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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!
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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}
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53\ifhtml
54\date{\today} % latex2html does not know about datetime
55\fi
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57
58
59
60\input{version} % Get version info - this file may be modified by
61                % update_anuga_user_manual.py - if not a dummy
62                % will be used.
63               
64%\release{1.0}   % release version; this is used to define the
65%                % \version macro
66
67\makeindex          % tell \index to actually write the .idx file
68\makemodindex       % If this contains a lot of module sections.
69
70\setcounter{tocdepth}{3}
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
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83%Subversion keywords:
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85%$LastChangedDate: 2008-07-16 01:42:15 +0000 (Wed, 16 Jul 2008) $
86%$LastChangedRevision: 5506 $
87%$LastChangedBy: ole $
88
89\input{copyright}
90
91
92\begin{abstract}
93\label{def:anuga}
94
95\noindent \anuga\index{\anuga} is a hydrodynamic modelling tool that
96allows users to model realistic flow problems in complex geometries.
97Examples include dam breaks or the effects of natural hazards such
98as riverine flooding, storm surges and tsunami.
99
100The user must specify a study area represented by a mesh of triangular
101cells, the topography and bathymetry, frictional resistance, initial
102values for water level (called \emph{stage}\index{stage} within \anuga),
103boundary
104conditions and forces such as windstress or pressure gradients if
105applicable.
106
107\anuga tracks the evolution of water depth and horizontal momentum
108within each cell over time by solving the shallow water wave equation
109governing equation using a finite-volume method.
110
111\anuga also incorporates a mesh generator %, called \code{graphical
112                                %mesh generator},
113that
114allows the user to set up the geometry of the problem interactively as
115well as tools for interpolation and surface fitting, and a number of
116auxiliary tools for visualising and interrogating the model output.
117
118Most \anuga components are written in the object-oriented programming
119language Python and most users will interact with \anuga by writing
120small Python programs based on the \anuga library
121functions. Computationally intensive components are written for
122efficiency in C routines working directly with the Numerical Python
123structures.
124
125
126\end{abstract}
127
128\tableofcontents
129
130
131\chapter{Introduction}
132
133
134\section{Purpose}
135
136The purpose of this user manual is to introduce the new user to the
137inundation software, describe what it can do and give step-by-step
138instructions for setting up and running hydrodynamic simulations.
139
140\section{Scope}
141
142This manual covers only what is needed to operate the software after
143installation and configuration. It does not includes instructions
144for installing the software or detailed API documentation, both of
145which will be covered in separate publications and by documentation
146in the source code.
147
148\section{Audience}
149
150Readers are assumed to be familiar with the Python Programming language and
151its object oriented approach.
152Python tutorials include
153\url{http://docs.python.org/tut},
154\url{http://www.sthurlow.com/python}, and
155%\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}.
156\url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}.
157
158
159Readers also need to have a general understanding of scientific modelling,
160as well as
161enough programming experience to adapt the code to different
162requirements.
163
164
165
166\pagebreak
167\chapter{Background}
168
169
170Modelling the effects on the built environment of natural hazards such
171as riverine flooding, storm surges and tsunami is critical for
172understanding their economic and social impact on our urban
173communities.  Geoscience Australia and the Australian National
174University are developing a hydrodynamic inundation modelling tool
175called \anuga to help simulate the impact of these hazards.
176
177The core of \anuga is the fluid dynamics module, called \code{shallow\_water},
178which is based on a finite-volume method for solving the Shallow Water
179Wave Equation.  The study area is represented by a mesh of triangular
180cells.  By solving the governing equation within each cell, water
181depth and horizontal momentum are tracked over time.
182
183A major capability of \anuga is that it can model the process of
184wetting and drying as water enters and leaves an area.  This means
185that it is suitable for simulating water flow onto a beach or dry land
186and around structures such as buildings.  \anuga is also capable
187of modelling hydraulic jumps due to the ability of the finite-volume
188method to accommodate discontinuities in the solution.
189
190To set up a particular scenario the user specifies the geometry
191(bathymetry and topography), the initial water level (stage),
192boundary conditions such as tide, and any forcing terms that may
193drive the system such as rain_fall, abstraction of water, wind stress or atmospheric pressure
194gradients. Gravity and frictional resistance from the different
195terrains in the model are represented by predefined forcing terms.
196See section \ref{sec:forcing terms} for details on forcing terms available in ANUGA.
197
198The built-in mesh generator, called \code{graphical\_mesh\_generator},
199allows the user to set up the geometry
200of the problem interactively and to identify boundary segments and
201regions using symbolic tags.  These tags may then be used to set the
202actual boundary conditions and attributes for different regions
203(e.g.\ the Manning friction coefficient) for each simulation.
204
205Most \anuga components are written in the object-oriented programming
206language Python.  Software written in Python can be produced quickly
207and can be readily adapted to changing requirements throughout its
208lifetime.  Computationally intensive components are written for
209efficiency in C routines working directly with the Numerical Python
210structures.  The animation tool developed for \anuga is based on
211OpenSceneGraph, an Open Source Software (OSS) component allowing high
212level interaction with sophisticated graphics primitives.
213See \cite{nielsen2005} for more background on \anuga.
