as
519follows:
520
521\begin{itemize}
522    \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as
523      as present in its neighbour volume but momentum vector
524      reversed 180 degrees (reflected).
525      Specific to the shallow water equation as it works with the
526      momentum quantities assumed to be the second and third conserved
527      quantities. A reflective boundary condition models a solid wall.
528    \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as
529      those present in its neighbour volume. This is one way of modelling
530      outflow from a domain, but it should be used with caution if flow is
531      not steady state as replication of momentum at the boundary
532      may cause occasional spurious effects. If this occurs,
533      consider using e.g. a Dirichlet boundary condition.
534    \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies
535      constant values for stage, $x$-momentum and $y$-momentum at the boundary.
536    \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet
537      boundary but with behaviour varying with time.
538\end{itemize}
539
540\label{ref:tagdescription}Before describing how these boundary
541conditions are assigned, we recall that a mesh is specified using
542three variables \code{points}, \code{vertices} and \code{boundary}.
543In the code we are discussing, these three variables are returned by
544the function \code{rectangular}; however, the example given in
545Section \ref{sec:realdataexample} illustrates another way of
546assigning the values, by means of the function
547\code{create\_mesh\_from\_regions}.
548
549These variables store the data determining the mesh as follows. (You
550may find that the example given in Section \ref{sec:meshexample}
551helps to clarify the following discussion, even though that example
552is a \emph{non-rectangular} mesh.)
553
554\begin{itemize}
555\item The variable \code{points} stores a list of 2-tuples giving the
556coordinates of the mesh points.
557
558\item The variable \code{vertices} stores a list of 3-tuples of
559numbers, representing vertices of triangles in the mesh. In this
560list, the triangle whose vertices are \code{points[i]},
561\code{points[j]}, \code{points[k]} is represented by the 3-tuple
562\code{(i, j, k)}.
563
564\item The variable \code{boundary} is a Python dictionary that
565not only stores the edges that make up the boundary but also assigns
566symbolic tags to these edges to distinguish different parts of the
567boundary. An edge with endpoints \code{points[i]} and
568\code{points[j]} is represented by the 2-tuple \code{(i, j)}. The
569keys for the dictionary are the 2-tuples \code{(i, j)} corresponding
570to boundary edges in the mesh, and the values are the tags are used
571to label them. In the present example, the value \code{boundary[(i,
572j)]} assigned to \code{(i, j)]} is one of the four tags
573\code{`left'}, \code{`right'}, \code{`top'} or \code{`bottom'},
574depending on whether the boundary edge represented by \code{(i, j)}
575occurs at the left, right, top or bottom of the rectangle bounding
576the mesh. The function \code{rectangular} automatically assigns
577these tags to the boundary edges when it generates the mesh.
578\end{itemize}
579
580The tags provide the means to assign different boundary conditions
581to an edge depending on which part of the boundary it belongs to.
582(In Section \ref{sec:realdataexample} we describe an example that
583uses different boundary tags --- in general, the possible tags are entirely selectable by the user when generating the mesh and not
584limited to `left', `right', `top' and `bottom' as in this example.)
585All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by ANUGA.
586
587
588Using the boundary objects described above, we assign a boundary
589condition to each part of the boundary by means of a statement like
590
591{\small \begin{verbatim}
592    domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br})
593\end{verbatim}}
594
595It is critical that all tags are assoctiated with a boundary conditing in this statement. If not the program will halt with a statement like
596
597\begin{verbatim}
598
599Traceback (most recent call last):
600  File "mesh_test.py", line 114, in ?
601    domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br})
602  File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary
603    raise msg
604ERROR (domain.py): Tag "exterior" has not been bound to a boundary object.
605All boundary tags defined in domain must appear in the supplied dictionary.
606The tags are: ['ocean', 'east', 'north', 'exterior', 'south']
607\end{verbatim}
608
609
610The command \code{set\_boundary} stipulates that, in the current example, the right
611boundary varies with time, as defined by the lambda function, while the other
612boundaries are all reflective.
613
614The reader may wish to experiment by varying the choice of boundary
615types for one or more of the boundaries. (In the case of \code{Bd}
616and \code{Bw}, the three arguments in each case represent the
617\code{stage}, $x$-momentum and $y$-momentum, respectively.)
618
619{\small \begin{verbatim}
620    Bw = Time_boundary(domain=domain,
621                       f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
622\end{verbatim}}
623
624
625
626\subsection{Evolution}\index{evolution}
627
628The final statement \nopagebreak[3]
629{\small \begin{verbatim}
630    for t in domain.evolve(yieldstep = 0.1, duration = 4.0):
631        print domain.timestepping_statistics()
632\end{verbatim}}
633
634causes the configuration of the domain to `evolve', over a series of
635steps indicated by the values of \code{yieldstep} and
636\code{duration}, which can be altered as required.  The value of
637\code{yieldstep} controls the time interval between successive model
638outputs.  Behind the scenes more time steps are generally taken.
639
640
641\subsection{Output}
642
643The output is a NetCDF file with the extension \code{.sww}. It
644contains stage and momentum information and can be used with the
645ANUGA viewer \code{animate} (see Section \ref{sec:animate})
646visualisation package
647to generate a visual display. See Section \ref{sec:file formats}
648(page \pageref{sec:file formats}) for more on NetCDF and other file
649formats.
650
651The following is a listing of the screen output seen by the user
652when this example is run:
653
654\verbatiminput{examples/runupoutput.txt}
655
656
657\section{How to Run the Code}
658
659The code can be run in various ways:
660
661\begin{itemize}
662  \item{from a Windows or Unix command line} as in\ \code{python runup.py}
663  \item{within the Python IDLE environment}
664  \item{within emacs}
665  \item{within Windows, by double-clicking the \code{runup.py}
666  file.}
667\end{itemize}
668
669
670\section{Exploring the Model Output}
671
672The following figures are screenshots from the \anuga visualisation
673tool \code{animate}. Figure \ref{fig:runupstart} shows the domain
674with water surface as specified by the initial condition, $t=0$.
675Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and
676$t=4$ where the system has been evolved and the wave is encroaching
677on the previously dry bed.  All figures are screenshots from an
678interactive animation tool called animate which is part of \anuga and
679distributed as in the package anuga\_viewer.
680Animate is described in more detail is Section \ref{sec:animate}.
681
682\begin{figure}[hbt]
683
684  \centerline{\includegraphics[width=75mm, height=75mm]
685    {graphics/bedslopestart.jpg}}
686
687  \caption{Runup example viewed with the ANUGA viewer}
688  \label{fig:runupstart}
689\end{figure}
690
691
692\begin{figure}[hbt]
693
694  \centerline{
695   \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg}
696    \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg}
697   }
698
699  \caption{Runup example viewed with ANGUA viewer}
700  \label{fig:runup2}
701\end{figure}
702
703
704
705\clearpage
706
707%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
708
709\section{A slightly more complex example}
710\label{sec:channelexample}
711
712\subsection{Overview}
713
714The next example is about waterflow in a channel with varying boundary conditions and
715more complex topograhies. These examples build on the
716concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
717The example will be built up through three progressively more complex scripts.
718
719\subsection{Overview}
720As in the case of \file{runup.py}, the actions carried
721out by the program can be organised according to this outline:
722
723\begin{enumerate}
724
725   \item Set up a triangular mesh.
726
727   \item Set certain parameters governing the mode of
728operation of the model---specifying, for instance, where to store the
729model output.
730
731   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
732
733   \item Set up the boundary conditions.
734
735   \item Carry out the evolution of the model through a series of time
736steps and output the results, providing a results file that can be
737visualised.
738
739\end{enumerate}
740
741
742\subsection{The Code}
743
744Here is the code for the first version of the channel flow \file{channel1.py}:
745
746\verbatiminput{demos/channel1.py}
747
748In discussing the details of this example, we follow the outline
749given above, discussing each major step of the code in turn.
750
751\subsection{Establishing the Mesh}\index{mesh, establishing}
752
753In this example we use a similar simple structured triangular mesh as in \code{runup.py}
754for simplicity, but this time we will use a symmetric one and also
755change the physical extent of the domain. The assignment
756
757{\small \begin{verbatim}
758    points, vertices, boundary = rectangular_cross(m, n,
759                                                   len1=length, len2=width)
760\end{verbatim}}
761returns a m x n mesh similar to the one used in the previous example, except that now the
762extent in the x and y directions are given by the value of \code{length} and \code{width}
763respectively.
764
765Defining m and n in terms of the extent as in this example provides a convenient way of
766controlling the resolution: By defining dx and dy to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows:
767
768{\small \begin{verbatim}
769length = 10.
770width = 5.
771dx = dy = 1           # Resolution: Length of subdivisions on both axes
772
773points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
774                                               len1=length, len2=width)
775\end{verbatim}}
776which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decrease the values of dx and dy.
777
778The rest of this script is as in the previous example.
779% except for an application of the 'expression' form of \code{set\_quantity} where we use the value of \code{elevation} to define the (dry) initial condition for \code{stage}:
780%{\small \begin{verbatim}
781%  domain.set_quantity('stage', expression='elevation')
782%\end{verbatim}}
783
784\section{Model Output}
785
786The following figure is a screenshot from the \anuga visualisation
787tool \code{animate} of output from this example.
788\begin{figure}[hbt]
789  \centerline{\includegraphics[height=75mm]
790    {graphics/channel1.png}}%
791
792  \caption{Simple channel example viewed with the ANUGA viewer.}
793  \label{fig:channel1}
794\end{figure}
795
796
797\subsection{Changing boundary conditions on the fly}
798\label{sec:change boundary}
799
800Here is the code for the second version of the channel flow \file{channel2.py}:
801\verbatiminput{demos/channel2.py}
802This example differs from the first version in that a constant outflow boundary condition has
803been defined
804{\small \begin{verbatim}
805    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
806\end{verbatim}}
807and that it is applied to the right hand side boundary when the water level there exceeds 0m.
808{\small \begin{verbatim}
809for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
810    domain.write_time()
811
812    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:
813        print 'Stage > 0: Changing to outflow boundary'
814        domain.set_boundary({'right': Bo})
815\end{verbatim}}
816\label{sec:change boundary code}
817
818The if statement in the timestepping loop (evolve) gets the quantity
819\code{stage} and obtain the interpolated value at the point (10m,
8202.5m) which is on the right boundary. If the stage exceeds 0m a
821message is printed and the old boundary condition at tag 'right' is
822replaced by the outflow boundary using the method
823{\small \begin{verbatim}
824    domain.set_boundary({'right': Bo})
825\end{verbatim}}
826This type of dynamically varying boundary could for example be
827used to model the
828breakdown of a sluice door when water exceeds a certain level.
829
830\subsection{Output}
831
832The text output from this example looks like this
833{\small \begin{verbatim}
834...
835Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
836Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
837Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
838Stage > 0: Changing to outflow boundary
839Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
840Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
841...
842\end{verbatim}}
843
844
845\subsection{Flow through more complex topograhies}
846
847Here is the code for the third version of the channel flow \file{channel3.py}:
848\verbatiminput{demos/channel3.py}
849
850This example differs from the first two versions in that the topography
851contains obstacles.
852
853This is accomplished here by defining the function \code{topography} as follows
854{\small \begin{verbatim}
855def topography(x,y):
856    """Complex topography defined by a function of vectors x and y
857    """
858
859    z = -x/10
860
861    N = len(x)
862    for i in range(N):
863
864        # Step
865        if 10 < x[i] < 12:
866            z[i] += 0.4 - 0.05*y[i]
867
868        # Constriction
869        if 27 < x[i] < 29 and y[i] > 3:
870            z[i] += 2
871
872        # Pole
873        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
874            z[i] += 2
875
876    return z
877\end{verbatim}}
878
879In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
880
881A screenshot of this model at time == 15s is
882\begin{figure}[hbt]
883
884  \centerline{\includegraphics[height=75mm]
885    {graphics/channel3.png}}
886
887  \caption{More complex flow in a channel}
888  \label{fig:channel3}
889\end{figure}
890
891
892
893
894\clearpage
895
896%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
897
898\section{An Example with Real Data}
899\label{sec:realdataexample} The following discussion builds on the
900concepts introduced through the \file{runup.py} example and
901introduces a second example, \file{runcairns.py}.  This refers to
902a {\bf hypothetical} scenario using real-life data,
903in which the domain of interest surrounds the
904Cairns region. Two scenarios are given; firstly, a
905hypothetical tsunami wave is generated by a submarine mass failure
906situated on the edge of the continental shelf, and secondly, a fixed wave
907of given amplitude and period is introduced through the boundary.
908
909{\bf
910Each scenario has been designed to generate a tsunami which will
911inundate the Cairns region. To achieve this, suitably large
912parameters were chosen and were not based on any known tsunami sources
913or realistic amplitudes.
914}
915
916\subsection{Overview}
917As in the case of \file{runup.py}, the actions carried
918out by the program can be organised according to this outline:
919
920\begin{enumerate}
921
922   \item Set up a triangular mesh.
923
924   \item Set certain parameters governing the mode of
925operation of the model---specifying, for instance, where to store the
926model output.
927
928   \item Input various quantities describing physical measurements, such
929as the elevation, to be specified at each mesh point (vertex).
930
931   \item Set up the boundary conditions.
932
933   \item Carry out the evolution of the model through a series of time
934steps and output the results, providing a results file that can be
935visualised.
936
937\end{enumerate}
938
939
940
941\subsection{The Code}
942
943Here is the code for \file{runcairns.py}:
944
945\verbatiminput{demos/cairns/runcairns.py}
946
947In discussing the details of this example, we follow the outline
948given above, discussing each major step of the code in turn.
949
950\subsection{Establishing the Mesh}\index{mesh, establishing}
951
952One obvious way that the present example differs from
953\file{runup.py} is in the use of a more complex method to
954create the mesh. Instead of imposing a mesh structure on a
955rectangular grid, the technique used for this example involves
956building mesh structures inside polygons specified by the user,
957using a mesh-generator.
958
959In its simplest form, the mesh-generator creates the mesh within a single
960polygon whose vertices are at geographical locations specified by
961the user. The user specifies the \emph{resolution}---that is, the
962maximal area of a triangle used for triangulation---and a triangular
963mesh is created inside the polygon using a mesh generation engine.
964On any given platform, the same mesh will be returned.
965%Figure
966%\ref{fig:pentagon} shows a simple example of this, in which the
967%triangulation is carried out within a pentagon.
968
969
970%\begin{figure}[hbt]
971
972%  \caption{Mesh points are created inside the polygon}
973  %\label{fig:pentagon}
974%\end{figure}
975
976Boundary tags are not restricted to \code{`left'}, \code{`bottom'},
977\code{`right'} and \code{`top'}, as in the case of
978\file{runup.py}. Instead the user specifies a list of
979tags appropriate to the configuration being modelled.
980
981In addition, the mesh-generator provides a way to adapt to geographic or
982other features in the landscape, whose presence may require an
983increase in resolution. This is done by allowing the user to specify
984a number of \emph{interior polygons}, each with a specified
985resolution. It is also
986possible to specify one or more `holes'---that is, areas bounded by
987polygons in which no triangulation is required.
988
989%\begin{figure}[hbt]
990%  \caption{Interior meshes with individual resolution}
991%  \label{fig:interior meshes}
992%\end{figure}
993
994In its general form, the mesh-generator takes for its input a bounding
995polygon and (optionally) a list of interior polygons. The user
996specifies resolutions, both for the bounding polygon and for each of
997the interior polygons. Given this data, the mesh-generator first creates a
998triangular mesh with varying resolution.
999
1000The function used to implement this process is
1001\function{create\_mesh\_from\_regions}. Its arguments include the
1002bounding polygon and its resolution, a list of boundary tags, and a
1003list of pairs \code{[polygon, resolution]}, specifying the interior
1004polygons and their resolutions.
1005
1006The resulting mesh is output to a \emph{mesh file}\index{mesh
1007file}\label{def:mesh file}. This term is used to describe a file of
1008a specific format used to store the data specifying a mesh. (There
1009are in fact two possible formats for such a file: it can either be a
1010binary file, with extension \code{.msh}, or an ASCII file, with
1011extension \code{.tsh}. In the present case, the binary file format
1012\code{.msh} is used. See Section \ref{sec:file formats} (page
1013\pageref{sec:file formats}) for more on file formats.)
1014
1015In practice, the details of the polygons used are read from a
1016separate file \file{project.py}. Here is a complete listing of
1017\file{project.py}:
1018
1019\verbatiminput{demos/cairns/project.py}
1020
1021Figure \ref{fig:cairns3d} illustrates the landscape of the region
1022for the Cairns example. Understanding the landscape is important in
1023determining the location and resolution of interior polygons. The
1024supporting data is found in the ASCII grid, \code{cairns.asc}, which
1025has been sourced from the publically available Australian Bathymetry
1026and Topography Grid 2005, \cite{grid250}. The required resolution
1027for inundation modelling will depend on the underlying topography and
1028bathymetry; as the terrain becomes more complex, the desired resolution
1029would decrease to the order of tens of metres.
1030
1031\begin{figure}[hbt]
1032\centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}}
1033\caption{Landscape of the Cairns scenario.}
1034\label{fig:cairns3d}
1035
1036\end{figure}
1037The following statements are used to read in the specific polygons
1038from \code{project.cairns} and assign a defined resolution to
1039each polygon.
1040
1041{\small \begin{verbatim}
1042    islands_res = 100000
1043    cairns_res = 100000
1044    shallow_res = 500000
1045    interior_regions = [[project.poly_cairns, cairns_res],
1046                        [project.poly_island0, islands_res],
1047                        [project.poly_island1, islands_res],
1048                        [project.poly_island2, islands_res],
1049                        [project.poly_island3, islands_res],
1050                        [project.poly_shallow, shallow_res]]
1051\end{verbatim}}
1052
1053Figure \ref{fig:cairnspolys}
1054illustrates the polygons used for the Cairns scenario.
1055
1056\begin{figure}[hbt]
1057
1058  \centerline{\includegraphics[scale=0.5]
1059      {graphics/cairnsmodel.jpg}}
1060  \caption{Interior and bounding polygons for the Cairns example.}
1061  \label{fig:cairnspolys}
1062\end{figure}
1063
1064The statement
1065
1066
1067{\small \begin{verbatim}
1068remainder_res = 10000000
1069create_mesh_from_regions(project.bounding_polygon,
1070                         boundary_tags={'top': [0],
1071                                        'ocean_east': [1],
1072                                        'bottom': [2],
1073                                        'onshore': [3]},
1074                         maximum_triangle_area=remainder_res,
1075                         filename=meshname,
1076                         interior_regions=interior_regions,
1077                         use_cache=True,
1078                         verbose=True)
1079\end{verbatim}}
1080is then used to create the mesh, taking the bounding polygon to be
1081the polygon \code{bounding\_polygon} specified in \file{project.py}.
1082The argument \code{boundary\_tags} assigns a dictionary, whose keys
1083are the names of the boundary tags used for the bounding
1084polygon---\code{`top'}, \code{`ocean\_east'}, \code{`bottom'}, and
1085\code{`onshore'}--- and whose values identify the indices of the
1086segments associated with each of these tags.