214
215\chapter{Restrictions and limitations on \anuga}
216\label{ch:limitations}
217
218Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a
219number of limitations that any potential user need to be aware of. They are
220
221\begin{itemize}
222  \item The mathematical model is the 2D shallow water wave equation.
223  As such it cannot resolve vertical convection and consequently not breaking
224  waves or 3D turbulence (e.g.\ vorticity).
225  \item The surface is assumed to be open, e.g. \anuga cannot model
226  flow under ceilings or in pipes
227  \item All spatial coordinates are assumed to be UTM (meters). As such,
228  ANUGA is unsuitable for modelling flows in areas larger than one UTM zone
229  (6 degrees wide).
230  \item Fluid is assumed to be inviscid
231  \item The finite volume is a very robust and flexible numerical technique,
232  but it is not the fastest method around. If the geometry is sufficiently
233  simple and if there is no need for wetting or drying, a finite-difference
234  method may be able to solve the problem faster than \anuga.
235  %\item Mesh resolutions near coastlines with steep gradients need to be...
236  \item Frictional resistance is implemented using Manning's formula, but
237  \anuga has not yet been fully validated in regard to bottom roughness
238  \item ANUGA contains no tsunami-genic functionality relating to
239  earthquakes.
240\end{itemize}
241
242
243
244\chapter{Getting Started}
245\label{ch:getstarted}
246
247This section is designed to assist the reader to get started with
248\anuga by working through some examples. Two examples are discussed;
249the first is a simple example to illustrate many of the ideas, and
250the second is a more realistic example.
251
252\section{A Simple Example}
253\label{sec:simpleexample}
254
255\subsection{Overview}
256
257What follows is a discussion of the structure and operation of a
258script called \file{runup.py}.
259
260This example carries out the solution of the shallow-water wave
261equation in the simple case of a configuration comprising a flat
262bed, sloping at a fixed angle in one direction and having a
263constant depth across each line in the perpendicular direction.
264
265The example demonstrates the basic ideas involved in setting up a
266complex scenario. In general the user specifies the geometry
267(bathymetry and topography), the initial water level, boundary
268conditions such as tide, and any forcing terms that may drive the
269system such as rain_fall, abstraction of water, wind stress or atmospheric pressure gradients.
270Frictional resistance from the different terrains in the model is
271represented by predefined forcing terms. In this example, the
272boundary is reflective on three sides and a time dependent wave on
273one side.
274
275The present example represents a simple scenario and does not
276include any forcing terms, nor is the data taken from a file as it
277would typically be.
278
279The conserved quantities involved in the
280problem are stage (absolute height of water surface),
281$x$-momentum and $y$-momentum. Other quantities
282involved in the computation are the friction and elevation.
283
284Water depth can be obtained through the equation
285
286\begin{tabular}{rcrcl}
287  \code{depth} &=& \code{stage} &$-$& \code{elevation}
288\end{tabular}
289
290
291\subsection{Outline of the Program}
292
293In outline, \file{runup.py} performs the following steps:
294
295\begin{enumerate}
296
297   \item Sets up a triangular mesh.
298
299   \item Sets certain parameters governing the mode of
300operation of the model-specifying, for instance, where to store the model output.
301
302   \item Inputs various quantities describing physical measurements, such
303as the elevation, to be specified at each mesh point (vertex).
304
305   \item Sets up the boundary conditions.
306
307   \item Carries out the evolution of the model through a series of time
308steps and outputs the results, providing a results file that can
309be visualised.
310
311\end{enumerate}
312
313\subsection{The Code}
314
315%FIXME: we are using the \code function here.
316%This should be used wherever possible
317For reference we include below the complete code listing for
318\file{runup.py}. Subsequent paragraphs provide a
319`commentary' that describes each step of the program and explains it
320significance.
321
322\verbatiminput{demos/runup.py}
323
324\subsection{Establishing the Mesh}\index{mesh, establishing}
325
326The first task is to set up the triangular mesh to be used for the
327scenario. This is carried out through the statement:
328
329{\small \begin{verbatim}
330    points, vertices, boundary = rectangular_cross(10, 10)
331\end{verbatim}}
332
333The function \function{rectangular_cross} is imported from a module
334\module{mesh\_factory} defined elsewhere. (\anuga also contains
335several other schemes that can be used for setting up meshes, but we
336shall not discuss these.) The above assignment sets up a $10 \times
33710$ rectangular mesh, triangulated in a regular way. The assignment
338
339{\small \begin{verbatim}
340    points, vertices, boundary = rectangular_cross(m, n)
341\end{verbatim}}
342
343returns:
344
345\begin{itemize}
346
347   \item a list \code{points} giving the coordinates of each mesh point,
348
349   \item a list \code{vertices} specifying the three vertices of each triangle, and
350
351   \item a dictionary \code{boundary} that stores the edges on
352   the boundary and associates each with one of the symbolic tags \code{`left'}, \code{`right'},
353   \code{`top'} or \code{`bottom'}.
354
355\end{itemize}
356
357(For more details on symbolic tags, see page
358\pageref{ref:tagdescription}.)