1087The polygon may be arranged either clock-wise or counter clock-wise and the
1088indices refer to edges in the order they appear: Edge 0 connects vertex 0 and vertex 1, edge 1 connects vertex 1 and 2; and so forth.
1089(Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges)
1090If polygons intersect, or edges coincide the resolution may be undefined in some regions.
1091Use the underlying mesh interface for such cases. See Section
1092\ref{sec:mesh interface}.
1093
1094Note that every point on each polygon defining the mesh will be used as vertices in triangles.
1095Consequently, polygons with points very close together will cause triangles with very small
1096areas to be generated irrespective of the requested resolution.
1097Make sure points on polygons are spaced to be no closer than the smallest resolution requested.
1098
1099
1100\subsection{Initialising the Domain}
1101
1102As with \file{runup.py}, once we have created the mesh, the next
1103step is to create the data structure \code{domain}. We did this for
1104\file{runup.py} by inputting lists of points and triangles and
1105specifying the boundary tags directly. However, in the present case,
1106we use a method that works directly with the mesh file
1107\code{meshname}, as follows:
1108
1109
1110{\small \begin{verbatim}
1111    domain = Domain(meshname, use_cache=True, verbose=True)
1112\end{verbatim}}
1113
1114Providing a filename instead of the lists used in \file{runup.py}
1115above causes \code{Domain} to convert a mesh file \code{meshname}
1116into an instance of \code{Domain}, allowing us to use methods like
1117\method{set\_quantity} to set quantities and to apply other
1118operations.
1119
1120%(In principle, the
1121%second argument of \function{pmesh\_to\_domain\_instance} can be any
1122%subclass of \class{Domain}, but for applications involving the
1123%shallow-water wave equation, the second argument of
1124%\function{pmesh\_to\_domain\_instance} can always be set simply to
1125%\class{Domain}.)
1126
1127The following statements specify a basename and data directory, and
1128identify quantities to be stored. For the first two, values are
1129taken from \file{project.py}.
1130
1131{\small \begin{verbatim}
1132    domain.set_name(project.basename)
1133    domain.set_datadir(project.outputdir)
1134    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
1135        'ymomentum'])
1136\end{verbatim}}
1137
1138
1139\subsection{Initial Conditions}
1140Quantities for \file{runcairns.py} are set
1141using similar methods to those in \file{runup.py}. However,
1142in this case, many of the values are read from the auxiliary file
1143\file{project.py} or, in the case of \code{elevation}, from an
1144ancillary points file.
1145
1146
1147
1148\subsubsection{Stage}
1149
1150For the scenario we are modelling in this case, we use a callable
1151object \code{tsunami\_source}, assigned by means of a function
1152\function{slide\_tsunami}. This is similar to how we set elevation in
1153\file{runup.py} using a function---however, in this case the
1154function is both more complex and more interesting.
1155
1156The function returns the water displacement for all \code{x} and
1157\code{y} in the domain. The water displacement is a double Gaussian
1158function that depends on the characteristics of the slide (length,
1159width, thickness, slope, etc), its location (origin) and the depth at that
1160location. For this example, we choose to apply the slide function
1161at a specified time into the simulation. {\bf Note, the parameters used
1162in this example have been deliberately chosen to generate a suitably
1163large amplitude tsunami which would inundate the Cairns region.}
1164
1165\subsubsection{Friction}
1166
1167We assign the friction exactly as we did for \file{runup.py}:
1168
1169{\small \begin{verbatim}
1170    domain.set_quantity('friction', 0.0)
1171\end{verbatim}}
1172
1173
1174\subsubsection{Elevation}
1175
1176The elevation is specified by reading data from a file:
1177
1178{\small \begin{verbatim}
1179    domain.set_quantity('elevation',
1180                        filename = project.dem_name + '.pts',
1181                        use_cache = True,
1182                        verbose = True)
1183\end{verbatim}}
1184
1185%However, before this step can be executed, some preliminary steps
1186%are needed to prepare the file from which the data is taken. Two
1187%source files are used for this data---their names are specified in
1188%the file \file{project.py}, in the variables \code{coarsedemname}
1189%and \code{finedemname}. They contain `coarse' and `fine' data,
1190%respectively---that is, data sampled at widely spaced points over a
1191%large region and data sampled at closely spaced points over a
1192%smaller subregion. The data in these files is combined through the
1193%statement
1194
1195%{\small \begin{verbatim}
1196%combine_rectangular_points_files(project.finedemname + '.pts',
1197%                                 project.coarsedemname + '.pts',
1198%                                 project.combineddemname + '.pts')
1199%\end{verbatim}}
1200%The effect of this is simply to combine the datasets by eliminating
1201%any coarse data associated with points inside the smaller region
1202%common to both datasets. The name to be assigned to the resulting
1203%dataset is also derived from the name stored in the variable
1204%\code{combinedname} in the file \file{project.py}.
1205
1206\subsection{Boundary Conditions}\index{boundary conditions}
1207
1208Setting boundaries follows a similar pattern to the one used for
1209\file{runup.py}, except that in this case we need to associate a
1210boundary type with each of the
1211boundary tag names introduced when we established the mesh. In place of the four
1212boundary types introduced for \file{runup.py}, we use the reflective
1213boundary for each of the
1214eight tagged segments defined by \code{create_mesh_from_regions}:
1215
1216{\small \begin{verbatim}
1217Bd = Dirichlet_boundary([0.0,0.0,0.0])
1218domain.set_boundary( {'ocean_east': Bd, 'bottom': Bd, 'onshore': Bd,
1219                          'top': Bd} )
1220\end{verbatim}}
1221
1222\subsection{Evolution}
1223
1224With the basics established, the running of the `evolve' step is
1225very similar to the corresponding step in \file{runup.py}. For the slide
1226scenario,
1227the simulation is run for 5000 seconds with the output stored every ten seconds.
1228For this example, we choose to apply the slide at 60 seconds into the simulation.
1229
1230{\small \begin{verbatim}
1231    import time t0 = time.time()
1232
1233
1234    for t in domain.evolve(yieldstep = 10, finaltime = 60):
1235            domain.write_time()
1236            domain.write_boundary_statistics(tags = 'ocean_east')
1237
1238        # add slide
1239        thisstagestep = domain.get_quantity('stage')
1240        if allclose(t, 60):
1241            slide = Quantity(domain)
1242            slide.set_values(tsunami_source)
1243            domain.set_quantity('stage', slide + thisstagestep)
1244
1245        for t in domain.evolve(yieldstep = 10, finaltime = 5000,
1246                               skip_initial_step = True):
1247            domain.write_time()
1248        domain.write_boundary_statistics(tags = 'ocean_east')
1249\end{verbatim}}
1250
1251For the fixed wave scenario, the simulation is run to 10000 seconds,
1252with the first half of the simulation stored at two minute intervals,
1253and the second half of the simulation stored at ten second intervals.
1254This functionality is especially convenient as it allows the detailed
1255parts of the simulation to be viewed at higher time resolution.
1256
1257
1258{\small \begin{verbatim}
1259
1260# save every two mins leading up to wave approaching land
1261    for t in domain.evolve(yieldstep = 120, finaltime = 5000):
1262        domain.write_time()
1263        domain.write_boundary_statistics(tags = 'ocean_east')
1264
1265    # save every 30 secs as wave starts inundating ashore
1266    for t in domain.evolve(yieldstep = 10, finaltime = 10000,
1267                           skip_initial_step = True):
1268        domain.write_time()
1269        domain.write_boundary_statistics(tags = 'ocean_east')
1270
1271\end{verbatim}}
1272
1273\section{Exploring the Model Output}
1274
1275Now that the scenario has been run, the user can view the output in a number of ways.
1276As described earlier, the user may run animate to view a three-dimensional representation
1277of the simulation.
1278
1279The user may also be interested in a maximum inundation map. This simply shows the
1280maximum water depth over the domain and is achieved with the function sww2dem (described in
1281Section \ref{sec:basicfileconversions}).
1282\file{ExportResults.py} demonstrates how this function can be used:
1283
1284\verbatiminput{demos/cairns/ExportResults.py}
1285
1286The script generates an maximum water depth ASCII grid at a defined
1287resolution (here 100 m$^2$) which can then be viewed in a GIS environment, for
1288example. The parameters used in the function are defined in \file{project.py}.
1289Figures \ref{fig:maxdepthcairnsslide} and \ref{fig:maxdepthcairnsfixedwave} show
1290the maximum water depth within the defined region for the slide and fixed wave scenario
1291respectively. {\bf Note, these inundation maps have been based on purely hypothetical
1292scenarios and were designed explicitly for demonstration purposes only.}
1293The user could develop a maximum absolute momentum or other expressions which can be
1294derived from the quantities.
1295It must be noted here that depth is more meaningful when the elevation is positive
1296(\code{depth} = \code{stage} $-$ \code{elevation}) as it describes the water height
1297above the available elevation. When the elevation is negative, depth is meauring the
1298water height from the sea floor. With this in mind, maximum inundation maps are
1299typically "clipped" to the coastline. However, the data input here did not contain a
1300coastline.
1301
1302\begin{figure}[hbt]
1303\centerline{\includegraphics[scale=0.5]{graphics/slidedepth.jpg}}
1304\caption{Maximum inundation map for the Cairns slide scenario. \bf Note, this
1305inundaiton map has been based on a purely hypothetical scenario which was
1306designed explictiy for demonstration purposes only.}
1307\label{fig:maxdepthcairnsslide}
1308\end{figure}
1309
1310\begin{figure}[hbt]
1311\centerline{\includegraphics[scale=0.5]{graphics/fixedwavedepth.jpg}}
1312\caption{Maximum inundation map for the Cairns fixed wave scenario.
1313\bf Note, this
1314inundaiton map has been based on a purely hypothetical scenario which was
1315designed explictiy for demonstration purposes only.}
1316\label{fig:maxdepthcairnsfixedwave}
1317\end{figure}
1318
1319The user may also be interested in interrogating the solution at a particular spatial
1320location to understand the behaviour of the system through time. To do this, the user
1321must first define the locations of interest. A number of locations have been
1322identified for the Cairns scenario, as shown in Figure \ref{fig:cairnsgauges}.
1323
1324\begin{figure}[hbt]
1325\centerline{\includegraphics[scale=0.5]{graphics/cairnsgauges.jpg}}
1326\caption{Point locations to show time series information for the Cairns scenario.}
1327\label{fig:cairnsgauges}
1328\end{figure}
1329
1330These locations
1331must be stored in either a .csv or .txt file. The corresponding .csv file for
1332the gauges shown in Figure \ref{fig:cairnsgauges} is \file{gauges.csv}
1333
1334\verbatiminput{demos/cairns/gauges.csv}
1335
1336Header information has been included to identify the location in terms of eastings and
1337northings, and each gauge is given a name. The elevation column can be zero here.
1338This information is then passed to the function \code{sww2csv_gauges} (shown in
1339\file{GetTimeseries.py} which generates the csv files for each point location. The csv files
1340can then be used in \code{csv2timeseries_graphs} to create the timeseries plot for each desired
1341quantity. \code{csv2timeseries_graphs} relies on \code{pylab} to be installed which is not part
1342of the standard \code{anuga} release, however it can be downloaded and installed from \code{http://matplotlib.sourceforge.net/}
1343
1344\verbatiminput{demos/cairns/GetTimeseries.py}
1345
1346Here, the time series for the quantities stage, depth and speed will be generated for
1347each gauge defined in the gauge file. As described earlier, depth is more meaningful
1348for onshore gauges, and stage is more appropriate for offshore gauges.
1349
1350As an example output,
1351Figure \ref{fig:reef} shows the time series for the quantity stage for the
1352Elford Reef location for each scenario (the elevation at this location is negative,
1353therefore stage is the more appropriate quantity to plot). Note the large negative stage value when the slide was
1354introduced. This is due to the double gaussian form of the initial surface
1355displacement of the slide. By contrast, the time series for depth is shown for the onshore location of the Cairns
1356Airport in Figure \ref{fig:airportboth}.
1357
1358\begin{figure}[hbt]
1359\centerline{\includegraphics[scale=0.5]{graphics/gaugeElfordReefstage.png}}
1360\caption{Time series information of the quantity stage for the Elford Reef location for the
1361fixed wave and slide scenario.}
1362\label{fig:reef}
1363\end{figure}
1364
1365\begin{figure}[hbt]
1366\centerline{\includegraphics[scale=0.5]{graphics/gaugeCairnsAirportdepth.png}}
1367\caption{Time series information of the quantity depth for the Cairns Airport
1368location for the slide and fixed wave scenario.}
1369\label{fig:airportboth}
1370\end{figure}
1371
1372
1373%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1374%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1375
1376\chapter{\anuga Public Interface}
1377\label{ch:interface}
1378
1379This chapter gives an overview of the features of \anuga available
1380to the user at the public interface. These are grouped under the
1381following headings, which correspond to the outline of the examples
1382described in Chapter \ref{ch:getstarted}:
1383
1384\begin{itemize}
1385    \item Establishing the Mesh
1386    \item Initialising the Domain
1387    \item Specifying the Quantities
1388    \item Initial Conditions
1389    \item Boundary Conditions
1390    \item Forcing Functions
1391    \item Evolution
1392\end{itemize}
1393
1394The listings are intended merely to give the reader an idea of what
1395each feature is, where to find it and how it can be used---they do
1396not give full specifications; for these the reader
1397may consult the code. The code for every function or class contains
1398a documentation string, or `docstring', that specifies the precise
1399syntax for its use. This appears immediately after the line
1400introducing the code, between two sets of triple quotes.
1401
1402Each listing also describes the location of the module in which
1403the code for the feature being described can be found. All modules
1404are in the folder \file{inundation} or one of its subfolders, and the
1405location of each module is described relative to \file{inundation}. Rather
1406than using pathnames, whose syntax depends on the operating system,
1407we use the format adopted for importing the function or class for
1408use in Python code. For example, suppose we wish to specify that the
1409function \function{create\_mesh\_from\_regions} is in a module called
1410\module{mesh\_interface} in a subfolder of \module{inundation} called
1411\code{pmesh}. In Linux or Unix syntax, the pathname of the file
1412containing the function, relative to \file{inundation}, would be
1413
1414\begin{center}
1415%    \code{pmesh/mesh\_interface.py}
1416    \code{pmesh}$\slash$\code{mesh\_interface.py}
1417\end{center}
1418\label{sec:mesh interface}
1419
1420while in Windows syntax it would be
1421
1422\begin{center}
1423    \code{pmesh}$\backslash$\code{mesh\_interface.py}
1424\end{center}
1425
1426Rather than using either of these forms, in this chapter we specify
1427the location simply as \code{pmesh.mesh\_interface}, in keeping with
1428the usage in the Python statement for importing the function,
1429namely:
1430\begin{center}
1431    \code{from pmesh.mesh\_interface import create\_mesh\_from\_regions}
1432\end{center}
1433
1434Each listing details the full set of parameters for the class or
1435function; however, the description is generally limited to the most
1436important parameters and the reader is again referred to the code
1437for more details.
1438
1439The following parameters are common to many functions and classes
1440and are omitted from the descriptions given below:
1441
1442%\begin{center}
1443\begin{tabular}{ll}  %\hline
1444%\textbf{Name } & \textbf{Description}\\
1445%\hline
1446\emph{use\_cache} & Specifies whether caching is to be used for improved performance. See Section \ref{sec:caching} for details on the underlying caching functionality\\
1447\emph{verbose} & If \code{True}, provides detailed terminal output
1448to the user\\  % \hline
1449\end{tabular}
1450%\end{center}
1451
1452\section{Mesh Generation}
1453
1454Before discussing the part of the interface relating to mesh
1455generation, we begin with a description of a simple example of a
1456mesh and use it to describe how mesh data is stored.
1457
1458\label{sec:meshexample} Figure \ref{fig:simplemesh} represents a
1459very simple mesh comprising just 11 points and 10 triangles.
1460
1461
1462\begin{figure}[h]
1463  \begin{center}
1464    \includegraphics[width=90mm, height=90mm]{triangularmesh.jpg}
1465  \end{center}
1466
1467  \caption{A simple mesh}
1468  \label{fig:simplemesh}
1469\end{figure}
1470
1471
1472The variables \code{points}, \code{vertices} and \code{boundary}
1473represent the data displayed in Figure \ref{fig:simplemesh} as
1474follows. The list \code{points} stores the coordinates of the
1475points, and may be displayed schematically as in Table
1476\ref{tab:points}.
1477
1478
1479\begin{table}
1480  \begin{center}
1481    \begin{tabular}[t]{|c|cc|} \hline
1482      index & \code{x} & \code{y}\\  \hline
1483      0 & 1 & 1\\
1484      1 & 4 & 2\\
1485      2 & 8 & 1\\
1486      3 & 1 & 3\\
1487      4 & 5 & 5\\
1488      5 & 8 & 6\\
1489      6 & 11 & 5\\
1490      7 & 3 & 6\\
1491      8 & 1 & 8\\
1492      9 & 4 & 9\\
1493      10 & 10 & 7\\  \hline
1494    \end{tabular}
1495  \end{center}
1496
1497  \caption{Point coordinates for mesh in
1498    Figure \protect \ref{fig:simplemesh}}
1499  \label{tab:points}
1500\end{table}
1501
1502The list \code{vertices} specifies the triangles that make up the
1503mesh. It does this by specifying, for each triangle, the indices
1504(the numbers shown in the first column above) that correspond to the
1505three points at its vertices, taken in an anti-clockwise order
1506around the triangle. Thus, in the example shown in Figure
1507\ref{fig:simplemesh}, the variable \code{vertices} contains the
1508entries shown in Table \ref{tab:vertices}. The starting point is
1509arbitrary so triangle $(0,1,3)$ is considered the same as $(1,3,0)$
1510and $(3,0,1)$.
1511
1512
1513\begin{table}
1514  \begin{center}
1515    \begin{tabular}{|c|ccc|} \hline
1516      index & \multicolumn{3}{c|}{\code{vertices}}\\ \hline
1517      0 & 0 & 1 & 3\\
1518      1 & 1 & 2 & 4\\
1519      2 & 2 & 5 & 4\\
1520      3 & 2 & 6 & 5\\
1521      4 & 4 & 5 & 9\\
1522      5 & 4 & 9 & 7\\
1523      6 & 3 & 4 & 7\\
1524      7 & 7 & 9 & 8\\
1525      8 & 1 & 4 & 3\\
1526      9 & 5 & 10 & 9\\  \hline
1527    \end{tabular}
1528  \end{center}
1529
1530  \caption{Vertices for mesh in Figure \protect \ref{fig:simplemesh}}
1531  \label{tab:vertices}
1532\end{table}
1533
1534Finally, the variable \code{boundary} identifies the boundary
1535triangles and associates a tag with each.
1536
1537\refmodindex[pmesh.meshinterface]{pmesh.mesh\_interface}\label{sec:meshgeneration}
1538
1539\begin{funcdesc}  {create\_mesh\_from\_regions}{bounding_polygon,
1540                             boundary_tags,
1541                             maximum_triangle_area,
1542                             filename=None,
1543                             interior_regions=None,
1544                             poly_geo_reference=None,
1545                             mesh_geo_reference=None,
1546                             minimum_triangle_angle=28.0}
1547Module: \module{pmesh.mesh\_interface}
1548
1549This function allows a user to initiate the automatic creation of a
1550mesh inside a specified polygon (input \code{bounding_polygon}).
1551Among the parameters that can be set are the \emph{resolution}
1552(maximal area for any triangle in the mesh) and the minimal angle
1553allowable in any triangle. The user can specify a number of internal
1554polygons within each of which the resolution of the mesh can be
1555specified. \code{interior_regions} is a paired list containing the
1556interior polygon and its resolution.  Additionally, the user specifies
1557a list of boundary tags, one for each edge of the bounding polygon.
1558
1559\textbf{WARNING}. Note that the dictionary structure used for the
1560parameter \code{boundary\_tags} is different from that used for the
1561variable \code{boundary} that occurs in the specification of a mesh.
1562In the case of \code{boundary}, the tags are the \emph{values} of
1563the dictionary, whereas in the case of \code{boundary_tags}, the
1564tags are the \emph{keys} and the \emph{value} corresponding to a
1565particular tag is a list of numbers identifying boundary edges
1566labelled with that tag. Because of this, it is theoretically
1567possible to assign the same edge to more than one tag. However, an
1568attempt to do this will cause an error.
1569
1570\textbf{WARNING}. Do not have polygon lines cross or be on-top of each
1571    other. This can result in regions of unspecified resolutions. Do
1572    not have polygon close to each other. This can result in the area
1573    between the polygons having small triangles.  For more control
1574    over the mesh outline use the methods described below.
1575
1576\end{funcdesc}
1577
1578
1579
1580\subsection{Advanced mesh generation}
1581
1582For more control over the creation of the mesh outline, use the
1583methods of the class \class{Mesh}.
1584
1585
1586\begin{classdesc}  {Mesh}{userSegments=None,
1587                 userVertices=None,
1588                 holes=None,
1589                 regions=None}
1590Module: \module{pmesh.mesh}
1591
1592A class used to build a mesh outline and generate a two-dimensional
1593triangular mesh. The mesh outline is used to describe features on the
1594mesh, such as the mesh boundary. Many of this classes methods are used
1595to build a mesh outline, such as \code{add\_vertices} and
1596\code{add\_region\_from\_polygon}.
1597
1598\end{classdesc}
1599
1600
1601\subsubsection{Key Methods of Class Mesh}
1602
1603
1604\begin{methoddesc} {add\_hole}{x,y}
1605Module: \module{pmesh.mesh},  Class: \class{Mesh}
1606
1607This method is used to build the mesh outline.  It defines a hole,
1608when the boundary of the hole has already been defined, by selecting a
1609point within the boundary.
1610
1611\end{methoddesc}
1612
1613
1614\begin{methoddesc}  {add\_hole\_from\_polygon}{self, polygon, tags=None}
1615Module: \module{pmesh.mesh},  Class: \class{Mesh}
1616
1617This method is used to add a `hole' within a region ---that is, to
1618define a interior region where the triangular mesh will not be
1619generated---to a \class{Mesh} instance. The region boundary is described by
1620the polygon passed in.  Additionally, the user specifies a list of
1621boundary tags, one for each edge of the bounding polygon.
1622\end{methoddesc}
1623
1624
1625\begin{methoddesc}  {add\_points_and_segments}{self, points, segments,
1626    segment\_tags=None}
1627Module: \module{pmesh.mesh},  Class: \class{Mesh}
1628
1629This method is used to build the mesh outline. It adds points and
1630segments connecting the points.  A tag for each segment can optionally
1631be added.
1632
1633\end{methoddesc}
1634
1635\begin{methoddesc} {add\_region}{x,y}
1636Module: \module{pmesh.mesh},  Class: \class{Mesh}
1637
1638This method is used to build the mesh outline.  It defines a region,
1639when the boundary of the region has already been defined, by selecting
1640a point within the boundary.  A region instance is returned.  This can
1641be used to set the resolution.
1642
1643\end{methoddesc}
1644
1645\begin{methoddesc}  {add\_region\_from\_polygon}{self, polygon,
1646segment_tags=None, region_tag=None
1647                                max_triangle_area=None}
1648Module: \module{pmesh.mesh},  Class: \class{Mesh}
1649
1650This method is used to build the mesh outline.  It adds a region to a
1651\class{Mesh} instance.  Regions are commonly used to describe an area
1652with an increased density of triangles, by setting
1653\code{max_triangle_area}.  The
1654region boundary is described by the input \code{polygon}.  Additionally, the
1655user specifies a list of segment tags, one for each edge of the
1656bounding polygon.  The regional tag is set using  \code{region}.
1657
1658\end{methoddesc}
1659
1660
1661
1662
1663
1664\begin{methoddesc} {add\_vertices}{point_data}
1665Module: \module{pmesh.mesh},  Class: \class{Mesh}
1666
1667Add user vertices. The point_data can be a list of (x,y) values, a numeric
1668array or a geospatial_data instance.
1669\end{methoddesc}
1670
1671\begin{methoddesc} {auto\_segment}{raw_boundary=raw_boundary,
1672                    remove_holes=remove_holes,
1673                    smooth_indents=smooth_indents,
1674                    expand_pinch=expand_pinch}
1675Module: \module{pmesh.mesh},  Class: \class{Mesh}
1676
1677Add segments between some of the user vertices to give the vertices an
1678outline.  The outline is an alpha shape. This method is
1679useful since a set of user vertices need to be outlined by segments
1680before generate_mesh is called.
1681
1682\end{methoddesc}
1683
1684\begin{methoddesc}  {export\_mesh_file}{self,ofile}
1685Module: \module{pmesh.mesh},  Class: \class{Mesh}
1686
1687This method is used to save the mesh to a file. \code{ofile} is the
1688name of the mesh file to be written, including the extension.  Use
1689the extension \code{.msh} for the file to be in NetCDF format and
1690\code{.tsh} for the file to be ASCII format.
1691\end{methoddesc}
1692
1693\begin{methoddesc}  {generate\_mesh}{self,
1694                      maximum_triangle_area=None,
1695                      minimum_triangle_angle=28.0,
1696                      verbose=False}
1697Module: \module{pmesh.mesh},  Class: \class{Mesh}
1698
1699This method is used to generate the triangular mesh.  The  maximal
1700area of any triangle in the mesh can be specified, which is used to
1701control the triangle density, along with the
1702minimum angle in any triangle.
1703\end{methoddesc}
1704
1705
1706
1707\begin{methoddesc}  {import_ungenerate_file}{self,ofile, tag=None,
1708region_tag=None}
1709Module: \module{pmesh.mesh},  Class: \class{Mesh}
1710
1711This method is used to import a polygon file in the ungenerate format,
1712which is used by arcGIS. The polygons from the file are converted to
1713vertices and segments. \code{ofile} is the name of the polygon file.
1714\code{tag} is the tag given to all the polygon's segments.
1715\code{region_tag} is the tag given to all the polygon's segments.  If
1716it is a string the one value will be assigned to all regions.  If it
1717is a list the first value in the list will be applied to the first
1718polygon etc.
1719
1720This function can be used to import building footprints.
1721\end{methoddesc}
1722
1723%%%%%%
1724\section{Initialising the Domain}
1725
1726%Include description of the class Domain and the module domain.
1727
1728%FIXME (Ole): This is also defined in a later chapter
1729%\declaremodule{standard}{...domain}
1730
1731\begin{classdesc} {Domain} {source=None,
1732                 triangles=None,
1733                 boundary=None,
1734                 conserved_quantities=None,
1735                 other_quantities=None,
1736                 tagged_elements=None,
1737                 use_inscribed_circle=False,
1738                 mesh_filename=None,
1739                 use_cache=False,
1740                 verbose=False,
1741                 full_send_dict=None,
1742                 ghost_recv_dict=None,
1743                 processor=0,
1744                 numproc=1}
1745Module: \refmodule{abstract_2d_finite_volumes.domain}
1746
1747This class is used to create an instance of a data structure used to
1748store and manipulate data associated with a mesh. The mesh is
1749specified either by assigning the name of a mesh file to
1750\code{source} or by specifying the points, triangle and boundary of the
1751mesh.
1752\end{classdesc}
1753
1754\subsection{Key Methods of Domain}
1755
1756\begin{methoddesc} {set\_name}{name}
1757    Module: \refmodule{abstract\_2d\_finite\_volumes.domain},
1758    page \pageref{mod:domain}
1759
1760    Assigns the name \code{name} to the domain.
1761\end{methoddesc}
1762
1763\begin{methoddesc} {get\_name}{}
1764    Module: \module{abstract\_2d\_finite\_volumes.domain}
1765
1766    Returns the name assigned to the domain by \code{set\_name}. If no name has been
1767    assigned, returns \code{`domain'}.
1768\end{methoddesc}
1769
1770\begin{methoddesc} {set\_datadir}{name}
1771    Module: \module{abstract\_2d\_finite\_volumes.domain}
1772
1773    Specifies the directory used for SWW files, assigning it to the
1774    pathname \code{name}. The default value, before
1775    \code{set\_datadir} has been run, is the value \code{default\_datadir}
1776    specified in \code{config.py}.
1777
1778    Since different operating systems use different formats for specifying pathnames,
1779    it is necessary to specify path separators using the Python code \code{os.sep}, rather than
1780    the operating-specific ones such as `$\slash$' or `$\backslash$'.
1781    For this to work you will need to include the statement \code{import os}
1782    in your code, before the first appearance of \code{set\_datadir}.
1783
1784    For example, to set the data directory to a subdirectory
1785    \code{data} of the directory \code{project}, you could use
1786    the statements:
1787
1788    {\small \begin{verbatim}
1789        import os
1790        domain.set_datadir{'project' + os.sep + 'data'}
1791    \end{verbatim}}
1792\end{methoddesc}
1793
1794\begin{methoddesc} {get\_datadir}{}
1795    Module: \module{abstract\_2d\_finite\_volumes.domain}
1796
1797    Returns the data directory set by \code{set\_datadir} or,
1798    if \code{set\_datadir} has not
1799    been run, returns the value \code{default\_datadir} specified in
1800    \code{config.py}.
1801\end{methoddesc}
1802
1803
1804\begin{methoddesc} {set\_minimum_allowed_height}{}
1805    Module: \module{shallow\_water.shallow\_water\_domain}
1806
1807    Set the minimum depth (in meters) that will be recognised in
1808    the numerical scheme (including limiters and flux computations)
1809
1810    Default value is $10^{-3}$ m, but by setting this to a greater value,
1811    e.g.\ for large scale simulations, the computation time can be
1812    significantly reduced.
1813\end{methoddesc}
1814
1815
1816\begin{methoddesc} {set\_minimum_storable_height}{}
1817    Module: \module{shallow\_water.shallow\_water\_domain}
1818
1819    Sets the minimum depth that will be recognised when writing
1820    to an sww file. This is useful for removing thin water layers
1821    that seems to be caused by friction creep.
1822\end{methoddesc}
1823
1824
1825\begin{methoddesc} {set\_maximum_allowed_speed}{}
1826    Module: \module{shallow\_water.shallow\_water\_domain}
1827
1828    Set the maximum particle speed that is allowed in water
1829    shallower than minimum_allowed_height. This is useful for
1830    controlling speeds in very thin layers of water and at the same time
1831    allow some movement avoiding pooling of water.
1832\end{methoddesc}
1833
1834
1835\begin{methoddesc} {set\_time}{time=0.0}
1836    Module: \module{abstract\_2d\_finite\_volumes.domain}
1837
1838    Sets the initial time, in seconds, for the simulation. The
1839    default is 0.0.
1840\end{methoddesc}
1841
1842\begin{methoddesc} {set\_default\_order}{n}
1843    Sets the default (spatial) order to the value specified by
1844    \code{n}, which must be either 1 or 2. (Assigning any other value
1845    to \code{n} will cause an error.)
1846\end{methoddesc}
1847
1848
1849\begin{methoddesc} {set\_store\_vertices\_uniquely}{flag}
1850Decide whether vertex values should be stored uniquely as
1851computed in the model or whether they should be reduced to one
1852value per vertex using averaging.
1853
1854Triangles stored in the sww file can be discontinuous reflecting
1855the internal representation of the finite-volume scheme
1856(this is a feature allowing for arbitrary steepness).
1857However, for visual purposes and also for use with \code{Field\_boundary}
1858(and \code{File\_boundary}) it is often desirable to store triangles
1859with values at each vertex point as the average of the potentially
1860discontinuous numbers found at vertices of different triangles sharing the
1861same vertex location.
1862
1863Storing one way or the other is controlled in ANUGA through the method
1864\code{domain.store\_vertices\_uniquely}. Options are
1865\begin{itemize}
1866  \item \code{domain.store\_vertices\_uniquely(True)}: Allow discontinuities in the sww file
1867  \item \code{domain.store\_vertices\_uniquely(False)}: (Default).
1868  Average values
1869  to ensure continuity in sww file. The latter also makes for smaller
1870  sww files.
1871\end{itemize}
1872
1873\end{methoddesc}
1874
1875
1876% Structural methods
1877\begin{methoddesc}{get\_nodes}{absolute=False}
1878    Return x,y coordinates of all nodes in mesh.
1879
1880    The nodes are ordered in an Nx2 array where N is the number of nodes.
1881    This is the same format they were provided in the constructor
1882    i.e. without any duplication.
1883
1884    Boolean keyword argument absolute determines whether coordinates
1885    are to be made absolute by taking georeference into account
1886    Default is False as many parts of ANUGA expects relative coordinates.
1887\end{methoddesc}
1888
1889
1890\begin{methoddesc}{get\_vertex_coordinates}{absolute=False}
1891
1892    Return vertex coordinates for all triangles.
1893
1894    Return all vertex coordinates for all triangles as a 3*M x 2 array
1895    where the jth vertex of the ith triangle is located in row 3*i+j and
1896    M the number of triangles in the mesh.
1897
1898    Boolean keyword argument absolute determines whether coordinates
1899    are to be made absolute by taking georeference into account
1900    Default is False as many parts of ANUGA expects relative coordinates.
1901\end{methoddesc}
1902
1903
1904\begin{methoddesc}{get\_triangles}{indices=None}
1905
1906        Return Mx3 integer array where M is the number of triangles.
1907        Each row corresponds to one triangle and the three entries are
1908        indices into the mesh nodes which can be obtained using the method
1909        get\_nodes()
1910
1911        Optional argument, indices is the set of triangle ids of interest.
1912\end{methoddesc}
1913
1914\begin{methoddesc}{get\_disconnected\_triangles}{}
1915
1916Get mesh based on nodes obtained from get_vertex_coordinates.
1917
1918        Return array Mx3 array of integers where each row corresponds to
1919        a triangle. A triangle is a triplet of indices into
1920        point coordinates obtained from get_vertex_coordinates and each
1921        index appears only once.\\
1922
1923        This provides a mesh where no triangles share nodes
1924        (hence the name disconnected triangles) and different
1925        nodes may have the same coordinates.\\
1926
1927        This version of the mesh is useful for storing meshes with
1928        discontinuities at each node and is e.g. used for storing
1929        data in sww files.\\
1930
1931        The triangles created will have the format
1932
1933    {\small \begin{verbatim}
1934        [[0,1,2],
1935         [3,4,5],
1936         [6,7,8],
1937         ...
1938         [3*M-3 3*M-2 3*M-1]]
1939     \end{verbatim}}
1940\end{methoddesc}
1941
1942
1943
1944%%%%%%
1945\section{Initial Conditions}
1946\label{sec:Initial Conditions}
1947In standard usage of partial differential equations, initial conditions
1948refers to the values associated to the system variables (the conserved
1949quantities here) for \code{time = 0}. In setting up a scenario script
1950as described in Sections \ref{sec:simpleexample} and \ref{sec:realdataexample},
1951\code{set_quantity} is used to define the initial conditions of variables
1952other than the conserved quantities, such as friction. Here, we use the terminology
1953of initial conditions to refer to initial values for variables which need
1954prescription to solve the shallow water wave equation. Further, it must be noted
1955that \code{set_quantity} does not necessarily have to be used in the initial
1956condition setting; it can be used at any time throughout the simulation.
1957
1958\begin{methoddesc}{set\_quantity}{name,
1959    numeric = None,
1960    quantity = None,
1961    function = None,
1962    geospatial_data = None,
1963    filename = None,
1964    attribute_name = None,
1965    alpha = None,
1966    location = 'vertices',
1967    indices = None,
1968    verbose = False,
1969    use_cache = False}
1970  Module: \module{abstract\_2d\_finite\_volumes.domain}
1971  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
1972
1973This function is used to assign values to individual quantities for a
1974domain. It is very flexible and can be used with many data types: a
1975statement of the form \code{domain.set\_quantity(name, x)} can be used
1976to define a quantity having the name \code{name}, where the other
1977argument \code{x} can be any of the following:
1978
1979\begin{itemize}
1980\item a number, in which case all vertices in the mesh gets that for
1981the quantity in question.
1982\item a list of numbers or a Numeric array ordered the same way as the mesh vertices.
1983\item a function (e.g.\ see the samples introduced in Chapter 2)
1984\item an expression composed of other quantities and numbers, arrays, lists (for
1985example, a linear combination of quantities, such as
1986\code{domain.set\_quantity('stage','elevation'+x))}
1987\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.
1988\item a geospatial dataset (See Section \ref{sec:geospatial}).
1989Optional argument attribute\_name applies here as with files.
1990\end{itemize}
1991
1992
1993Exactly one of the arguments
1994  numeric, quantity, function, points, filename
1995must be present.
1996
1997
1998Set quantity will look at the type of the second argument (\code{numeric}) and
1999determine what action to take.
2000
2001Values can also be set using the appropriate keyword arguments.
2002If 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)}
2003are all equivalent.
2004
2005
2006Other optional arguments are
2007\begin{itemize}
2008\item \code{indices} which is a list of ids of triangles to which set\_quantity should apply its assignment of values.
2009\item \code{location} determines which part of the triangles to assign
2010  to. Options are 'vertices' (default), 'edges', 'unique vertices', and 'centroids'.
2011\end{itemize}
2012
2013%%%
2014\anuga provides a number of predefined initial conditions to be used
2015with \code{set\_quantity}. See for example callable object
2016\code{slump\_tsunami} below.
2017
2018\end{methoddesc}
2019
2020
2021
2022
2023\begin{funcdesc}{set_region}{tag, quantity, X, location='vertices'}
2024  Module: \module{abstract\_2d\_finite\_volumes.domain}
2025
2026  (see also \module{abstract\_2d\_finite\_volumes.quantity.set\_values})
2027
2028This function is used to assign values to individual quantities given
2029a regional tag.   It is similar to \code{set\_quantity}.
2030For example, if in the mesh-generator a regional tag of 'ditch' was
2031used, set\_region can be used to set elevation of this region to
2032-10m. X is the constant or function to be applied to the quantity,
2033over the tagged region.  Location describes how the values will be
2034applied.  Options are 'vertices' (default), 'edges', 'unique
2035vertices', and 'centroids'.