359
360An example of a general unstructured mesh and the associated data
361structures \code{points}, \code{vertices} and \code{boundary} is
362given in Section \ref{sec:meshexample}.
363
364
365
366
367\subsection{Initialising the Domain}
368
369These variables are then used to set up a data structure
370\code{domain}, through the assignment:
371
372{\small \begin{verbatim}
373    domain = Domain(points, vertices, boundary)
374\end{verbatim}}
375
376This creates an instance of the \class{Domain} class, which
377represents the domain of the simulation. Specific options are set at
378this point, including the basename for the output file and the
379directory to be used for data:
380
381{\small \begin{verbatim}
382    domain.set_name('runup')
383\end{verbatim}}
384
385{\small \begin{verbatim}
386    domain.set_datadir('.')
387\end{verbatim}}
388
389In addition, the following statement now specifies that the
390quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are
391to be stored:
392
393{\small \begin{verbatim}
394    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
395    'ymomentum'])
396\end{verbatim}}
397
398
399\subsection{Initial Conditions}
400
401The next task is to specify a number of quantities that we wish to
402set for each mesh point. The class \class{Domain} has a method
403\method{set\_quantity}, used to specify these quantities. It is a
404flexible method that allows the user to set quantities in a variety
405of ways---using constants, functions, numeric arrays, expressions
406involving other quantities, or arbitrary data points with associated
407values, all of which can be passed as arguments. All quantities can
408be initialised using \method{set\_quantity}. For a conserved
409quantity (such as \code{stage, xmomentum, ymomentum}) this is called
410an \emph{initial condition}. However, other quantities that aren't
411updated by the equation are also assigned values using the same
412interface. The code in the present example demonstrates a number of
413forms in which we can invoke \method{set\_quantity}.
414
415
416\subsubsection{Elevation}
417
418The elevation, or height of the bed, is set using a function,
419defined through the statements below, which is specific to this
420example and specifies a particularly simple initial configuration
421for demonstration purposes:
422
423{\small \begin{verbatim}
424    def f(x,y):
425        return -x/2
426\end{verbatim}}
427
428This simply associates an elevation with each point \code{(x, y)} of
429the plane.  It specifies that the bed slopes linearly in the
430\code{x} direction, with slope $-\frac{1}{2}$,  and is constant in
431the \code{y} direction.
432
433Once the function \function{f} is specified, the quantity
434\code{elevation} is assigned through the simple statement:
435
436{\small \begin{verbatim}
437    domain.set_quantity('elevation', f)
438\end{verbatim}}
439
440NOTE: If using function to set \code{elevation} it must be vector
441compatible. For example square root will not work.
442
443\subsubsection{Friction}
444
445The assignment of the friction quantity (a forcing term)
446demonstrates another way we can use \method{set\_quantity} to set
447quantities---namely, assign them to a constant numerical value:
448
449{\small \begin{verbatim}
450    domain.set_quantity('friction', 0.1)
451\end{verbatim}}
452
453This specifies that the Manning friction coefficient is set to 0.1
454at every mesh point.
455
456\subsubsection{Stage}
457
458The stage (the height of the water surface) is related to the
459elevation and the depth at any time by the equation
460
461{\small \begin{verbatim}
462    stage = elevation + depth
463\end{verbatim}}
464
465
466For this example, we simply assign a constant value to \code{stage},
467using the statement
468
469{\small \begin{verbatim}
470    domain.set_quantity('stage', -.4)
471\end{verbatim}}
472
473which specifies that the surface level is set to a height of $-0.4$,
474i.e. 0.4 units (m) below the zero level.
475
476Although it is not necessary for this example, it may be useful to
477digress here and mention a variant to this requirement, which allows
478us to illustrate another way to use \method{set\_quantity}---namely,
479incorporating an expression involving other quantities. Suppose,
480instead of setting a constant value for the stage, we wished to
481specify a constant value for the \emph{depth}. For such a case we
482need to specify that \code{stage} is everywhere obtained by adding
483that value to the value already specified for \code{elevation}. We
484would do this by means of the statements:
485
486{\small \begin{verbatim}
487    h = 0.05 # Constant depth
488    domain.set_quantity('stage', expression = 'elevation + %f' %h)
489\end{verbatim}}
490
491That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus
492the value of \code{elevation} already defined.
493
494The reader will probably appreciate that this capability to
495incorporate expressions into statements using \method{set\_quantity}
496greatly expands its power.) See Section \ref{sec:Initial Conditions} for more
497details.
498
499\subsection{Boundary Conditions}\index{boundary conditions}
500
501The boundary conditions are specified as follows:
502
503{\small \begin{verbatim}
504    Br = Reflective_boundary(domain)
505
506    Bt = Transmissive_boundary(domain)
507
508    Bd = Dirichlet_boundary([0.2,0.,0.])
509
510    Bw = Time_boundary(domain=domain,
511                f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
512\end{verbatim}}
513
514The effect of these statements is to set up a selection of different
515alternative boundary conditions and store them in variables that can be
516assigned as needed. Each boundary condition specifies the
517behaviour at a boundary in terms of the behaviour in neighbouring
518elements. The boundary conditions introduced here may be briefly described as
519follows:
520
521\begin{itemize}
522    \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as
523      as present in its neighbour volume but momentum vector
524      reversed 180 degrees (reflected).