2036
2037This method can also be called with a list of region objects.  This is
2038useful for adding quantities in regions, and having one quantity
2039value based on another quantity. See  \module{abstract\_2d\_finite\_volumes.region} for
2040more details.
2041\end{funcdesc}
2042
2043
2044
2045
2046\begin{funcdesc}{slump_tsunami}{length, depth, slope, width=None, thickness=None,
2047                x0=0.0, y0=0.0, alpha=0.0,
2048                gravity=9.8, gamma=1.85,
2049                massco=1, dragco=1, frictionco=0, psi=0,
2050                dx=None, kappa=3.0, kappad=0.8, zsmall=0.01,
2051                domain=None,
2052                verbose=False}
2053Module: \module{shallow\_water.smf}
2054
2055This function returns a callable object representing an initial water
2056displacement generated by a submarine sediment failure. These failures can take the form of
2057a submarine slump or slide. In the case of a slide, use \code{slide_tsunami} instead.
2058
2059The arguments include as a minimum, the slump or slide length, the water depth to the centre of sediment
2060mass, and the bathymetric slope. Other slump or slide parameters can be included if they are known.
2061\end{funcdesc}
2062
2063
2064%%%
2065\begin{funcdesc}{file\_function}{filename,
2066    domain = None,
2067    quantities = None,
2068    interpolation_points = None,
2069    verbose = False,
2070    use_cache = False}
2071Module: \module{abstract\_2d\_finite\_volumes.util}
2072
2073Reads the time history of spatial data for
2074specified interpolation points from a NetCDF file (\code{filename})
2075and returns
2076a callable object. \code{filename} could be a \code{sww} file.
2077Returns interpolated values based on the input
2078file using the underlying \code{interpolation\_function}.
2079
2080\code{quantities} is either the name of a single quantity to be
2081interpolated or a list of such quantity names. In the second case, the resulting
2082function will return a tuple of values---one for each quantity.
2083
2084\code{interpolation\_points} is a list of absolute coordinates or a
2085geospatial object
2086for points at which values are sought.
2087
2088The model time stored within the file function can be accessed using
2089the method \code{f.get\_time()}
2090
2091
2092The underlying algorithm used is as follows:\\
2093Given a time series (i.e.\ a series of values associated with
2094different times), whose values are either just numbers or a set of
2095 numbers defined at the vertices of a triangular mesh (such as those
2096 stored in SWW files), \code{Interpolation\_function} is used to
2097 create a callable object that interpolates a value for an arbitrary
2098 time \code{t} within the model limits and possibly a point \code{(x,
2099 y)} within a mesh region.
2100
2101 The actual time series at which data is available is specified by
2102 means of an array \code{time} of monotonically increasing times. The
2103 quantities containing the values to be interpolated are specified in
2104 an array---or dictionary of arrays (used in conjunction with the
2105 optional argument \code{quantity\_names}) --- called
2106 \code{quantities}. The optional arguments \code{vertex\_coordinates}
2107 and \code{triangles} represent the spatial mesh associated with the
2108 quantity arrays. If omitted the function created by
2109 \code{Interpolation\_function} will be a function of \code{t} only.
2110
2111 Since, in practice, values need to be computed at specified points,
2112 the syntax allows the user to specify, once and for all, a list
2113 \code{interpolation\_points} of points at which values are required.
2114 In this case, the function may be called using the form \code{f(t,
2115 id)}, where \code{id} is an index for the list
2116 \code{interpolation\_points}.
2117
2118
2119\end{funcdesc}
2120
2121%%%
2122%% \begin{classdesc}{Interpolation\_function}{self,
2123%%     time,
2124%%     quantities,
2125%%     quantity_names = None,
2126%%     vertex_coordinates = None,
2127%%     triangles = None,
2128%%     interpolation_points = None,
2129%%     verbose = False}
2130%% Module: \module{abstract\_2d\_finite\_volumes.least\_squares}
2131
2132%% Given a time series (i.e.\ a series of values associated with
2133%% different times), whose values are either just numbers or a set of
2134%% numbers defined at the vertices of a triangular mesh (such as those
2135%% stored in SWW files), \code{Interpolation\_function} is used to
2136%% create a callable object that interpolates a value for an arbitrary
2137%% time \code{t} within the model limits and possibly a point \code{(x,
2138%% y)} within a mesh region.
2139
2140%% The actual time series at which data is available is specified by
2141%% means of an array \code{time} of monotonically increasing times. The
2142%% quantities containing the values to be interpolated are specified in
2143%% an array---or dictionary of arrays (used in conjunction with the
2144%% optional argument \code{quantity\_names}) --- called
2145%% \code{quantities}. The optional arguments \code{vertex\_coordinates}
2146%% and \code{triangles} represent the spatial mesh associated with the
2147%% quantity arrays. If omitted the function created by
2148%% \code{Interpolation\_function} will be a function of \code{t} only.
2149
2150%% Since, in practice, values need to be computed at specified points,
2151%% the syntax allows the user to specify, once and for all, a list
2152%% \code{interpolation\_points} of points at which values are required.
2153%% In this case, the function may be called using the form \code{f(t,
2154%% id)}, where \code{id} is an index for the list
2155%% \code{interpolation\_points}.
2156
2157%% \end{classdesc}
2158
2159%%%
2160%\begin{funcdesc}{set\_region}{functions}
2161%[Low priority. Will be merged into set\_quantity]
2162
2163%Module:\module{abstract\_2d\_finite\_volumes.domain}
2164%\end{funcdesc}
2165
2166
2167
2168%%%%%%
2169\section{Boundary Conditions}\index{boundary conditions}
2170
2171\anuga provides a large number of predefined boundary conditions,
2172represented by objects such as \code{Reflective\_boundary(domain)} and
2173\code{Dirichlet\_boundary([0.2, 0.0, 0.0])}, described in the examples
2174in Chapter 2. Alternatively, you may prefer to ``roll your own'',
2175following the method explained in Section \ref{sec:roll your own}.
2176
2177These boundary objects may be used with the function \code{set\_boundary} described below
2178to assign boundary conditions according to the tags used to label boundary segments.
2179
2180\begin{methoddesc}{set\_boundary}{boundary_map}
2181Module: \module{abstract\_2d\_finite\_volumes.domain}
2182
2183This function allows you to assign a boundary object (corresponding to a
2184pre-defined or user-specified boundary condition) to every boundary segment that
2185has been assigned a particular tag.
2186
2187This is done by specifying a dictionary \code{boundary\_map}, whose values are the boundary objects
2188and whose keys are the symbolic tags.
2189
2190\end{methoddesc}
2191
2192\begin{methoddesc} {get\_boundary\_tags}{}
2193Module: \module{abstract\_2d\_finite\_volumes.domain}
2194
2195Returns a list of the available boundary tags.
2196\end{methoddesc}
2197
2198%%%
2199\subsection{Predefined boundary conditions}
2200
2201\begin{classdesc}{Reflective\_boundary}{Boundary}
2202Module: \module{shallow\_water}
2203
2204Reflective boundary returns same conserved quantities as those present in
2205the neighbouring volume but reflected.
2206
2207This class is specific to the shallow water equation as it works with the
2208momentum quantities assumed to be the second and third conserved quantities.
2209\end{classdesc}
2210
2211%%%
2212\begin{classdesc}{Transmissive\_boundary}{domain = None}
2213Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2214
2215A transmissive boundary returns the same conserved quantities as
2216those present in the neighbouring volume.
2217
2218The underlying domain must be specified when the boundary is instantiated.
2219\end{classdesc}
2220
2221%%%
2222\begin{classdesc}{Dirichlet\_boundary}{conserved_quantities=None}
2223Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2224
2225A Dirichlet boundary returns constant values for each of conserved
2226quantities. In the example of \code{Dirichlet\_boundary([0.2, 0.0, 0.0])},
2227the \code{stage} value at the boundary is 0.2 and the \code{xmomentum} and
2228\code{ymomentum} at the boundary are set to 0.0. The list must contain
2229a value for each conserved quantity.
2230\end{classdesc}
2231
2232%%%
2233\begin{classdesc}{Time\_boundary}{domain = None, f = None}
2234Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2235
2236A time-dependent boundary returns values for the conserved
2237quantities as a function \code{f(t)} of time. The user must specify
2238the domain to get access to the model time.
2239\end{classdesc}
2240
2241%%%
2242\begin{classdesc}{File\_boundary}{Boundary}
2243Module: \module{abstract\_2d\_finite\_volumes.generic\_boundary\_conditions}
2244
2245This method may be used if the user wishes to apply a SWW file or
2246a time series file to a boundary segment or segments.
2247The boundary values are obtained from a file and interpolated to the
2248appropriate segments for each conserved quantity.
2249\end{classdesc}
2250
2251
2252
2253%%%
2254\begin{classdesc}{Transmissive\_Momentum\_Set\_Stage\_boundary}{Boundary}
2255Module: \module{shallow\_water}
2256
2257This boundary returns same momentum conserved quantities as
2258those present in its neighbour volume but sets stage as in a Time\_boundary.
2259The underlying domain must be specified when boundary is instantiated
2260
2261This type of boundary is useful when stage is known at the boundary as a
2262function of time, but momenta (or speeds) aren't.
2263
2264This class is specific to the shallow water equation as it works with the
2265momentum quantities assumed to be the second and third conserved quantities.
2266\end{classdesc}
2267
2268
2269\begin{classdesc}{Dirichlet\_Discharge\_boundary}{Boundary}
2270Module: \module{shallow\_water}
2271
2272Sets stage (stage0)
2273Sets momentum (wh0) in the inward normal direction.
2274\end{classdesc}
2275
2276
2277
2278\subsection{User-defined boundary conditions}
2279\label{sec:roll your own}
2280
2281All boundary classes must inherit from the generic boundary class
2282\code{Boundary} and have a method called \code{evaluate} which must
2283take as inputs \code{self, vol\_id, edge\_id} where self refers to the
2284object itself and vol\_id and edge\_id are integers referring to
2285particular edges. The method must return a list of three floating point
2286numbers representing values for \code{stage},
2287\code{xmomentum} and \code{ymomentum}, respectively.
2288
2289The constructor of a particular boundary class may be used to specify
2290particular values or flags to be used by the \code{evaluate} method.
2291Please refer to the source code for the existing boundary conditions
2292for examples of how to implement boundary conditions.
2293
2294
2295
2296\section{Forcing Terms}
2297\label{forcing terms}
2298
2299\anuga provides a number of predefined forcing functions to be used with simulations.
2300Gravity and friction are always calculated using the elevation and friction quantities, but the user may additionally add forcing terms to the list
2301\code{domain.forcing\_terms} and have them affect the model.
2302 
2303Currently, predifiend forcing terms are
2304
2305\begin{funcdesc}{General\_forcing}{}
2306  Module: \module{shallow\_water.shallow\_water\_domain}
2307
2308  This is a general class to modify any quantity according to a given rate of change.
2309  Other specific forcing terms are based on this class but it can be used by itself as well (e.g.\ to modify momentum).
2310 
2311  The General\_forcing class takes as input:
2312  \begin{itemize} 
2313    \item \code{domain}: a reference to the domain being evolved
2314    \item \code{quantity\_name}: The name of the quantity that will be affected by this forcing term
2315    \item \code{rate}: The rate at which the quantity should change. The parameter \code{rate} can be eithe a constant or a
2316                function of time. Positive values indicate increases,
2317                negative values indicate decreases.
2318                The parametr \code{rate} can be \code{None} at initialisation but must be specified
2319                before forcing term is applied (i.e. simulation has started).
2320                The default value is 0.0 - i.e.\ no forcing.
2321    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2322    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2323  \end{itemize}
2324  Note specifying both center, radius and polygon will cause an exception to be thrown.
2325
2326   
2327  Example:
2328  {\scriptsize \begin{verbatim} 
2329        xmom = General_forcing(domain, 'xmomentum', polygon=P)
2330        ymom = General_forcing(domain, 'ymomentum', polygon=P)
2331
2332        xmom.rate = f
2333        ymom.rate = g
2334 
2335        domain.forcing_terms.append(xmom)
2336        domain.forcing_terms.append(ymom)       
2337  \end{verbatim}}
2338  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.
2339  P is assumed to be polygon, specified as a list of points, e.g. a square \code{P = [[x0, y0], [x1, y0], [x1, y1], [x0, y1]]}
2340 
2341\end{funcdesc} 
2342
2343
2344\begin{funcdesc}{Inflow}{}
2345  Module: \module{shallow\_water.shallow\_water\_domain}
2346
2347  This is a general class for infiltration and abstraction of water according to a given rate of change.
2348  This class will always modify the \code{stage} quantity.
2349 
2350  Inflow is based on the General_forcing class so the functionality is similar.
2351 
2352  The Inflow class takes as input:
2353  \begin{itemize} 
2354    \item \code{domain}: a reference to the domain being evolved
2355    \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
2356                function of time. Positive values indicate inflow,
2357                negative values indicate outflow.
2358               
2359                Note: The specified flow will be divided by the area of
2360                the inflow region and then applied to update the
2361                stage quantity.     
2362    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2363    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2364  \end{itemize}
2365
2366   
2367  Example:
2368  {\scriptsize \begin{verbatim} 
2369    hydrograph = Inflow(center=(320, 300), radius=10,
2370                        rate=file_function('QPMF_Rot_Sub13.tms'))
2371
2372    domain.forcing_terms.append(hydrograph)
2373  \end{verbatim}}
2374  Here, \code{'QPMF_Rot_Sub13.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for a hydrograph.
2375\end{funcdesc} 
2376
2377
2378\begin{funcdesc}{Rainfall}{}
2379  Module: \module{shallow\_water.shallow\_water\_domain}
2380
2381  This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon.
2382  This class will always modify the \code{stage} quantity.
2383 
2384  Rainfall is based on the General_forcing class so the functionality is similar.
2385 
2386  The Rainfall class takes as input:
2387  \begin{itemize} 
2388    \item \code{domain}: a reference to the domain being evolved
2389    \item \code{rate}: Total rain rate over the specified domain. 
2390                  Note: Raingauge Data needs to reflect the time step.
2391                  For example: if rain gauge is mm read every \code{dt} seconds, then the input
2392                  here is as \code{mm/dt} so 10 mm in 5 minutes becomes
2393                  10/(5x60) = 0.0333mm/s.
2394       
2395                  This parameter can be either a constant or a
2396                  function of time. Positive values indicate rain being added (or be used for general infiltration),
2397                  negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction).
2398    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2399    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2400  \end{itemize}
2401 
2402  Example:
2403  {\scriptsize \begin{verbatim} 
2404 
2405    catchmentrainfall = Rainfall(rain=file_function('Q100_2hr_Rain.tms')) 
2406    domain.forcing_terms.append(catchmentrainfall)
2407
2408  \end{verbatim}}
2409  Here, \code{'Q100_2hr_Rain.tms'} is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for the rainfall.
2410\end{funcdesc} 
2411
2412
2413
2414\begin{funcdesc}{Culvert\_flow}{}
2415  Module: \module{culver\_flows.culvert\_class}
2416
2417  This is a general class for implementing flow through a culvert.
2418  This class modifies the quantities \code{stage, xmomentum, ymomentum} in areas at both ends of the culvert.
2419 
2420  The Culvert\_flow forcing term uses \code{Inflow} and {General\_forcing} to update the quantities. The flow drection is determined on-the-fly so
2421  openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow and Outflow.
2422 
2423  The Culvert\_flow class takes as input:
2424  \begin{itemize} 
2425    \item \code{domain}: a reference to the domain being evolved
2426    \item \code{label}: Short text naming the culvert
2427    \item \code{description}: Text describing it
2428    \item \code{end_point0}: Coordinates of one opening
2429    \item \code{end_point1}: Coordinates of other opening
2430    \item \code{width}:
2431    \item \code{height}:
2432    \item \code{diameter}:
2433    \item \code{manning}: Mannings Roughness for Culvert
2434    \item \code{invert_level0}: Invert level if not the same as the Elevation on the Domain
2435    \item \code{invert_level1}: Invert level if not the same as the Elevation on the Domain
2436    \item \code{culvert_routine}: Function specifying the calculation of flow based on energy difference between the two openings (see below)
2437  \end{itemize}
2438
2439  The user can specify different culvert routines. Hower ANUGA currently specifies one, namely the \code{boyd\_generalised\_culvert\_model} as used in the example below.
2440     
2441  Example:
2442  {\scriptsize \begin{verbatim} 
2443    from anuga.culvert_flows.culvert_class import Culvert_flow
2444    from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model 
2445
2446    culvert1 = Culvert_flow(domain,
2447                           label='Culvert No. 1',
2448                           description='This culvert is a test unit 1.2m Wide by 0.75m High',   
2449                           end_point0=[9.0, 2.5],
2450                           end_point1=[13.0, 2.5],
2451                           width=1.20,height=0.75,
2452                           culvert_routine=boyd_generalised_culvert_model,       
2453                           verbose=True)
2454
2455    culvert2 = Culvert_flow(domain,
2456                           label='Culvert No. 2',
2457                           description='This culvert is a circular test with d=1.2m',   
2458                           end_point0=[9.0, 1.5],
2459                           end_point1=[30.0, 3.5],
2460                           diameter=1.20,
2461                           invert_level0=7,
2462                           culvert_routine=boyd_generalised_culvert_model,       
2463                           verbose=True)
2464                           
2465    domain.forcing_terms.append(culvert1)
2466    domain.forcing_terms.append(culvert2)
2467
2468   
2469  \end{verbatim}}
2470\end{funcdesc} 
2471
2472
2473
2474
2475
2476
2477\section{Evolution}\index{evolution}
2478
2479  \begin{methoddesc}{evolve}{yieldstep = None, finaltime = None, duration = None, skip_initial_step = False}
2480
2481  Module: \module{abstract\_2d\_finite\_volumes.domain}
2482
2483  This function (a method of \class{domain}) is invoked once all the
2484  preliminaries have been completed, and causes the model to progress
2485  through successive steps in its evolution, storing results and
2486  outputting statistics whenever a user-specified period
2487  \code{yieldstep} is completed (generally during this period the
2488  model will evolve through several steps internally
2489  as the method forces the water speed to be calculated
2490  on successive new cells). The user
2491  specifies the total time period over which the evolution is to take
2492  place, by specifying values (in seconds) for either \code{duration}
2493  or \code{finaltime}, as well as the interval in seconds after which
2494  results are to be stored and statistics output.
2495
2496  You can include \method{evolve} in a statement of the type:
2497
2498  {\small \begin{verbatim}
2499      for t in domain.evolve(yieldstep, finaltime):
2500          <Do something with domain and t>
2501  \end{verbatim}}
2502
2503  \end{methoddesc}
2504
2505
2506
2507\subsection{Diagnostics}
2508\label{sec:diagnostics}
2509
2510
2511  \begin{funcdesc}{statistics}{}
2512  Module: \module{abstract\_2d\_finite\_volumes.domain}
2513
2514  \end{funcdesc}
2515
2516  \begin{funcdesc}{timestepping\_statistics}{}
2517  Module: \module{abstract\_2d\_finite\_volumes.domain}
2518
2519  Returns a string of the following type for each
2520  timestep:
2521
2522  \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12
2523  (12)}
2524
2525  Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and
2526  the number of first-order steps, respectively.\\
2527
2528  The optional keyword argument \code{track_speeds=True} will
2529  generate a histogram of speeds generated by each triangle. The
2530  speeds relate to the size of the timesteps used by ANUGA and
2531  this diagnostics may help pinpoint problem areas where excessive speeds
2532  are generated.
2533
2534  \end{funcdesc}
2535
2536
2537  \begin{funcdesc}{boundary\_statistics}{quantities = None, tags = None}
2538  Module: \module{abstract\_2d\_finite\_volumes.domain}
2539
2540  Returns a string of the following type when \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']}:
2541
2542  {\small \begin{verbatim}
2543 Boundary values at time 0.5000:
2544    top:
2545        stage in [ -0.25821218,  -0.02499998]
2546    bottom:
2547        stage in [ -0.27098821,  -0.02499974]
2548  \end{verbatim}}
2549
2550  \end{funcdesc}
2551
2552
2553  \begin{funcdesc}{get\_quantity}{name, location='vertices', indices = None}
2554  Module: \module{abstract\_2d\_finite\_volumes.domain}
2555
2556  Allow access to individual quantities and their methods
2557
2558  \end{funcdesc}
2559
2560
2561  \begin{funcdesc}{set\_quantities\_to\_be\_monitored}{}
2562  Module: \module{abstract\_2d\_finite\_volumes.domain}
2563
2564  Selects quantities and derived quantities for which extrema attained at internal timesteps
2565  will be collected.
2566
2567  Information can be tracked in the evolve loop by printing \code{quantity\_statistics} and
2568  collected data will be stored in the sww file.
2569
2570  Optional parameters \code{polygon} and \code{time\_interval} may be specified to restrict the
2571  extremum computation.
2572  \end{funcdesc}
2573
2574  \begin{funcdesc}{quantity\_statistics}{}
2575  Module: \module{abstract\_2d\_finite\_volumes.domain}
2576
2577  Reports on extrema attained by selected quantities.
2578
2579  Returns a string of the following type for each
2580  timestep:
2581
2582  \begin{verbatim}
2583  Monitored quantities at time 1.0000:
2584    stage-elevation:
2585      values since time = 0.00 in [0.00000000, 0.30000000]
2586      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2587      maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667)
2588    ymomentum:
2589      values since time = 0.00 in [0.00000000, 0.06241221]
2590      minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667)
2591      maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667)
2592    xmomentum:
2593      values since time = 0.00 in [-0.06062178, 0.47886313]
2594      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2595      maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667)
2596  \end{verbatim}
2597
2598  The quantities (and derived quantities) listed here must be selected at model
2599  initialisation using the method \code{domain.set_quantities_to_be_monitored}.\\
2600
2601  The optional keyword argument \code{precision='\%.4f'} will
2602  determine the precision used for floating point values in the output.
2603  This diagnostics helps track extrema attained by the selected quantities
2604  at every internal timestep.
2605
2606  These values are also stored in the sww file for post processing.
2607
2608  \end{funcdesc}
2609
2610
2611
2612  \begin{funcdesc}{get\_values}{location='vertices', indices = None}
2613  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2614
2615  Extract values for quantity as an array
2616
2617  \end{funcdesc}
2618
2619
2620  \begin{funcdesc}{get\_integral}{}
2621  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2622
2623  Return computed integral over entire domain for this quantity
2624
2625  \end{funcdesc}
2626
2627
2628
2629
2630  \begin{funcdesc}{get\_maximum\_value}{indices = None}
2631  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2632
2633  Return maximum value of quantity (on centroids)
2634
2635  Optional argument indices is the set of element ids that
2636  the operation applies to. If omitted all elements are considered.
2637
2638  We do not seek the maximum at vertices as each vertex can
2639  have multiple values - one for each triangle sharing it.
2640  \end{funcdesc}
2641
2642
2643
2644  \begin{funcdesc}{get\_maximum\_location}{indices = None}
2645  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2646
2647  Return location of maximum value of quantity (on centroids)
2648
2649  Optional argument indices is the set of element ids that
2650  the operation applies to.
2651
2652  We do not seek the maximum at vertices as each vertex can
2653  have multiple values - one for each triangle sharing it.
2654
2655  If there are multiple cells with same maximum value, the
2656  first cell encountered in the triangle array is returned.
2657  \end{funcdesc}
2658
2659
2660
2661  \begin{funcdesc}{get\_wet\_elements}{indices=None}
2662  Module: \module{shallow\_water.shallow\_water\_domain}
2663
2664  Return indices for elements where h $>$ minimum_allowed_height
2665  Optional argument indices is the set of element ids that the operation applies to.
2666  \end{funcdesc}
2667
2668
2669  \begin{funcdesc}{get\_maximum\_inundation\_elevation}{indices=None}
2670  Module: \module{shallow\_water.shallow\_water\_domain}
2671
2672  Return highest elevation where h $>$ 0.\\
2673  Optional argument indices is the set of element ids that the operation applies to.\\
2674
2675  Example to find maximum runup elevation:\\
2676     z = domain.get_maximum_inundation_elevation()
2677  \end{funcdesc}
2678
2679
2680  \begin{funcdesc}{get\_maximum\_inundation\_location}{indices=None}
2681  Module: \module{shallow\_water.shallow\_water\_domain}
2682
2683  Return location (x,y) of highest elevation where h $>$ 0.\\
2684  Optional argument indices is the set of element ids that the operation applies to.\\
2685
2686  Example to find maximum runup location:\\
2687     x, y = domain.get_maximum_inundation_location()
2688  \end{funcdesc}
2689
2690
2691\section{Queries of SWW model output files}
2692After a model has been run, it is often useful to extract various information from the sww
2693output file (see Section \ref{sec:sww format}). This is typically more convenient than using the
2694diagnostics described in Section \ref{sec:diagnostics} which rely on the model running - something
2695that can be very time consuming. The sww files are easy and quick to read and offer much information
2696about the model results such as runup heights, time histories of selected quantities,
2697flow through cross sections and much more.
2698
2699\begin{funcdesc}{get\_maximum\_inundation\_elevation}{filename, polygon=None,
2700    time_interval=None, verbose=False}
2701  Module: \module{shallow\_water.data\_manager}
2702
2703  Return highest elevation where depth is positive ($h > 0$)
2704
2705  Example to find maximum runup elevation:\\
2706  max_runup = get_maximum_inundation_elevation(filename,
2707  polygon=None,
2708  time_interval=None,
2709  verbose=False)
2710
2711
2712  filename is a NetCDF sww file containing ANUGA model output.
2713  Optional arguments polygon and time_interval restricts the maximum runup calculation
2714  to a points that lie within the specified polygon and time interval.
2715
2716  If no inundation is found within polygon and time_interval the return value
2717  is None signifying "No Runup" or "Everything is dry".
2718
2719  See doc string for general function get_maximum_inundation_data for details.
2720\end{funcdesc}
2721
2722
2723\begin{funcdesc}{get\_maximum\_inundation\_location}{filename, polygon=None,
2724    time_interval=None, verbose=False}
2725  Module: \module{shallow\_water.data\_manager}
2726
2727  Return location (x,y) of highest elevation where depth is positive ($h > 0$)
2728
2729  Example to find maximum runup location:\\
2730  max_runup_location = get_maximum_inundation_location(filename,
2731  polygon=None,
2732  time_interval=None,
2733  verbose=False)
2734
2735
2736  filename is a NetCDF sww file containing ANUGA model output.
2737  Optional arguments polygon and time_interval restricts the maximum runup calculation
2738  to a points that lie within the specified polygon and time interval.
2739
2740  If no inundation is found within polygon and time_interval the return value
2741  is None signifying "No Runup" or "Everything is dry".
2742
2743  See doc string for general function get_maximum_inundation_data for details.
2744\end{funcdesc}
2745
2746
2747\begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report = None, reportname = None,
2748plot_quantity = None, generate_fig = False, surface = None, time_min = None, time_max = None, time_thinning = 1,
2749time_unit = None, title_on = None, use_cache = False, verbose = False}
2750
2751  Module: \module{anuga.abstract\_2d\_finite\_volumes.util}
2752
2753  Return csv files for the location in the \code{gauge_filename} and can also return plots of them
2754
2755  See doc string for general function sww2timeseries for details.
2756
2757\end{funcdesc}
2758
2759
2760\begin{funcdesc}{get\_flow\_through\_cross\_section}{filename, cross\_section, verbose=False}
2761  Module: \module{shallow\_water.data\_manager}
2762
2763  Obtain flow $[m^2]$ perpendicular to specified cross section.
2764
2765  Inputs:
2766  \begin{itemize} 
2767        \item filename: Name of sww file containing ANUGA model output.
2768        \item polyline: Representation of desired cross section - it may contain multiple
2769          sections allowing for complex shapes. Assume absolute UTM coordinates.
2770  \end{itemize} 
2771
2772  Output:
2773  \begin{itemize}
2774    \item time: All stored times in sww file
2775    \item Q: Hydrograph of total flow across given segments for all stored times.
2776  \end{itemize} 
2777 
2778  The normal flow is computed for each triangle intersected by the polyline and
2779  added up.  Multiple segments at different angles are specified the normal flows
2780  may partially cancel each other.
2781 
2782  Example to find flow through cross section:
2783 
2784  \begin{verbatim} 
2785  cross_section = [[x, 0], [x, width]]
2786  time, Q = get_flow_through_cross_section(filename,
2787                                           cross_section,
2788                                           verbose=False)
2789  \end{verbatim} 
2790
2791
2792  See doc string for general function get_maximum_inundation_data for details.
2793 
2794\end{funcdesc}
2795
2796
2797
2798\section{Other}
2799
2800  \begin{funcdesc}{domain.create\_quantity\_from\_expression}{string}
2801
2802  Handy for creating derived quantities on-the-fly as for example
2803  \begin{verbatim}
2804  Depth = domain.create_quantity_from_expression('stage-elevation')
2805
2806  exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5')
2807  Absolute_momentum = domain.create_quantity_from_expression(exp)
2808  \end{verbatim}
2809
2810  %See also \file{Analytical\_solution\_circular\_hydraulic\_jump.py} for an example of use.
2811  \end{funcdesc}
2812
2813
2814
2815
2816
2817%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2818%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2819
2820\chapter{\anuga System Architecture}
2821
2822
2823\section{File Formats}
2824\label{sec:file formats}
2825
2826\anuga makes use of a number of different file formats. The
2827following table lists all these formats, which are described in more
2828detail in the paragraphs below.
2829
2830\bigskip
2831
2832\begin{center}
2833
2834\begin{tabular}{|ll|}  \hline
2835
2836\textbf{Extension} & \textbf{Description} \\
2837\hline\hline
2838
2839\code{.sww} & NetCDF format for storing model output
2840\code{f(t,x,y)}\\
2841
2842\code{.tms} & NetCDF format for storing time series \code{f(t)}\\
2843
2844\code{.csv/.txt} & ASCII format called points csv for storing
2845arbitrary points and associated attributes\\
2846
2847\code{.pts} & NetCDF format for storing arbitrary points and
2848associated attributes\\
2849
2850\code{.asc} & ASCII format of regular DEMs as output from ArcView\\
2851
2852\code{.prj} & Associated ArcView file giving more metadata for
2853\code{.asc} format\\
2854
2855\code{.ers} & ERMapper header format of regular DEMs for ArcView\\
2856
2857\code{.dem} & NetCDF representation of regular DEM data\\
2858
2859\code{.tsh} & ASCII format for storing meshes and associated
2860boundary and region info\\
2861
2862\code{.msh} & NetCDF format for storing meshes and associated
2863boundary and region info\\
2864
2865\code{.nc} & Native ferret NetCDF format\\
2866
2867\code{.geo} & Houdinis ASCII geometry format (?) \\  \par \hline
2868%\caption{File formats used by \anuga}
2869\end{tabular}
2870
2871
2872\end{center}
2873
2874The above table shows the file extensions used to identify the
2875formats of files. However, typically, in referring to a format we
2876capitalise the extension and omit the initial full stop---thus, we
2877refer, for example, to `SWW files' or `PRJ files'.
2878
2879\bigskip
2880
2881A typical dataflow can be described as follows:
2882
2883\subsection{Manually Created Files}
2884
2885\begin{tabular}{ll}
2886ASC, PRJ & Digital elevation models (gridded)\\
2887NC & Model outputs for use as boundary conditions (e.g. from MOST)
2888\end{tabular}
2889
2890\subsection{Automatically Created Files}
2891
2892\begin{tabular}{ll}
2893ASC, PRJ  $\rightarrow$  DEM  $\rightarrow$  PTS & Convert
2894DEMs to native \code{.pts} file\\
2895
2896NC $\rightarrow$ SWW & Convert MOST boundary files to
2897boundary \code{.sww}\\
2898
2899PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\
2900
2901TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using
2902\code{animate}\\
2903
2904TSH + Boundary SWW $\rightarrow$ SWW & Simulation using
2905\code{\anuga}\\
2906
2907Polygonal mesh outline $\rightarrow$ & TSH or MSH
2908\end{tabular}
2909
2910
2911
2912
2913\bigskip
2914
2915\subsection{SWW and TMS Formats}
2916\label{sec:sww format}
2917
2918The SWW and TMS formats are both NetCDF formats, and are of key
2919importance for \anuga.
2920
2921An SWW file is used for storing \anuga output and therefore pertains
2922to a set of points and a set of times at which a model is evaluated.
2923It contains, in addition to dimension information, the following
2924variables:
2925
2926\begin{itemize}
2927    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2928    \item \code{elevation}, a Numeric array storing bed-elevations
2929    \item \code{volumes}, a list specifying the points at the vertices of each of the
2930    triangles
2931    % Refer here to the example to be provided in describing the simple example
2932    \item \code{time}, a Numeric array containing times for model
2933    evaluation
2934\end{itemize}
2935
2936
2937The contents of an SWW file may be viewed using the anuga viewer
2938\code{animate}, which creates an on-screen geometric
2939representation. See section \ref{sec:animate} (page
2940\pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more
2941on \code{animate}.
2942
2943Alternatively, there are tools, such as \code{ncdump}, that allow
2944you to convert an NetCDF file into a readable format such as the
2945Class Definition Language (CDL). The following is an excerpt from a
2946CDL representation of the output file \file{runup.sww} generated
2947from running the simple example \file{runup.py} of
2948Chapter \ref{ch:getstarted}:
2949
2950\verbatiminput{examples/bedslopeexcerpt.cdl}
2951
2952The SWW format is used not only for output but also serves as input
2953for functions such as \function{file\_boundary} and
2954\function{file\_function}, described in Chapter \ref{ch:interface}.
2955
2956A TMS file is used to store time series data that is independent of
2957position.
2958
2959
2960\subsection{Mesh File Formats}
2961
2962A mesh file is a file that has a specific format suited to
2963triangular meshes and their outlines. A mesh file can have one of
2964two formats: it can be either a TSH file, which is an ASCII file, or
2965an MSH file, which is a NetCDF file. A mesh file can be generated
2966from the function \function{create\_mesh\_from\_regions} (see
2967Section \ref{sec:meshgeneration}) and used to initialise a domain.
2968
2969A mesh file can define the outline of the mesh---the vertices and
2970line segments that enclose the region in which the mesh is
2971created---and the triangular mesh itself, which is specified by
2972listing the triangles and their vertices, and the segments, which
2973are those sides of the triangles that are associated with boundary
2974conditions.
2975
2976In addition, a mesh file may contain `holes' and/or `regions'. A
2977hole represents an area where no mesh is to be created, while a
2978region is a labelled area used for defining properties of a mesh,
2979such as friction values.  A hole or region is specified by a point
2980and bounded by a number of segments that enclose that point.
2981
2982A mesh file can also contain a georeference, which describes an
2983offset to be applied to $x$ and $y$ values---eg to the vertices.
2984
2985
2986\subsection{Formats for Storing Arbitrary Points and Attributes}
2987
2988
2989A CSV/TXT file is used to store data representing
2990arbitrary numerical attributes associated with a set of points.
2991
2992The format for an CSV/TXT file is:\\
2993%\begin{verbatim}
2994
2995            first line:     \code{[column names]}\\
2996            other lines:  \code{[x value], [y value], [attributes]}\\
2997
2998            for example:\\
2999            \code{x, y, elevation, friction}\\
3000            \code{0.6, 0.7, 4.9, 0.3}\\
3001            \code{1.9, 2.8, 5, 0.3}\\
3002            \code{2.7, 2.4, 5.2, 0.3}
3003
3004        The delimiter is a comma. The first two columns are assumed to
3005        be x, y coordinates.
3006       
3007
3008A PTS file is a NetCDF representation of the data held in an points CSV
3009file. If the data is associated with a set of $N$ points, then the
3010data is stored using an $N \times 2$ Numeric array of float
3011variables for the points and an $N \times 1$ Numeric array for each
3012attribute.
3013
3014%\end{verbatim}
3015
3016\subsection{ArcView Formats}
3017
3018Files of the three formats ASC, PRJ and ERS are all associated with
3019data from ArcView.
3020
3021An ASC file is an ASCII representation of DEM output from ArcView.
3022It contains a header with the following format:
3023
3024\begin{tabular}{l l}
3025\code{ncols}      &   \code{753}\\
3026\code{nrows}      &   \code{766}\\
3027\code{xllcorner}  &   \code{314036.58727982}\\
3028\code{yllcorner}  & \code{6224951.2960092}\\
3029\code{cellsize}   & \code{100}\\
3030\code{NODATA_value} & \code{-9999}
3031\end{tabular}
3032
3033The remainder of the file contains the elevation data for each grid point
3034in the grid defined by the above information.
3035
3036A PRJ file is an ArcView file used in conjunction with an ASC file
3037to represent metadata for a DEM.
3038
3039
3040\subsection{DEM Format}
3041
3042A DEM file is a NetCDF representation of regular DEM data.
3043
3044
3045\subsection{Other Formats}
3046
3047
3048
3049
3050\subsection{Basic File Conversions}
3051\label{sec:basicfileconversions}
3052
3053  \begin{funcdesc}{sww2dem}{basename_in, basename_out = None,
3054            quantity = None,
3055            timestep = None,
3056            reduction = None,
3057            cellsize = 10,
3058            NODATA_value = -9999,
3059            easting_min = None,
3060            easting_max = None,
3061            northing_min = None,
3062            northing_max = None,
3063            expand_search = False,
3064            verbose = False,
3065            origin = None,
3066            datum = 'WGS84',
3067            format = 'ers'}
3068  Module: \module{shallow\_water.data\_manager}
3069
3070  Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or
3071  ERS) of a desired grid size \code{cellsize} in metres.
3072  The easting and northing values are used if the user wished to clip the output
3073  file to a specified rectangular area. The \code{reduction} input refers to a function
3074  to reduce the quantities over all time step of the SWW file, example, maximum.