525      Specific to the shallow water equation as it works with the
526      momentum quantities assumed to be the second and third conserved
527      quantities. A reflective boundary condition models a solid wall.
528    \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as
529      those present in its neighbour volume. This is one way of modelling
530      outflow from a domain, but it should be used with caution if flow is
531      not steady state as replication of momentum at the boundary
532      may cause occasional spurious effects. If this occurs,
533      consider using e.g. a Dirichlet boundary condition.
534    \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies
535      constant values for stage, $x$-momentum and $y$-momentum at the boundary.
536    \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet
537      boundary but with behaviour varying with time.
538\end{itemize}
539
540\label{ref:tagdescription}Before describing how these boundary
541conditions are assigned, we recall that a mesh is specified using
542three variables \code{points}, \code{vertices} and \code{boundary}.
543In the code we are discussing, these three variables are returned by
544the function \code{rectangular}; however, the example given in
545Section \ref{sec:realdataexample} illustrates another way of
546assigning the values, by means of the function
547\code{create\_mesh\_from\_regions}.
548
549These variables store the data determining the mesh as follows. (You
550may find that the example given in Section \ref{sec:meshexample}
551helps to clarify the following discussion, even though that example
552is a \emph{non-rectangular} mesh.)
553
554\begin{itemize}
555\item The variable \code{points} stores a list of 2-tuples giving the
556coordinates of the mesh points.
557
558\item The variable \code{vertices} stores a list of 3-tuples of
559numbers, representing vertices of triangles in the mesh. In this
560list, the triangle whose vertices are \code{points[i]},
561\code{points[j]}, \code{points[k]} is represented by the 3-tuple
562\code{(i, j, k)}.
563
564\item The variable \code{boundary} is a Python dictionary that
565not only stores the edges that make up the boundary but also assigns
566symbolic tags to these edges to distinguish different parts of the
567boundary. An edge with endpoints \code{points[i]} and
568\code{points[j]} is represented by the 2-tuple \code{(i, j)}. The
569keys for the dictionary are the 2-tuples \code{(i, j)} corresponding
570to boundary edges in the mesh, and the values are the tags are used
571to label them. In the present example, the value \code{boundary[(i,
572j)]} assigned to \code{(i, j)]} is one of the four tags
573\code{`left'}, \code{`right'}, \code{`top'} or \code{`bottom'},
574depending on whether the boundary edge represented by \code{(i, j)}
575occurs at the left, right, top or bottom of the rectangle bounding
576the mesh. The function \code{rectangular} automatically assigns
577these tags to the boundary edges when it generates the mesh.
578\end{itemize}
579
580The tags provide the means to assign different boundary conditions
581to an edge depending on which part of the boundary it belongs to.
582(In Section \ref{sec:realdataexample} we describe an example that
583uses different boundary tags --- in general, the possible tags are entirely selectable by the user when generating the mesh and not
584limited to `left', `right', `top' and `bottom' as in this example.)
585All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by ANUGA.
586
587
588Using the boundary objects described above, we assign a boundary
589condition to each part of the boundary by means of a statement like
590
591{\small \begin{verbatim}
592    domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br})
593\end{verbatim}}
594
595It is critical that all tags are assoctiated with a boundary conditing in this statement. If not the program will halt with a statement like
596
597\begin{verbatim}
598
599Traceback (most recent call last):
600  File "mesh_test.py", line 114, in ?
601    domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br})
602  File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary
603    raise msg
604ERROR (domain.py): Tag "exterior" has not been bound to a boundary object.
605All boundary tags defined in domain must appear in the supplied dictionary.
606The tags are: ['ocean', 'east', 'north', 'exterior', 'south']
607\end{verbatim}
608
609
610The command \code{set\_boundary} stipulates that, in the current example, the right
611boundary varies with time, as defined by the lambda function, while the other
612boundaries are all reflective.
613
614The reader may wish to experiment by varying the choice of boundary
615types for one or more of the boundaries. (In the case of \code{Bd}
616and \code{Bw}, the three arguments in each case represent the
617\code{stage}, $x$-momentum and $y$-momentum, respectively.)
618
619{\small \begin{verbatim}
620    Bw = Time_boundary(domain=domain,
621                       f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0])
622\end{verbatim}}
623
624
625
626\subsection{Evolution}\index{evolution}
627
628The final statement \nopagebreak[3]
629{\small \begin{verbatim}
630    for t in domain.evolve(yieldstep = 0.1, duration = 4.0):
631        print domain.timestepping_statistics()
632\end{verbatim}}
633
634causes the configuration of the domain to `evolve', over a series of
635steps indicated by the values of \code{yieldstep} and
636\code{duration}, which can be altered as required.  The value of
637\code{yieldstep} controls the time interval between successive model
638outputs.  Behind the scenes more time steps are generally taken.
639
640
641\subsection{Output}
642
643The output is a NetCDF file with the extension \code{.sww}. It
644contains stage and momentum information and can be used with the
645ANUGA viewer \code{animate} (see Section \ref{sec:animate})
646visualisation package
647to generate a visual display. See Section \ref{sec:file formats}
648(page \pageref{sec:file formats}) for more on NetCDF and other file
649formats.