3075  \end{funcdesc}
3076
3077
3078  \begin{funcdesc}{dem2pts}{basename_in, basename_out=None,
3079            easting_min=None, easting_max=None,
3080            northing_min=None, northing_max=None,
3081            use_cache=False, verbose=False}
3082  Module: \module{shallow\_water.data\_manager}
3083
3084  Takes DEM data (a NetCDF file representation of data from a regular Digital
3085  Elevation Model) and converts it to PTS format.
3086  \end{funcdesc}
3087
3088
3089
3090%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3091%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3092
3093\chapter{\anuga mathematical background}
3094\label{cd:mathematical background}
3095
3096\section{Introduction}
3097
3098This chapter outlines the mathematics underpinning \anuga.
3099
3100
3101
3102\section{Model}
3103\label{sec:model}
3104
3105The shallow water wave equations are a system of differential
3106conservation equations which describe the flow of a thin layer of
3107fluid over terrain. The form of the equations are:
3108\[
3109\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
3110x}+\frac{\partial \GG}{\partial y}=\SSS
3111\]
3112where $\UU=\left[ {{\begin{array}{*{20}c}
3113 h & {uh} & {vh} \\
3114\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
3115$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
3116entering the system are bed elevation $z$ and stage (absolute water
3117level) $w$, where the relation $w = z + h$ holds true at all times.
3118The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
3119by
3120\[
3121\EE=\left[ {{\begin{array}{*{20}c}
3122 {uh} \hfill \\
3123 {u^2h+gh^2/2} \hfill \\
3124 {uvh} \hfill \\
3125\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
3126 {vh} \hfill \\
3127 {vuh} \hfill \\
3128 {v^2h+gh^2/2} \hfill \\
3129\end{array} }} \right]
3130\]
3131and the source term (which includes gravity and friction) is given
3132by
3133\[
3134\SSS=\left[ {{\begin{array}{*{20}c}
3135 0 \hfill \\
3136 -{gh(z_{x} + S_{fx} )} \hfill \\
3137 -{gh(z_{y} + S_{fy} )} \hfill \\
3138\end{array} }} \right]
3139\]
3140where $S_f$ is the bed friction. The friction term is modelled using
3141Manning's resistance law
3142\[
3143S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
3144=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
3145\]
3146in which $\eta$ is the Manning resistance coefficient.
3147
3148As demonstrated in our papers, \cite{ZR1999,nielsen2005} these
3149equations provide an excellent model of flows associated with
3150inundation such as dam breaks and tsunamis.
3151
3152\section{Finite Volume Method}
3153\label{sec:fvm}
3154
3155We use a finite-volume method for solving the shallow water wave
3156equations \cite{ZR1999}. The study area is represented by a mesh of
3157triangular cells as in Figure~\ref{fig:mesh} in which the conserved
3158quantities of  water depth $h$, and horizontal momentum $(uh, vh)$,
3159in each volume are to be determined. The size of the triangles may
3160be varied within the mesh to allow greater resolution in regions of
3161particular interest.
3162
3163\begin{figure}
3164\begin{center}
3165\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five}
3166\caption{Triangular mesh used in our finite volume method. Conserved
3167quantities $h$, $uh$ and $vh$ are associated with the centroid of
3168each triangular cell.} \label{fig:mesh}
3169\end{center}
3170\end{figure}
3171
3172The equations constituting the finite-volume method are obtained by
3173integrating the differential conservation equations over each
3174triangular cell of the mesh. Introducing some notation we use $i$ to
3175refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the
3176set of indices referring to the cells neighbouring the $i$th cell.
3177Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is
3178the length of the edge between the $i$th and $j$th cells.
3179
3180By applying the divergence theorem we obtain for each volume an
3181equation which describes the rate of change of the average of the
3182conserved quantities within each cell, in terms of the fluxes across
3183the edges of the cells and the effect of the source terms. In
3184particular, rate equations associated with each cell have the form
3185$$
3186 \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i
3187$$
3188where
3189\begin{itemize}
3190\item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell,
3191\item $\SSS_i$ is the source term associated with the $i$th cell,
3192and
3193\item $\HH_{ij}$ is the outward normal flux of
3194material across the \textit{ij}th edge.
3195\end{itemize}
3196
3197
3198%\item $l_{ij}$ is the length of the edge between the $i$th and $j$th
3199%cells
3200%\item $m_{ij}$ is the midpoint of
3201%the \textit{ij}th edge,
3202%\item
3203%$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing
3204%normal along the \textit{ij}th edge, and The
3205
3206The flux $\HH_{ij}$ is evaluated using a numerical flux function
3207$\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow
3208water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$
3209$$
3210H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 .
3211$$
3212
3213Then
3214$$
3215\HH_{ij}  = \HH(\UU_i(m_{ij}),
3216\UU_j(m_{ij}); \mathbf{n}_{ij})
3217$$
3218where $m_{ij}$ is the midpoint of the \textit{ij}th edge and
3219$\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the
3220\textit{ij}th edge. The function $\UU_i(x)$ for $x \in
3221T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and
3222neighbouring  cells.
3223
3224We use a second order reconstruction to produce a piece-wise linear
3225function construction of the conserved quantities for  all $x \in
3226T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This
3227function is allowed to be discontinuous across the edges of the
3228cells, but the slope of this function is limited to avoid
3229artificially introduced oscillations.
3230
3231Godunov's method (see \cite{Toro1992}) involves calculating the
3232numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly
3233solving the corresponding one dimensional Riemann problem normal to
3234the edge. We use the central-upwind scheme of \cite{KurNP2001} to
3235calculate an approximation of the flux across each edge.
3236
3237\begin{figure}
3238\begin{center}
3239\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct}
3240\caption{From the values of the conserved quantities at the centroid
3241of the cell and its neighbouring cells, a discontinuous piecewise
3242linear reconstruction of the conserved quantities is obtained.}
3243\label{fig:mesh:reconstruct}
3244\end{center}
3245\end{figure}
3246
3247In the computations presented in this paper we use an explicit Euler
3248time stepping method with variable timestepping adapted to the
3249observed CFL condition.
3250
3251
3252\section{Flux limiting}
3253
3254The shallow water equations are solved numerically using a
3255finite volume method on unstructured triangular grid.
3256The upwind central scheme due to Kurganov and Petrova is used as an
3257approximate Riemann solver for the computation of inviscid flux functions.
3258This makes it possible to handle discontinuous solutions.
3259
3260To alleviate the problems associated with numerical instabilities due to
3261small water depths near a wet/dry boundary we employ a new flux limiter that
3262ensures that unphysical fluxes are never encounted.
3263
3264
3265Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction,
3266$w$ the absolute water level (stage) and
3267$z$ the bed elevation. The latter are assumed to be relative to the
3268same height datum.
3269The conserved quantities tracked by ANUGA are momentum in the
3270$x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$)
3271and depth ($h = w-z$).
3272
3273The flux calculation requires access to the velocity vector $(u, v)$
3274where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively.
3275In the presence of very small water depths, these calculations become
3276numerically unreliable and will typically cause unphysical speeds.
3277
3278We have employed a flux limiter which replaces the calculations above with
3279the limited approximations.
3280\begin{equation}
3281  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
3282\end{equation}
3283where $h_0$ is a regularisation parameter that controls the minimal
3284magnitude of the denominator. Taking the limits we have for $\hat{u}$
3285\[
3286  \lim_{h \rightarrow 0} \hat{u} =
3287  \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0
3288\]
3289and
3290\[
3291  \lim_{h \rightarrow \infty} \hat{u} =
3292  \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u
3293\]
3294with similar results for $\hat{v}$.
3295
3296The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator)
3297\[
3298  1 - h_0/h^2 = 0
3299\]
3300or
3301\[
3302  h_0 = h^2
3303\]
3304
3305
3306ANUGA has a global parameter $H_0$ that controls the minimal depth which
3307is considered in the various equations. This parameter is typically set to
3308$10^{-3}$. Setting
3309\[
3310  h_0 = H_0^2
3311\]
3312provides a reasonable balance between accurracy and stability. In fact,
3313setting $h=H_0$ will scale the predicted speed by a factor of $0.5$:
3314\[
3315  \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \frac{\mu}{2 H_0}
3316\]
3317In general, for multiples of the minimal depth $N H_0$ one obtains
3318\[
3319  \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
3320  \frac{\mu}{H_0 (1 + 1/N^2)}
3321\]
3322which converges quadratically to the true value with the multiple N.
3323
3324
3325%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.
3326
3327
3328
3329
3330
3331\section{Slope limiting}
3332A 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.
3333
3334However 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.
3335
3336
3337Let $w, z, h$  be the stage, bed elevation and depth at the centroid and
3338let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$.
3339Define the minimal depth across all vertices as $\hmin$ as
3340\[
3341  \hmin = \min_i h_i
3342\]
3343
3344Let $\tilde{w_i}$ be the stage obtained from a gradient limiter
3345limiting on stage only. The corresponding depth is then defined as
3346\[
3347  \tilde{h_i} = \tilde{w_i} - z_i
3348\]
3349We would use this limiter in deep water which we will define (somewhat boldly)
3350as
3351\[
3352  \hmin \ge \epsilon
3353\]
3354
3355
3356Similarly, let $\bar{w_i}$ be the stage obtained from a gradient
3357limiter limiting on depth respecting the bed slope.
3358The corresponding depth is defined as
3359\[
3360  \bar{h_i} = \bar{w_i} - z_i
3361\]
3362
3363
3364We introduce the concept of a balanced stage $w_i$ which is obtained as
3365the linear combination
3366
3367\[
3368  w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i}
3369\]
3370or
3371\[
3372  w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i}
3373\]
3374where $\alpha \in [0, 1]$.
3375
3376Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope
3377is ignored we have immediately that
3378\[
3379  \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0
3380\]
3381%where the maximal bed elevation range $dz$ is defined as
3382%\[
3383%  dz = \max_i |z_i - z|
3384%\]
3385
3386If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that
3387no negative depths occur. Formally, we will require that
3388\[
3389  \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i
3390\]
3391or
3392\begin{equation}
3393  \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i
3394  \label{eq:limiter bound}
3395\end{equation}
3396
3397There are two cases:
3398\begin{enumerate}
3399  \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage)
3400  vertex is at least as far away from the bed than the shallow water
3401  (limited using depth). In this case we won't need any contribution from
3402  $\bar{h_i}$ and can accept any $\alpha$.
3403
3404  E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to
3405  \[
3406    \tilde{h_i} > \epsilon
3407  \]
3408  whereas $\alpha=0$ yields
3409  \[
3410    \bar{h_i} > \epsilon
3411  \]
3412  all well and good.
3413  \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is
3414  closer to the bed than the shallow water vertex or even below the bed.
3415  In this case we need to find an $\alpha$ that will ensure a positive depth.
3416  Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one
3417  obtains the bound
3418  \[
3419    \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i
3420  \]
3421\end{enumerate}
3422
3423Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one
3424arrives at the definition
3425\[
3426  \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}}
3427\]
3428which will guarantee that no vertex 'cuts' through the bed. Finally, should
3429$\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting
3430$\alpha=0$ and similarly capping $\alpha$ at 1 just in case.
3431
3432%Furthermore,
3433%dropping the $\epsilon$ ensures that alpha is always positive and also
3434%provides a numerical safety {??)
3435
3436
3437
3438
3439
3440%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3441%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3442
3443\chapter{Basic \anuga Assumptions}
3444
3445
3446Physical model time cannot be earlier than 1 Jan 1970 00:00:00.
3447If one wished to recreate scenarios prior to that date it must be done
3448using some relative time (e.g. 0).
3449
3450
3451All spatial data relates to the WGS84 datum (or GDA94) and has been
3452projected into UTM with false easting of 500000 and false northing of
34531000000 on the southern hemisphere (0 on the northern).
3454
3455It is assumed that all computations take place within one UTM zone and
3456all locations must consequently be specified in Cartesian coordinates
3457(eastings, northings) or (x,y) where the unit is metres.
3458
3459DEMs, meshes and boundary conditions can have different origins within
3460one UTM zone. However, the computation will use that of the mesh for
3461numerical stability.
3462
3463When generating a mesh it is assumed that polygons do not cross.
3464Having polygons tht cross can cause the mesh generation to fail or bad
3465meshes being produced.
3466
3467
3468%OLD
3469%The dataflow is: (See data_manager.py and from scenarios)
3470%
3471%
3472%Simulation scenarios
3473%--------------------%
3474%%
3475%
3476%Sub directories contain scrips and derived files for each simulation.
3477%The directory ../source_data contains large source files such as
3478%DEMs provided externally as well as MOST tsunami simulations to be used
3479%as boundary conditions.
3480%
3481%Manual steps are:
3482%  Creation of DEMs from argcview (.asc + .prj)
3483%  Creation of mesh from pmesh (.tsh)
3484%  Creation of tsunami simulations from MOST (.nc)
3485%%
3486%
3487%Typical scripted steps are%
3488%
3489%  prepare_dem.py:  Convert asc and prj files supplied by arcview to
3490%                   native dem and pts formats%
3491%
3492%  prepare_pts.py: Convert netcdf output from MOST to an sww file suitable
3493%                  as boundary condition%
3494%
3495%  prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares
3496%                   smoothing. The outputs are tsh files with elevation data.%
3497%
3498%  run_simulation.py: Use the above together with various parameters to
3499%                     run inundation simulation.
3500
3501
3502%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3503%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3504
3505\appendix
3506
3507\chapter{Supporting Tools}
3508\label{ch:supportingtools}
3509
3510This section describes a number of supporting tools, supplied with \anuga, that offer a
3511variety of types of functionality and enhance the basic capabilities of \anuga.
3512
3513\section{caching}
3514\label{sec:caching}
3515
3516The \code{cache} function is used to provide supervised caching of function
3517results. A Python function call of the form
3518
3519      {\small \begin{verbatim}
3520      result = func(arg1,...,argn)
3521      \end{verbatim}}
3522
3523  can be replaced by
3524
3525      {\small \begin{verbatim}
3526      from caching import cache
3527      result = cache(func,(arg1,...,argn))
3528      \end{verbatim}}
3529
3530  which returns the same output but reuses cached
3531  results if the function has been computed previously in the same context.
3532  \code{result} and the arguments can be simple types, tuples, list, dictionaries or
3533  objects, but not unhashable types such as functions or open file objects.
3534  The function \code{func} may be a member function of an object or a module.
3535
3536  This type of caching is particularly useful for computationally intensive
3537  functions with few frequently used combinations of input arguments. Note that
3538  if the inputs or output are very large caching may not save time because
3539  disc access may dominate the execution time.
3540
3541  If the function definition changes after a result has been cached, this will be
3542  detected by examining the functions \code{bytecode (co\_code, co\_consts,
3543  func\_defaults, co\_argcount)} and the function will be recomputed.
3544  However, caching will not detect changes in modules used by \code{func}.
3545  In this case cache must be cleared manually.
3546
3547  Options are set by means of the function \code{set\_option(key, value)},
3548  where \code{key} is a key associated with a
3549  Python dictionary \code{options}. This dictionary stores settings such as the name of
3550  the directory used, the maximum
3551  number of cached files allowed, and so on.
3552
3553  The \code{cache} function allows the user also to specify a list of dependent files. If any of these
3554  have been changed, the function is recomputed and the results stored again.
3555
3556  %Other features include support for compression and a capability to \ldots
3557
3558
3559   \textbf{USAGE:} \nopagebreak
3560
3561    {\small \begin{verbatim}
3562    result = cache(func, args, kwargs, dependencies, cachedir, verbose,
3563                   compression, evaluate, test, return_filename)
3564    \end{verbatim}}
3565
3566
3567\section{ANUGA viewer - animate}
3568\label{sec:animate}
3569 The output generated by \anuga may be viewed by
3570means of the visualisation tool \code{animate}, which takes the
3571\code{SWW} file output by \anuga and creates a visual representation
3572of the data. Examples may be seen in Figures \ref{fig:runupstart}
3573and \ref{fig:runup2}. To view an \code{SWW} file with
3574\code{animate} in the Windows environment, you can simply drag the
3575icon representing the file over an icon on the desktop for the
3576\code{animate} executable file (or a shortcut to it), or set up a
3577file association to make files with the extension \code{.sww} open
3578with \code{animate}. Alternatively, you can operate \code{animate}
3579from the command line, in both Windows and Linux environments.
3580
3581On successful operation, you will see an interactive moving-picture
3582display. You can use keys and the mouse to slow down, speed up or
3583stop the display, change the viewing position or carry out a number
3584of other simple operations. Help is also displayed when you press
3585the \code{h} key.
3586
3587The main keys operating the interactive screen are:\\
3588
3589\begin{center}
3590\begin{tabular}{|ll|}   \hline
3591
3592\code{w} & toggle wireframe \\
3593
3594space bar & start/stop\\
3595
3596up/down arrows & increase/decrease speed\\
3597
3598left/right arrows & direction in time \emph{(when running)}\\
3599& step through simulation \emph{(when stopped)}\\
3600
3601left mouse button & rotate\\
3602
3603middle mouse button & pan\\
3604
3605right mouse button & zoom\\  \hline
3606
3607\end{tabular}
3608\end{center}
3609
3610\vfill
3611
3612The following table describes how to operate animate from the command line:
3613
3614Usage: \code{animate [options] swwfile \ldots}\\  \nopagebreak
3615Options:\\  \nopagebreak
3616\begin{tabular}{ll}
3617  \code{--display <type>} & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\
3618                                    & \code{HEAD\_MOUNTED\_DISPLAY}\\
3619  \code{--rgba} & Request a RGBA colour buffer visual\\
3620  \code{--stencil} & Request a stencil buffer visual\\
3621  \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\
3622                                    & overridden by environmental variable\\
3623  \code{--stereo <mode>} & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\
3624                                    & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\
3625                                     & \code{ON | OFF} \\
3626  \code{-alphamax <float 0-1>} & Maximum transparency clamp value\\
3627  \code{-alphamin <float 0-1>} & Transparency value at \code{hmin}\\
3628\end{tabular}
3629
3630\begin{tabular}{ll}
3631  \code{-cullangle <float angle 0-90>} & Cull triangles steeper than this value\\
3632  \code{-help} & Display this information\\
3633  \code{-hmax <float>} & Height above which transparency is set to
3634                                     \code{alphamax}\\
3635\end{tabular}
3636
3637\begin{tabular}{ll}
3638
3639  \code{-hmin <float>} & Height below which transparency is set to
3640                                     zero\\
3641\end{tabular}
3642
3643\begin{tabular}{ll}
3644  \code{-lightpos <float>,<float>,<float>} & $x,y,z$ of bedslope directional light ($z$ is
3645                                     up, default is overhead)\\
3646\end{tabular}
3647
3648\begin{tabular}{ll}
3649  \code{-loop}  & Repeated (looped) playback of \code{.swm} files\\
3650
3651\end{tabular}
3652
3653\begin{tabular}{ll}
3654  \code{-movie <dirname>} & Save numbered images to named directory and
3655                                     quit\\
3656
3657  \code{-nosky} & Omit background sky\\
3658
3659
3660  \code{-scale <float>} & Vertical scale factor\\
3661  \code{-texture <file>} & Image to use for bedslope topography\\
3662  \code{-tps <rate>} & Timesteps per second\\
3663  \code{-version} & Revision number and creation (not compile)
3664                                     date\\
3665\end{tabular}
3666
3667\section{utilities/polygons}
3668
3669  \declaremodule{standard}{utilities.polygon}
3670  \refmodindex{utilities.polygon}
3671
3672  \begin{classdesc}{Polygon\_function}{regions, default=0.0, geo_reference=None}
3673  Module: \code{utilities.polygon}
3674
3675  Creates a callable object that returns one of a specified list of values when
3676  evaluated at a point \code{x, y}, depending on which polygon, from a specified list of polygons, the
3677  point belongs to. The parameter \code{regions} is a list of pairs
3678  \code{(P, v)}, where each \code{P} is a polygon and each \code{v}
3679  is either a constant value or a function of coordinates \code{x}
3680  and \code{y}, specifying the return value for a point inside \code{P}. The
3681  optional parameter \code{default} may be used to specify a value
3682  (or a function)
3683  for a point not lying inside any of the specified polygons. When a
3684  point lies in more than one polygon, the return value is taken to
3685  be the value for whichever of these polygon appears later in the
3686  list.