650
651The following is a listing of the screen output seen by the user
652when this example is run:
653
654\verbatiminput{examples/runupoutput.txt}
655
656
657\section{How to Run the Code}
658
659The code can be run in various ways:
660
661\begin{itemize}
662  \item{from a Windows or Unix command line} as in\ \code{python runup.py}
663  \item{within the Python IDLE environment}
664  \item{within emacs}
665  \item{within Windows, by double-clicking the \code{runup.py}
666  file.}
667\end{itemize}
668
669
670\section{Exploring the Model Output}
671
672The following figures are screenshots from the \anuga visualisation
673tool \code{animate}. Figure \ref{fig:runupstart} shows the domain
674with water surface as specified by the initial condition, $t=0$.
675Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and
676$t=4$ where the system has been evolved and the wave is encroaching
677on the previously dry bed.  All figures are screenshots from an
678interactive animation tool called animate which is part of \anuga and
679distributed as in the package anuga\_viewer.
680Animate is described in more detail is Section \ref{sec:animate}.
681
682\begin{figure}[hbt]
683
684  \centerline{\includegraphics[width=75mm, height=75mm]
685    {graphics/bedslopestart.jpg}}
686
687  \caption{Runup example viewed with the ANUGA viewer}
688  \label{fig:runupstart}
689\end{figure}
690
691
692\begin{figure}[hbt]
693
694  \centerline{
695   \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg}
696    \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg}
697   }
698
699  \caption{Runup example viewed with ANGUA viewer}
700  \label{fig:runup2}
701\end{figure}
702
703
704
705\clearpage
706
707%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
708
709\section{A slightly more complex example}
710\label{sec:channelexample}
711
712\subsection{Overview}
713
714The next example is about waterflow in a channel with varying boundary conditions and
715more complex topograhies. These examples build on the
716concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
717The example will be built up through three progressively more complex scripts.
718
719\subsection{Overview}
720As in the case of \file{runup.py}, the actions carried
721out by the program can be organised according to this outline:
722
723\begin{enumerate}
724
725   \item Set up a triangular mesh.
726
727   \item Set certain parameters governing the mode of
728operation of the model---specifying, for instance, where to store the
729model output.
730
731   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
732
733   \item Set up the boundary conditions.
734
735   \item Carry out the evolution of the model through a series of time
736steps and output the results, providing a results file that can be
737visualised.
738
739\end{enumerate}
740
741
742\subsection{The Code}
743
744Here is the code for the first version of the channel flow \file{channel1.py}:
745
746\verbatiminput{demos/channel1.py}
747
748In discussing the details of this example, we follow the outline
749given above, discussing each major step of the code in turn.
750
751\subsection{Establishing the Mesh}\index{mesh, establishing}
752
753In this example we use a similar simple structured triangular mesh as in \code{runup.py}
754for simplicity, but this time we will use a symmetric one and also
755change the physical extent of the domain. The assignment
756
757{\small \begin{verbatim}
758    points, vertices, boundary = rectangular_cross(m, n,
759                                                   len1=length, len2=width)
760\end{verbatim}}
761returns a m x n mesh similar to the one used in the previous example, except that now the
762extent in the x and y directions are given by the value of \code{length} and \code{width}
763respectively.
764
765Defining m and n in terms of the extent as in this example provides a convenient way of
766controlling the resolution: By defining dx and dy to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows:
767
768{\small \begin{verbatim}
769length = 10.
770width = 5.
771dx = dy = 1           # Resolution: Length of subdivisions on both axes
772
773points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
774                                               len1=length, len2=width)
775\end{verbatim}}
776which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decrease the values of dx and dy.
777
778The rest of this script is as in the previous example.
779% except for an application of the 'expression' form of \code{set\_quantity} where we use the value of \code{elevation} to define the (dry) initial condition for \code{stage}:
780%{\small \begin{verbatim}
781%  domain.set_quantity('stage', expression='elevation')
782%\end{verbatim}}
783
784\section{Model Output}
785
786The following figure is a screenshot from the \anuga visualisation
787tool \code{animate} of output from this example.
788\begin{figure}[hbt]
789  \centerline{\includegraphics[height=75mm]
790    {graphics/channel1.png}}%
791
792  \caption{Simple channel example viewed with the ANUGA viewer.}
793  \label{fig:channel1}
794\end{figure}
795
796
797\subsection{Changing boundary conditions on the fly}
798\label{sec:change boundary}
799
800Here is the code for the second version of the channel flow \file{channel2.py}:
801\verbatiminput{demos/channel2.py}
802This example differs from the first version in that a constant outflow boundary condition has
803been defined
804{\small \begin{verbatim}
805    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
806\end{verbatim}}
807and that it is applied to the right hand side boundary when the water level there exceeds 0m.