3687  %FIXME (Howard): CAN x, y BE VECTORS?
3688  The optional parameter geo\_reference refers to the status of points
3689  that are passed into the function. Typically they will be relative to
3690  some origin. In ANUGA, a typical call will take the form:
3691  {\small \begin{verbatim}
3692     set_quantity('elevation',
3693                  Polygon_function([(P1, v1), (P2, v2)],
3694                                   default=v3,
3695                                   geo_reference=domain.geo_reference))
3696  \end{verbatim}}
3697 
3698
3699  \end{classdesc}
3700
3701  \begin{funcdesc}{read\_polygon}{filename}
3702  Module: \code{utilities.polygon}
3703
3704  Reads the specified file and returns a polygon. Each
3705  line of the file must contain exactly two numbers, separated by a comma, which are interpreted
3706  as coordinates of one vertex of the polygon.
3707  \end{funcdesc}
3708
3709  \begin{funcdesc}{populate\_polygon}{polygon, number_of_points, seed = None, exclude = None}
3710  Module: \code{utilities.polygon}
3711
3712  Populates the interior of the specified polygon with the specified number of points,
3713  selected by means of a uniform distribution function.
3714  \end{funcdesc}
3715
3716  \begin{funcdesc}{point\_in\_polygon}{polygon, delta=1e-8}
3717  Module: \code{utilities.polygon}
3718
3719  Returns a point inside the specified polygon and close to the edge. The distance between
3720  the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the
3721  second argument \code{delta}, which is taken as $10^{-8}$ by default.
3722  \end{funcdesc}
3723
3724  \begin{funcdesc}{inside\_polygon}{points, polygon, closed = True, verbose = False}
3725  Module: \code{utilities.polygon}
3726
3727  Used to test whether the members of a list of points
3728  are inside the specified polygon. Returns a Numeric
3729  array comprising the indices of the points in the list that lie inside the polygon.
3730  (If none of the points are inside, returns \code{zeros((0,), 'l')}.)
3731  Points on the edges of the polygon are regarded as inside if
3732  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3733  \end{funcdesc}
3734
3735  \begin{funcdesc}{outside\_polygon}{points, polygon, closed = True, verbose = False}
3736  Module: \code{utilities.polygon}
3737
3738  Exactly like \code{inside\_polygon}, but with the words `inside' and `outside' interchanged.
3739  \end{funcdesc}
3740
3741  \begin{funcdesc}{is\_inside\_polygon}{point, polygon, closed=True, verbose=False}
3742  Module: \code{utilities.polygon}
3743
3744  Returns \code{True} if \code{point} is inside \code{polygon} or
3745  \code{False} otherwise. Points on the edges of the polygon are regarded as inside if
3746  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3747  \end{funcdesc}
3748
3749  \begin{funcdesc}{is\_outside\_polygon}{point, polygon, closed=True, verbose=False}
3750  Module: \code{utilities.polygon}
3751
3752  Exactly like \code{is\_outside\_polygon}, but with the words `inside' and `outside' interchanged.
3753  \end{funcdesc}
3754
3755  \begin{funcdesc}{point\_on\_line}{x, y, x0, y0, x1, y1}
3756  Module: \code{utilities.polygon}
3757
3758  Returns \code{True} or \code{False}, depending on whether the point with coordinates
3759  \code{x, y} is on the line passing through the points with coordinates \code{x0, y0}
3760  and \code{x1, y1} (extended if necessary at either end).
3761  \end{funcdesc}
3762
3763  \begin{funcdesc}{separate\_points\_by\_polygon}{points, polygon, closed = True, verbose = False}
3764    \indexedcode{separate\_points\_by\_polygon}
3765  Module: \code{utilities.polygon}
3766
3767  \end{funcdesc}
3768
3769  \begin{funcdesc}{polygon\_area}{polygon}
3770  Module: \code{utilities.polygon}
3771
3772  Returns area of arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html)
3773  \end{funcdesc}
3774
3775  \begin{funcdesc}{plot\_polygons}{polygons, style, figname, verbose = False}
3776    Module: \code{utilities.polygon}
3777 
3778    Plots each polygon contained in input polygon list, e.g.
3779   \code{polygons = [poly1, poly2, poly3]} where \code{poly1 = [[x11,y11],[x12,y12],[x13,y13]]}
3780   etc.  Each polygon can be closed for plotting purposes by assigning the style type to each
3781   polygon in the list, e.g. \code{style = ['line','line','line']}. The default will be a line
3782   type when \code{style = None}.
3783   The subsequent plot will be saved to \code{figname} or defaulted to \code{test_image.png}.
3784    The function returns a list containing the minimum and maximum of \code{x} and \code{y},
3785    i.e. \code{[x_{min}, x_{max}, y_{min}, y_{max}]}.
3786  \end{funcdesc}
3787
3788\section{coordinate\_transforms}
3789
3790\section{geospatial\_data}
3791\label{sec:geospatial}
3792
3793This describes a class that represents arbitrary point data in UTM
3794coordinates along with named attribute values.
3795
3796%FIXME (Ole): This gives a LaTeX error
3797%\declaremodule{standard}{geospatial_data}
3798%\refmodindex{geospatial_data}
3799
3800
3801
3802\begin{classdesc}{Geospatial\_data}
3803  {data_points = None,
3804    attributes = None,
3805    geo_reference = None,
3806    default_attribute_name = None,
3807    file_name = None}
3808Module: \code{geospatial\_data}
3809
3810This class is used to store a set of data points and associated
3811attributes, allowing these to be manipulated by methods defined for
3812the class.
3813
3814The data points are specified either by reading them from a NetCDF
3815or CSV file, identified through the parameter \code{file\_name}, or
3816by providing their \code{x}- and \code{y}-coordinates in metres,
3817either as a sequence of 2-tuples of floats or as an $M \times 2$
3818Numeric array of floats, where $M$ is the number of points.
3819Coordinates are interpreted relative to the origin specified by the
3820object \code{geo\_reference}, which contains data indicating the UTM
3821zone, easting and northing. If \code{geo\_reference} is not
3822specified, a default is used.
3823
3824Attributes are specified through the parameter \code{attributes},
3825set either to a list or array of length $M$ or to a dictionary whose
3826keys are the attribute names and whose values are lists or arrays of
3827length $M$. One of the attributes may be specified as the default
3828attribute, by assigning its name to \code{default\_attribute\_name}.
3829If no value is specified, the default attribute is taken to be the
3830first one.
3831\end{classdesc}
3832
3833
3834\begin{methoddesc}{import\_points\_file}{delimiter = None, verbose = False}
3835
3836\end{methoddesc}
3837
3838
3839\begin{methoddesc}{export\_points\_file}{ofile, absolute=False}
3840
3841\end{methoddesc}
3842
3843
3844\begin{methoddesc}{get\_data\_points}{absolute = True, as\_lat\_long =
3845    False}
3846    If \code{as\_lat\_long} is\code{True} the point information
3847    returned will be in Latitudes and Longitudes.
3848
3849\end{methoddesc}
3850
3851
3852\begin{methoddesc}{set\_attributes}{attributes}
3853
3854\end{methoddesc}
3855
3856
3857\begin{methoddesc}{get\_attributes}{attribute_name = None}
3858
3859\end{methoddesc}
3860
3861
3862\begin{methoddesc}{get\_all\_attributes}{}
3863
3864\end{methoddesc}
3865
3866
3867\begin{methoddesc}{set\_default\_attribute\_name}{default_attribute_name}
3868
3869\end{methoddesc}
3870
3871
3872\begin{methoddesc}{set\_geo\_reference}{geo_reference}
3873
3874\end{methoddesc}
3875
3876
3877\begin{methoddesc}{add}{}
3878
3879\end{methoddesc}
3880
3881
3882\begin{methoddesc}{clip}{}
3883Clip geospatial data by a polygon
3884
3885Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3886a Geospatial data object and \code{closed}(optional) which determines
3887whether points on boundary should be regarded as belonging to the polygon
3888(\code{closed=True}) or not (\code{closed=False}).
3889Default is \code{closed=True}.
3890
3891Returns new Geospatial data object representing points
3892inside specified polygon.
3893\end{methoddesc}
3894
3895
3896\begin{methoddesc}{clip_outside}{}
3897Clip geospatial data by a polygon
3898
3899Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3900a Geospatial data object and \code{closed}(optional) which determines
3901whether points on boundary should be regarded as belonging to the polygon
3902(\code{closed=True}) or not (\code{closed=False}).
3903Default is \code{closed=True}.
3904
3905Returns new Geospatial data object representing points
3906\emph{out}side specified polygon.
3907\end{methoddesc}
3908
3909\begin{methoddesc}{split}{factor=0.5, seed_num=None, verbose=False}
3910Returns two geospatial_data object, first is the size of the 'factor'
3911smaller the original and the second is the remainder. The two
3912new object are disjoin set of each other.
3913       
3914Points of the two new geospatial_data object are selected RANDOMLY.
3915       
3916Input - the (\code{factor}) which to split the object, if 0.1 then 10% of the
3917together object will be returned
3918       
3919Output - two geospatial_data objects that are disjoint sets of the original
3920\end{methoddesc}
3921
3922\begin{methoddesc}{find_optimal_smoothing_parameter}{data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000,
3923north_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}
3924
3925Removes a small random sample of points from 'data_file'. Creates
3926models from resulting points in 'data_file' with different alpha values from 'alpha_list' and cross validates
3927the predicted value to the previously removed point data. Returns the
3928alpha value which has the smallest covariance.
3929
3930data_file: must not contain points outside the boundaries defined
3931and it either a pts, txt or csv file.
3932   
3933alpha_list: the alpha values to test in a single list
3934   
3935mesh_file: name of the created mesh file or if passed in will read it.
3936NOTE, if there is a mesh file mesh_resolution, north_boundary, south... etc will be ignored.
3937   
3938mesh_resolution: the maximum area size for a triangle
3939   
3940north_boundary... west_boundary: the value of the boundary
3941   
3942plot_name: the name for the plot contain the results
3943   
3944seed_num: the seed to the random number generator
3945   
3946USAGE:
3947convariance_value, alpha = find_optimal_smoothing_parameter(data_file=fileName,
3948                                             alpha_list=[0.0001, 0.01, 1],
3949                                             mesh_file=None,
3950                                             mesh_resolution=3,
3951                                             north_boundary=5,
3952                                             south_boundary=-5,
3953                                             east_boundary=5,
3954                                             west_boundary=-5,
3955                                             plot_name='all_alphas',
3956                                             seed_num=100000,
3957                                             verbose=False)
3958   
3959OUTPUT: returns the minumum normalised covalance calculate AND the
3960alpha that created it. PLUS writes a plot of the results
3961           
3962NOTE: code will not work if the data_file extent is greater than the
3963boundary_polygon or any of the boundaries, eg north_boundary...west_boundary
3964\end{methoddesc}
3965
3966
3967
3968\section{Graphical Mesh Generator GUI}
3969The program \code{graphical\_mesh\_generator.py} in the pmesh module
3970allows the user to set up the mesh of the problem interactively.
3971It can be used to build the outline of a mesh or to visualise a mesh
3972automatically generated.
3973
3974Graphical Mesh Generator will let the user select various modes. The
3975current allowable modes are vertex, segment, hole or region.  The mode
3976describes what sort of object is added or selected in response to
3977mouse clicks.  When changing modes any prior selected objects become
3978deselected.
3979
3980In general the left mouse button will add an object and the right
3981mouse button will select an object.  A selected object can de deleted
3982by pressing the the middle mouse button (scroll bar).
3983
3984\section{alpha\_shape}
3985\emph{Alpha shapes} are used to generate close-fitting boundaries
3986around sets of points. The alpha shape algorithm produces a shape
3987that approximates to the `shape formed by the points'---or the shape
3988that would be seen by viewing the points from a coarse enough
3989resolution. For the simplest types of point sets, the alpha shape
3990reduces to the more precise notion of the convex hull. However, for
3991many sets of points the convex hull does not provide a close fit and
3992the alpha shape usually fits more closely to the original point set,
3993offering a better approximation to the shape being sought.
3994
3995In \anuga, an alpha shape is used to generate a polygonal boundary
3996around a set of points before mesh generation. The algorithm uses a
3997parameter $\alpha$ that can be adjusted to make the resultant shape
3998resemble the shape suggested by intuition more closely. An alpha
3999shape can serve as an initial boundary approximation that the user
4000can adjust as needed.
4001
4002The following paragraphs describe the class used to model an alpha
4003shape and some of the important methods and attributes associated
4004with instances of this class.
4005
4006\begin{classdesc}{Alpha\_Shape}{points, alpha = None}
4007Module: \code{alpha\_shape}
4008
4009To instantiate this class the user supplies the points from which
4010the alpha shape is to be created (in the form of a list of 2-tuples
4011\code{[[x1, y1],[x2, y2]}\ldots\code{]}, assigned to the parameter
4012\code{points}) and, optionally, a value for the parameter
4013\code{alpha}. The alpha shape is then computed and the user can then
4014retrieve details of the boundary through the attributes defined for
4015the class.
4016\end{classdesc}
4017
4018
4019\begin{funcdesc}{alpha\_shape\_via\_files}{point_file, boundary_file, alpha= None}
4020Module: \code{alpha\_shape}
4021
4022This function reads points from the specified point file
4023\code{point\_file}, computes the associated alpha shape (either
4024using the specified value for \code{alpha} or, if no value is
4025specified, automatically setting it to an optimal value) and outputs
4026the boundary to a file named \code{boundary\_file}. This output file
4027lists the coordinates \code{x, y} of each point in the boundary,
4028using one line per point.
4029\end{funcdesc}
4030
4031
4032\begin{methoddesc}{set\_boundary\_type}{self,raw_boundary=True,
4033                          remove_holes=False,
4034                          smooth_indents=False,
4035                          expand_pinch=False,
4036                          boundary_points_fraction=0.2}
4037Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4038
4039This function sets flags that govern the operation of the algorithm
4040that computes the boundary, as follows:
4041
4042\code{raw\_boundary = True} returns raw boundary, i.e. the regular edges of the
4043                alpha shape.\\
4044\code{remove\_holes = True} removes small holes (`small' is defined by
4045\code{boundary\_points\_fraction})\\
4046\code{smooth\_indents = True} removes sharp triangular indents in
4047boundary\\
4048\code{expand\_pinch = True} tests for pinch-off and
4049corrects---preventing a boundary vertex from having more than two edges.
4050\end{methoddesc}
4051
4052
4053\begin{methoddesc}{get\_boundary}{}
4054Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4055
4056Returns a list of tuples representing the boundary of the alpha
4057shape. Each tuple represents a segment in the boundary by providing
4058the indices of its two endpoints.
4059\end{methoddesc}
4060
4061
4062\begin{methoddesc}{write\_boundary}{file_name}
4063Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4064
4065Writes the list of 2-tuples returned by \code{get\_boundary} to the
4066file \code{file\_name}, using one line per tuple.
4067\end{methoddesc}
4068
4069\section{Numerical Tools}
4070
4071The following table describes some useful numerical functions that
4072may be found in the module \module{utilities.numerical\_tools}:
4073
4074\begin{tabular}{|p{8cm} p{8cm}|}  \hline
4075\code{angle(v1, v2=None)} & Angle between two-dimensional vectors
4076\code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if
4077\code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\
4078
4079\code{normal\_vector(v)} & Normal vector to \code{v}.\\
4080
4081\code{mean(x)} & Mean value of a vector \code{x}.\\
4082
4083\code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}.
4084If \code{y} is \code{None}, returns \code{cov(x, x)}.\\
4085
4086\code{err(x, y=0, n=2, relative=True)} & Relative error of
4087$\parallel$\code{x}$-$\code{y}$\parallel$ to
4088$\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm
4089if \code{n} = \code{None}). If denominator evaluates to zero or if
4090\code{y}
4091is omitted or if \code{relative = False}, absolute error is returned.\\
4092
4093\code{norm(x)} & 2-norm of \code{x}.\\
4094
4095\code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If
4096\code{y} is \code{None} returns autocorrelation of \code{x}.\\
4097
4098\code{ensure\_numeric(A, typecode = None)} & Returns a Numeric array
4099for any sequence \code{A}. If \code{A} is already a Numeric array it
4100will be returned unaltered. Otherwise, an attempt is made to convert
4101it to a Numeric array. (Needed because \code{array(A)} can
4102cause memory overflow.)\\
4103
4104\code{histogram(a, bins, relative=False)} & Standard histogram. If
4105\code{relative} is \code{True}, values will be normalised against
4106the total and thus represent frequencies rather than counts.\\
4107
4108\code{create\_bins(data, number\_of\_bins = None)} & Safely create
4109bins for use with histogram. If \code{data} contains only one point
4110or is constant, one bin will be created. If \code{number\_of\_bins}
4111is omitted, 10 bins will be created.\\  \hline
4112
4113\section{Finding the Optimal Alpha Value}
4114
4115The function ????
4116more to come very soon
4117
4118\end{tabular}
4119
4120
4121\chapter{Modules available in \anuga}
4122
4123
4124\section{\module{abstract\_2d\_finite\_volumes.general\_mesh} }
4125\declaremodule[generalmesh]{}{general\_mesh}
4126\label{mod:generalmesh}
4127
4128\section{\module{abstract\_2d\_finite\_volumes.neighbour\_mesh} }
4129\declaremodule[neighbourmesh]{}{neighbour\_mesh}
4130\label{mod:neighbourmesh}
4131
4132\section{\module{abstract\_2d\_finite\_volumes.domain} --- Generic module for 2D triangular domains for finite-volume computations of conservation laws}
4133\declaremodule{}{domain}
4134\label{mod:domain}
4135
4136
4137\section{\module{abstract\_2d\_finite\_volumes.quantity}}
4138\declaremodule{}{quantity}
4139\label{mod:quantity}
4140
4141\begin{verbatim}
4142Class Quantity - Implements values at each triangular element
4143
4144To create:
4145
4146   Quantity(domain, vertex_values)
4147
4148   domain: Associated domain structure. Required.