808{\small \begin{verbatim}
809for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
810    domain.write_time()
811
812    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:
813        print 'Stage > 0: Changing to outflow boundary'
814        domain.set_boundary({'right': Bo})
815\end{verbatim}}
816\label{sec:change boundary code}
817
818The if statement in the timestepping loop (evolve) gets the quantity
819\code{stage} and obtain the interpolated value at the point (10m,
8202.5m) which is on the right boundary. If the stage exceeds 0m a
821message is printed and the old boundary condition at tag 'right' is
822replaced by the outflow boundary using the method
823{\small \begin{verbatim}
824    domain.set_boundary({'right': Bo})
825\end{verbatim}}
826This type of dynamically varying boundary could for example be
827used to model the
828breakdown of a sluice door when water exceeds a certain level.
829
830\subsection{Output}
831
832The text output from this example looks like this
833{\small \begin{verbatim}
834...
835Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
836Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
837Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
838Stage > 0: Changing to outflow boundary
839Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
840Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
841...
842\end{verbatim}}
843
844
845\subsection{Flow through more complex topograhies}
846
847Here is the code for the third version of the channel flow \file{channel3.py}:
848\verbatiminput{demos/channel3.py}
849
850This example differs from the first two versions in that the topography
851contains obstacles.
852
853This is accomplished here by defining the function \code{topography} as follows
854{\small \begin{verbatim}
855def topography(x,y):
856    """Complex topography defined by a function of vectors x and y
857    """
858
859    z = -x/10
860
861    N = len(x)
862    for i in range(N):
863
864        # Step
865        if 10 < x[i] < 12:
866            z[i] += 0.4 - 0.05*y[i]
867
868        # Constriction
869        if 27 < x[i] < 29 and y[i] > 3:
870            z[i] += 2
871
872        # Pole
873        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
874            z[i] += 2
875
876    return z
877\end{verbatim}}
878
879In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
880
881A screenshot of this model at time == 15s is
882\begin{figure}[hbt]
883
884  \centerline{\includegraphics[height=75mm]
885    {graphics/channel3.png}}
886
887  \caption{More complex flow in a channel}
888  \label{fig:channel3}
889\end{figure}
890
891
892
893
894\clearpage
895
896%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
897
898\section{An Example with Real Data}
899\label{sec:realdataexample} The following discussion builds on the
900concepts introduced through the \file{runup.py} example and
901introduces a second example, \file{runcairns.py}.  This refers to
902a {\bf hypothetical} scenario using real-life data,
903in which the domain of interest surrounds the
904Cairns region. Two scenarios are given; firstly, a
905hypothetical tsunami wave is generated by a submarine mass failure
906situated on the edge of the continental shelf, and secondly, a fixed wave
907of given amplitude and period is introduced through the boundary.
908
909{\bf
910Each scenario has been designed to generate a tsunami which will
911inundate the Cairns region. To achieve this, suitably large
912parameters were chosen and were not based on any known tsunami sources
913or realistic amplitudes.
914}
915
916\subsection{Overview}
917As in the case of \file{runup.py}, the actions carried
918out by the program can be organised according to this outline:
919
920\begin{enumerate}
921
922   \item Set up a triangular mesh.
923
924   \item Set certain parameters governing the mode of
925operation of the model---specifying, for instance, where to store the
926model output.
927
928   \item Input various quantities describing physical measurements, such
929as the elevation, to be specified at each mesh point (vertex).
930
931   \item Set up the boundary conditions.
932
933   \item Carry out the evolution of the model through a series of time
934steps and output the results, providing a results file that can be
935visualised.
936
937\end{enumerate}
938
939
940
941\subsection{The Code}
942
943Here is the code for \file{runcairns.py}:
944
945\verbatiminput{demos/cairns/runcairns.py}
946
947In discussing the details of this example, we follow the outline
948given above, discussing each major step of the code in turn.
949
950\subsection{Establishing the Mesh}\index{mesh, establishing}
951
952One obvious way that the present example differs from
953\file{runup.py} is in the use of a more complex method to
954create the mesh. Instead of imposing a mesh structure on a
955rectangular grid, the technique used for this example involves
956building mesh structures inside polygons specified by the user,
957using a mesh-generator.
958
959In its simplest form, the mesh-generator creates the mesh within a single
960polygon whose vertices are at geographical locations specified by
961the user. The user specifies the \emph{resolution}---that is, the
962maximal area of a triangle used for triangulation---and a triangular
963mesh is created inside the polygon using a mesh generation engine.
964On any given platform, the same mesh will be returned.
965%Figure
966%\ref{fig:pentagon} shows a simple example of this, in which the
967%triangulation is carried out within a pentagon.
968
969
970%\begin{figure}[hbt]
971
972%  \caption{Mesh points are created inside the polygon}
973  %\label{fig:pentagon}
974%\end{figure}
975
976Boundary tags are not restricted to \code{`left'}, \code{`bottom'},
977\code{`right'} and \code{`top'}, as in the case of
978\file{runup.py}. Instead the user specifies a list of
979tags appropriate to the configuration being modelled.
980
981In addition, the mesh-generator provides a way to adapt to geographic or
982other features in the landscape, whose presence may require an
983increase in resolution. This is done by allowing the user to specify
984a number of \emph{interior polygons}, each with a specified
985resolution. It is also
986possible to specify one or more `holes'---that is, areas bounded by
987polygons in which no triangulation is required.
988
989%\begin{figure}[hbt]
990%  \caption{Interior meshes with individual resolution}
991%  \label{fig:interior meshes}
992%\end{figure}
993
994In its general form, the mesh-generator takes for its input a bounding
995polygon and (optionally) a list of interior polygons. The user
996specifies resolutions, both for the bounding polygon and for each of
997the interior polygons. Given this data, the mesh-generator first creates a
998triangular mesh with varying resolution.
999
1000The function used to implement this process is
1001\function{create\_mesh\_from\_regions}. Its arguments include the
1002bounding polygon and its resolution, a list of boundary tags, and a
1003list of pairs \code{[polygon, resolution]}, specifying the interior
1004polygons and their resolutions.
1005
1006The resulting mesh is output to a \emph{mesh file}\index{mesh
1007file}\label{def:mesh file}. This term is used to describe a file of
1008a specific format used to store the data specifying a mesh. (There
1009are in fact two possible formats for such a file: it can either be a
1010binary file, with extension \code{.msh}, or an ASCII file, with
1011extension \code{.tsh}. In the present case, the binary file format
1012\code{.msh} is used. See Section \ref{sec:file formats} (page
1013\pageref{sec:file formats}) for more on file formats.)
1014
1015In practice, the details of the polygons used are read from a
1016separate file \file{project.py}. Here is a complete listing of
1017\file{project.py}:
1018
1019\verbatiminput{demos/cairns/project.py}
1020
1021Figure \ref{fig:cairns3d} illustrates the landscape of the region
1022for the Cairns example. Understanding the landscape is important in
1023determining the location and resolution of interior polygons. The
1024supporting data is found in the ASCII grid, \code{cairns.asc}, which
1025has been sourced from the publically available Australian Bathymetry
1026and Topography Grid 2005, \cite{grid250}. The required resolution
1027for inundation modelling will depend on the underlying topography and
1028bathymetry; as the terrain becomes more complex, the desired resolution
1029would decrease to the order of tens of metres.
1030
1031\begin{figure}[hbt]
1032\centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}}
1033\caption{Landscape of the Cairns scenario.}
1034\label{fig:cairns3d}
1035
1036\end{figure}
1037The following statements are used to read in the specific polygons
1038from \code{project.cairns} and assign a defined resolution to
1039each polygon.
1040
1041{\small \begin{verbatim}
1042    islands_res = 100000
1043    cairns_res = 100000
1044    shallow_res = 500000
1045    interior_regions = [[project.poly_cairns, cairns_res],
1046                        [project.poly_island0, islands_res],
1047                        [project.poly_island1, islands_res],
1048                        [project.poly_island2, islands_res],
1049                        [project.poly_island3, islands_res],
1050                        [project.poly_shallow, shallow_res]]
1051\end{verbatim}}
1052
1053Figure \ref{fig:cairnspolys}
1054illustrates the polygons used for the Cairns scenario.
1055
1056\begin{figure}[hbt]
1057
1058  \centerline{\includegraphics[scale=0.5]
1059      {graphics/cairnsmodel.jpg}}
1060  \caption{Interior and bounding polygons for the Cairns example.}
1061  \label{fig:cairnspolys}
1062\end{figure}
1063
1064The statement
1065
1066
1067{\small \begin{verbatim}
1068remainder_res = 10000000
1069create_mesh_from_regions(project.bounding_polygon,
1070                         boundary_tags={'top': [0],
1071                                        'ocean_east': [1],
1072                                        'bottom': [2],
1073                                        'onshore': [3]},
1074                         maximum_triangle_area=remainder_res,
1075                         filename=meshname,
1076                         interior_regions=interior_regions,
1077                         use_cache=True,
1078                         verbose=True)
1079\end{verbatim}}
1080is then used to create the mesh, taking the bounding polygon to be
1081the polygon \code{bounding\_polygon} specified in \file{project.py}.
1082The argument \code{boundary\_tags} assigns a dictionary, whose keys
1083are the names of the boundary tags used for the bounding
1084polygon---\code{`top'}, \code{`ocean\_east'}, \code{`bottom'}, and
1085\code{`onshore'}--- and whose values identify the indices of the
1086segments associated with each of these tags.
1087The polygon may be arranged either clock-wise or counter clock-wise and the
1088indices refer to edges in the order they appear: Edge 0 connects vertex 0 and vertex 1, edge 1 connects vertex 1 and 2; and so forth.
1089(Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges)
1090If polygons intersect, or edges coincide the resolution may be undefined in some regions.
1091Use the underlying mesh interface for such cases. See Section
1092\ref{sec:mesh interface}.
1093
1094Note that every point on each polygon defining the mesh will be used as vertices in triangles.
1095Consequently, polygons with points very close together will cause triangles with very small
1096areas to be generated irrespective of the requested resolution.
1097Make sure points on polygons are spaced to be no closer than the smallest resolution requested.