4149
4150   vertex_values: N x 3 array of values at each vertex for each element.
4151                  Default None
4152
4153   If vertex_values are None Create array of zeros compatible with domain.
4154   Otherwise check that it is compatible with dimenions of domain.
4155   Otherwise raise an exception
4156
4157\end{verbatim}
4158
4159
4160
4161
4162\section{\module{shallow\_water} --- 2D triangular domains for finite-volume
4163computations of the shallow water wave equation. This module contains a specialisation
4164of class Domain from module domain.py consisting of methods specific to the Shallow Water
4165Wave Equation
4166}
4167\declaremodule[shallowwater]{}{shallow\_water}
4168\label{mod:shallowwater}
4169
4170
4171
4172
4173%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4174
4175\chapter{Frequently Asked Questions}
4176
4177
4178\section{General Questions}
4179
4180\subsubsection{What is \anuga?}
4181It is a software package suitable for simulating 2D water flows in
4182complex geometries.
4183
4184\subsubsection{Why is it called \anuga?}
4185The software was developed in collaboration between the
4186Australian National University (ANU) and Geoscience Australia (GA).
4187
4188\subsubsection{How do I obtain a copy of \anuga?}
4189See \url{https://datamining.anu.edu.au/anuga} for all things ANUGA.
4190
4191%\subsubsection{What developments are expected for \anuga in the future?}
4192%This
4193
4194\subsubsection{Are there any published articles about \anuga that I can reference?}
4195See \url{https://datamining.anu.edu.au/anuga} for links.
4196
4197
4198\subsubsection{How do I find out what version of \anuga I am running?}
4199Use the following code snippet
4200\begin{verbatim}
4201from anuga.utilities.system_tools import get_revision_number
4202print get_revision_number()
4203\end{verbatim}
4204This should work both for installations from SourceForge as well as when working off the repository.
4205
4206
4207
4208
4209\section{Modelling Questions}
4210
4211\subsubsection{Which type of problems are \anuga good for?}
4212General 2D waterflows in complex geometries such as
4213dam breaks, flows amoung structurs, coastal inundation etc.
4214
4215\subsubsection{Which type of problems are beyond the scope of \anuga?}
4216See Chapter \ref{ch:limitations}.
4217
4218\subsubsection{Can I start the simulation at an arbitrary time?}
4219Yes, using \code{domain.set\_time()} you can specify an arbitrary
4220starting time. This is for example useful in conjunction with a
4221file\_boundary, which may start hours before anything hits the model
4222boundary. By assigning a later time for the model to start,
4223computational resources aren't wasted.
4224
4225\subsubsection{Can I change values for any quantity during the simulation?}
4226Yes, using \code{domain.set\_quantity()} inside the domain.evolve
4227loop you can change values of any quantity. This is for example
4228useful if you wish to let the system settle for a while before
4229assigning an initial condition. Another example would be changing
4230the values for elevation to model e.g. erosion.
4231
4232\subsubsection{Can I change boundary conditions during the simulation?}
4233Yes - see example on page \pageref{sec:change boundary code} in Section
4234\ref{sec:change boundary}.
4235
4236\subsubsection{How do I access model time during the simulation?}
4237The variable \code{t} in the evolve for loop is the model time.
4238For 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})
4239one would write something like
4240{\small \begin{verbatim}
4241    for t in domain.evolve(yieldstep = 0.2, duration = 40.0):
4242
4243        if Numeric.allclose(t, 15):
4244            print 'Changing boundary to outflow'
4245            domain.set_boundary({'right': Bo})
4246
4247\end{verbatim}}
4248The 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()}.
4249
4250
4251\subsubsection{Why does a file\_function return a list of numbers when evaluated?}
4252Currently, file\_function works by returning values for the conserved
4253quantities \code{stage}, \code{xmomentum} and \code{ymomentum} at a given point in time
4254and space as a triplet. To access e.g.\ \code{stage} one must specify element 0 of the
4255triplet returned by file\_function.
4256
4257\subsubsection{Which diagnostics are available to troubleshoot a simulation?}
4258
4259\subsubsection{How do I use a DEM in my simulation?}
4260You use \code{dem2pts} to convert your DEM to the required .pts format. This .pts file is then called
4261when setting the elevation data to the mesh in \code{domain.set_quantity}
4262
4263\subsubsection{What sort of DEM resolution should I use?}
4264Try and work with the \emph{best} you have available. Onshore DEMs
4265are typically available in 25m, 100m and 250m grids. Note, offshore
4266data is often sparse, or non-existent.
4267
4268\subsubsection{What sort of mesh resolution should I use?}
4269The 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,
4270if 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,
4271you need a fine mesh over regions where the DEM changes rapidly, and other areas of significant interest, such as the coast.
4272If meshes are too coarse, discretisation errors in both stage and momentum may lead to unphysical results. All studies should include sensitivity and convergence studies based on different resolutions.
4273
4274
4275\subsubsection{How do I tag interior polygons?}
4276At the moment create_mesh_from_regions does not allow interior
4277polygons with symbolic tags. If tags are needed, the interior
4278polygons must be created subsequently. For example, given a filename
4279of polygons representing solid walls (in Arc Ungenerate format) can
4280be tagged as such using the code snippet:
4281\begin{verbatim}
4282  # Create mesh outline with tags
4283  mesh = create_mesh_from_regions(bounding_polygon,
4284                                  boundary_tags=boundary_tags)
4285  # Add buildings outlines with tags set to 'wall'. This would typically
4286  # bind to a Reflective boundary
4287  mesh.import_ungenerate_file(buildings_filename, tag='wall')
4288
4289  # Generate and write mesh to file
4290  mesh.generate_mesh(maximum_triangle_area=max_area)
4291  mesh.export_mesh_file(mesh_filename)
4292\end{verbatim}
4293
4294Note that a mesh object is returned from \code{create_mesh_from_regions}
4295when file name is omitted.
4296
4297\subsubsection{How often should I store the output?}
4298This 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
4299to look in detail at the evolution, then you will need to balance your storage requirements and the duration of the simulation.
4300If 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
4301quantities on a mesh with approximately 300000 triangles on a 2 min interval for 5 hours will result in approximately 350Mb SWW file
4302(as for the \file{run\_sydney\_smf.py} example).
4303
4304\subsubsection{How can I set the friction in different areas in the domain?}
4305The model area will typically be estimating the water height and momentum over varying
4306topographies which will have different friction values. One way of assigning
4307different friction values is to create polygons (say \code{poly1, poly2 and poly3}) describing each
4308area and then set the corresponding friction values in the following way
4309
4310\code{domain.set_quantity('friction',Polygon_function([(poly1,f1),(poly2,f2),
4311(poly3,f3))]))}
4312
4313The values of \code{f1,f2} and \code{f3} could be constant or functions
4314as determined by the user.
4315
4316\subsubsection{How can I combine data sets?}
4317
4318A user may have access to a range of different resolution DEMs and raw data points (such
4319as beach profiles, spot heights, single or multi-beam data etc) and will need
4320to combine them to create an overall elevation data set.
4321
4322If there are multiple DEMs, say of 10m and 25m resolution, then the technique is similar to
4323that defined in the Cairns example described earlier, that is
4324
4325{\small \begin{verbatim}
4326convert_dem_from_ascii2netcdf(10m_dem_name, use_cache=True, verbose=True)
4327convert_dem_from_ascii2netcdf(25m_dem_name, use_cache=True, verbose=True)
4328\end{verbatim}}
4329followed by
4330{\small \begin{verbatim}
4331dem2pts(10m_dem_name, use_cache=True, verbose=True)
4332dem2pts(25m_dem_name, use_cache=True, verbose=True)
4333\end{verbatim}}
4334These data sets can now be combined by
4335{\small \begin{verbatim}
4336from anuga.geospatial_data.geospatial_data import *
4337G1 = Geospatial_data(file_name = 10m_dem_name + '.pts')
4338G2 = Geospatial_data(file_name = 25m_dem_name + '.pts')
4339G = G1 + G2
4340G.export_points_file(combined_dem_name + ‘.pts’)
4341\end{verbatim}}
4342this is the basic way of combining data sets, however, the user will need to
4343assess the boundaries of each data set and whether they overlap. For example, consider
4344if the 10m DEM is describing by \code{poly1} and the 25m DEM is described by \code{poly2}
4345with \code{poly1} completely enclosed in \code{poly2} as shown in Figure \ref{fig:polydata}
4346\begin{figure}[hbt]
4347  \centerline{\includegraphics{graphics/polyanddata.jpg}}
4348  \caption{Polygons describing the extent of the 10m and 25m DEM.}
4349  \label{fig:polydata}
4350\end{figure}
4351To combine the data sets, the geospatial addition is updated to
4352{\small \begin{verbatim}
4353G = G1 + G2.clip_outside(Geospatial_data(poly1))
4354\end{verbatim}}
4355For this example, we assume that \code{poly2} is the domain, otherwise an additional dataset
4356would be required for the remainder of the domain.
4357
4358This technique can be expanded to handle point data sets as well. In the case
4359of a bathymetry data set available in text format in an \code{.csv} file, then
4360the geospatial addition is updated to
4361{\small \begin{verbatim}
4362G3 = Geospatial_data(file_name = bathy_data_name + '.csv')
4363G = G1 + G2.clip_outside(Geospatial_data(poly1)) + G3
4364\end{verbatim}}
4365The \code{.csv} file has the data stored as \code{x,y,elevation} with the text \code{elevation}
4366on the first line.
4367
4368The coastline could be included
4369as part of the clipping polygon to separate the offshore and onshore datasets if required.
4370Assume that \code{poly1} crosses the coastline
4371In this case, two new polygons could be created out of \code{poly1} which uses the coastline
4372as the divider. As shown in Figure \ref{fig:polycoast}, \code{poly3} describes the
4373onshore data and \code{poly4} describes the offshore data.
4374\begin{figure}[hbt]
4375  \centerline{\includegraphics{graphics/polyanddata2.jpg}}
4376  \caption{Inclusion of new polygons separating the 10m DEM area into an
4377  onshore (poly3) and offshore (poly4) data set.}
4378  \label{fig:polycoast}
4379\end{figure}
4380Let's include the bathymetry
4381data described above, so to combine the datasets in this case,
4382{\small \begin{verbatim}
4383G = G1.clip(Geospatial_data(poly3)) + G2.clip_outside(Geospatial_data(poly1)) + G3
4384\end{verbatim}}
4385
4386Finally, to fit the elevation data to the mesh, the script is adjusted in this way
4387{\small \begin{verbatim}
4388    domain.set_quantity('elevation',
4389                        filename = combined_dem_name + '.pts',
4390                        use_cache = True,
4391                        verbose = True)
4392\end{verbatim}}
4393\subsection{Boundary Conditions}
4394
4395\subsubsection{How do I create a Dirichlet boundary condition?}
4396
4397A Dirichlet boundary condition sets a constant value for the
4398conserved quantities at the boundaries. A list containing
4399the constant values for stage, xmomentum and ymomentum is constructed
4400and used in the function call, e.g. \code{Dirichlet_boundary([0.2,0.,0.])}
4401
4402\subsubsection{How do I know which boundary tags are available?}
4403The method \code{domain.get\_boundary\_tags()} will return a list of
4404available tags for use with
4405\code{domain.set\_boundary\_condition()}.
4406
4407\subsubsection{What is the difference between file_boundary and field_boundary?}
4408The only difference is field_boundary will allow you to change the level of the stage height when you read in the boundary condition.
4409This is very useful when running different tide heights in the same area as you need only to convert
4410one boundary condition to a SWW file, ideally for tide height of 0 m (saving disk space). Then you can
4411use field_boundary to read this SWW file and change the stage height (tide) on the fly depending on the scenario.
4412
4413
4414
4415
4416\subsection{Analysing Results}
4417
4418\subsubsection{How do I easily plot "tide gauges" timeseries graphs from a SWW file?}
4419
4420There is two ways to do this.
4421
44221) Create csv files from the sww file using \code{anuga.abstract_2d_finite_volumes.util sww2csv_gauges}
4423and then use \code{anuga.abstract_2d_finite_volumes.util csv2timeseries_graphs} to
4424create the plots. This code is newer, has unit tests and might be easier to use. Read doc strings for more information and
4425review section 4.7 of this manual.
4426
4427Or
4428
44292) Use \code{anuga.abstract_2d_finite_volumes.util sww2timeseries} to do the whole thing
4430however this doesn't have a much control on the file name and plots. Plus there is no unit tests yet.
4431
4432Read the doc string for more information.
4433
4434\subsubsection{How do I extract elevation and other quantities from a SWW file?}
4435
4436The function \code{sww2dem} can extract any quantity, or expression using
4437quantities, from a SWW file as used in
4438the Cairns example described earlier. This function is used in \code{ExportResults.py}
4439in the Cairns demo folder where stage, absolute momentum, depth, speed and elevation
4440can be exported from the input sww file. Note that depth, absolute momentum and speed
4441are expressions and stage and elevation are quantities. In addition to extracting a particular
4442quantity or expression, the user can define a region to extract these values by
4443defining the minimum and maximum of both the easting and northing coordinates. The function
4444also calls for a grid resolution, or cell size, to extract these values at. It is
4445recommended to align this resolution with the mesh resolution in the desired region and to not
4446generate a fine grid where the model output cannot support that resolution.
4447
4448 
4449
4450\chapter{Glossary}
4451
4452\begin{tabular}{|lp{10cm}|c|}  \hline
4453%\begin{tabular}{|llll|}  \hline
4454    \emph{Term} & \emph{Definition} & \emph{Page}\\  \hline
4455
4456    \indexedbold{\anuga} & Name of software (joint development between ANU and
4457    GA) & \pageref{def:anuga}\\
4458
4459    \indexedbold{bathymetry} & offshore elevation &\\
4460
4461    \indexedbold{conserved quantity} & conserved (stage, x and y
4462    momentum) & \\
4463
4464%    \indexedbold{domain} & The domain of a function is the set of all input values to the
4465%    function.&\\
4466
4467    \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations,
4468sampled systematically at equally spaced intervals.& \\
4469
4470    \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation
4471 that specifies the values the solution is to take on the boundary of the
4472 domain. & \pageref{def:dirichlet boundary}\\
4473
4474    \indexedbold{edge} & A triangular cell within the computational mesh can be depicted
4475    as a set of vertices joined by lines (the edges). & \\
4476
4477    \indexedbold{elevation} & refers to bathymetry and topography &\\
4478
4479    \indexedbold{evolution} & integration of the shallow water wave equations
4480    over time &\\
4481
4482    \indexedbold{finite volume method} & The method evaluates the terms in the shallow water
4483    wave equation as fluxes at the surfaces of each finite volume. Because the
4484    flux entering a given volume is identical to that leaving the adjacent volume,
4485    these methods are conservative. Another advantage of the finite volume method is
4486    that it is easily formulated to allow for unstructured meshes. The method is used
4487    in many computational fluid dynamics packages. & \\
4488
4489    \indexedbold{forcing term} & &\\
4490
4491    \indexedbold{flux} & the amount of flow through the volume per unit
4492    time & \\
4493
4494    \indexedbold{grid} & Evenly spaced mesh & \\
4495
4496    \indexedbold{latitude} & The angular distance on a mericlear north and south of the
4497    equator, expressed in degrees and minutes. & \\
4498
4499    \indexedbold{longitude} & The angular distance east or west, between the meridian
4500    of a particular place on Earth and that of the Prime Meridian (located in Greenwich,
4501    England) expressed in degrees or time.& \\
4502
4503    \indexedbold{Manning friction coefficient} & &\\
4504
4505    \indexedbold{mesh} & Triangulation of domain &\\
4506
4507    \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\
4508
4509    \indexedbold{NetCDF} & &\\
4510
4511    \indexedbold{node} & A point at which edges meet & \\
4512
4513    \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance
4514    north from a north-south reference line, usually a meridian used as the axis of
4515    origin within a map zone or projection. Northing is a UTM (Universal Transverse
4516    Mercator) coordinate. & \\
4517
4518
4519    \indexedbold{points file} & A PTS or CSV file & \\  \hline
4520
4521    \end{tabular}
4522
4523    \begin{tabular}{|lp{10cm}|c|}  \hline
4524
4525    \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon
4526    either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$
4527    Numeric array, where $N$ is the number of points.
4528
4529    The unit square, for example, would be represented either as
4530    \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1],
4531    [0,1] )}.
4532
4533    NOTE: For details refer to the module \module{utilities/polygon.py}. &
4534    \\     \indexedbold{resolution} &  The maximal area of a triangular cell in a
4535    mesh & \\
4536
4537
4538    \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved
4539    quantities as those present in the neighbouring volume but reflected. Specific to the
4540    shallow water equation as it works with the momentum quantities assumed to be the
4541    second and third conserved quantities. & \pageref{def:reflective boundary}\\
4542
4543    \indexedbold{stage} & &\\
4544
4545%    \indexedbold{try this}
4546
4547    \indexedbold{animate} & visualisation tool used with \anuga &
4548    \pageref{sec:animate}\\
4549
4550    \indexedbold{time boundary} & Returns values for the conserved
4551quantities as a function of time. The user must specify
4552the domain to get access to the model time. & \pageref{def:time boundary}\\
4553
4554    \indexedbold{topography} & onshore elevation &\\
4555
4556    \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\
4557
4558    \indexedbold{vertex} & A point at which edges meet. & \\
4559
4560    \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say
4561    only \code{x} and \code{y} and NOT \code{z}) &\\
4562
4563    \indexedbold{ymomentum}  & conserved quantity & \\  \hline
4564
4565    \end{tabular}
4566
4567
4568%The \code{\e appendix} markup need not be repeated for additional
4569%appendices.
4570
4571
4572%
4573%  The ugly "%begin{latexonly}" pseudo-environments are really just to
4574%  keep LaTeX2HTML quiet during the \renewcommand{} macros; they're
4575%  not really valuable.
4576%
4577%  If you don't want the Module Index, you can remove all of this up
4578%  until the second \input line.
4579%
4580
4581%begin{latexonly}
4582%\renewcommand{\indexname}{Module Index}
4583%end{latexonly}
4584\input{mod\jobname.ind}        % Module Index
4585%
4586%begin{latexonly}
4587%\renewcommand{\indexname}{Index}
4588%end{latexonly}
4589\input{\jobname.ind}            % Index
4590
4591
4592
4593\begin{thebibliography}{99}
4594\bibitem[nielsen2005]{nielsen2005}
4595{\it Hydrodynamic modelling of coastal inundation}.
4596Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman.
4597In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on
4598Modelling and Simulation. Modelling and Simulation Society of Australia and
4599New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\
4600http://www.mssanz.org.au/modsim05/papers/nielsen.pdf
4601
4602\bibitem[grid250]{grid250}
4603Australian Bathymetry and Topography Grid, June 2005.
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4626
4627\end{document}
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