1098
1099
1100\subsection{Initialising the Domain}
1101
1102As with \file{runup.py}, once we have created the mesh, the next
1103step is to create the data structure \code{domain}. We did this for
1104\file{runup.py} by inputting lists of points and triangles and
1105specifying the boundary tags directly. However, in the present case,
1106we use a method that works directly with the mesh file
1107\code{meshname}, as follows:
1108
1109
1110{\small \begin{verbatim}
1111    domain = Domain(meshname, use_cache=True, verbose=True)
1112\end{verbatim}}
1113
1114Providing a filename instead of the lists used in \file{runup.py}
1115above causes \code{Domain} to convert a mesh file \code{meshname}
1116into an instance of \code{Domain}, allowing us to use methods like
1117\method{set\_quantity} to set quantities and to apply other
1118operations.
1119
1120%(In principle, the
1121%second argument of \function{pmesh\_to\_domain\_instance} can be any
1122%subclass of \class{Domain}, but for applications involving the
1123%shallow-water wave equation, the second argument of
1124%\function{pmesh\_to\_domain\_instance} can always be set simply to
1125%\class{Domain}.)
1126
1127The following statements specify a basename and data directory, and
1128identify quantities to be stored. For the first two, values are
1129taken from \file{project.py}.
1130
1131{\small \begin{verbatim}
1132    domain.set_name(project.basename)
1133    domain.set_datadir(project.outputdir)
1134    domain.set_quantities_to_be_stored(['stage', 'xmomentum',
1135        'ymomentum'])
1136\end{verbatim}}
1137
1138
1139\subsection{Initial Conditions}
1140Quantities for \file{runcairns.py} are set
1141using similar methods to those in \file{runup.py}. However,
1142in this case, many of the values are read from the auxiliary file
1143\file{project.py} or, in the case of \code{elevation}, from an
1144ancillary points file.
1145
1146
1147
1148\subsubsection{Stage}
1149
1150For the scenario we are modelling in this case, we use a callable
1151object \code{tsunami\_source}, assigned by means of a function
1152\function{slide\_tsunami}. This is similar to how we set elevation in
1153\file{runup.py} using a function---however, in this case the
1154function is both more complex and more interesting.
1155
1156The function returns the water displacement for all \code{x} and
1157\code{y} in the domain. The water displacement is a double Gaussian
1158function that depends on the characteristics of the slide (length,
1159width, thickness, slope, etc), its location (origin) and the depth at that
1160location. For this example, we choose to apply the slide function
1161at a specified time into the simulation. {\bf Note, the parameters used
1162in this example have been deliberately chosen to generate a suitably
1163large amplitude tsunami which would inundate the Cairns region.}
1164
1165\subsubsection{Friction}
1166
1167We assign the friction exactly as we did for \file{runup.py}:
1168
1169{\small \begin{verbatim}
1170    domain.set_quantity('friction', 0.0)
1171\end{verbatim}}
1172
1173
1174\subsubsection{Elevation}
1175
1176The elevation is specified by reading data from a file:
1177
1178{\small \begin{verbatim}
1179    domain.set_quantity('elevation',
1180                        filename = project.dem_name + '.pts',
1181                        use_cache = True,
1182                        verbose = True)
1183\end{verbatim}}
1184
1185%However, before this step can be executed, some preliminary steps
1186%are needed to prepare the file from which the data is taken. Two
1187%source files are used for this data---their names are specified in
1188%the file \file{project.py}, in the variables \code{coarsedemname}
1189%and \code{finedemname}. They contain `coarse' and `fine' data,
1190%respectively---that is, data sampled at widely spaced points over a
1191%large region and data sampled at closely spaced points over a
1192%smaller subregion. The data in these files is combined through the
1193%statement
1194
1195%{\small \begin{verbatim}
1196%combine_rectangular_points_files(project.finedemname + '.pts',
1197%                                 project.coarsedemname + '.pts',
1198%                                 project.combineddemname + '.pts')
1199%\end{verbatim}}
1200%The effect of this is simply to combine the datasets by eliminating
1201%any coarse data associated with points inside the smaller region
1202%common to both datasets. The name to be assigned to the resulting
1203%dataset is also derived from the name stored in the variable
1204%\code{combinedname} in the file \file{project.py}.
1205
1206\subsection{Boundary Conditions}\index{boundary conditions}
1207
1208Setting boundaries follows a similar pattern to the one used for
1209\file{runup.py}, except that in this case we need to associate a
1210boundary type with each of the
1211boundary tag names introduced when we established the mesh. In place of the four
1212boundary types introduced for \file{runup.py}, we use the reflective
1213boundary for each of the
1214eight tagged segments defined by \code{create_mesh_from_regions}:
1215
1216{\small \begin{verbatim}
1217Bd = Dirichlet_boundary([0.0,0.0,0.0])
1218domain.set_boundary( {'ocean_east': Bd, 'bottom': Bd, 'onshore': Bd,
1219                          'top': Bd} )
1220\end{verbatim}}
1221
1222\subsection{Evolution}
1223
1224With the basics established, the running of the `evolve' step is
1225very similar to the corresponding step in \file{runup.py}. For the slide
1226scenario,
1227the simulation is run for 5000 seconds with the output stored every ten seconds.
1228For this example, we choose to apply the slide at 60 seconds into the simulation.
1229
1230{\small \begin{verbatim}
1231    import time t0 = time.time()
1232
1233
1234    for t in domain.evolve(yieldstep = 10, finaltime = 60):
1235            domain.write_time()
1236            domain.write_boundary_statistics(tags = 'ocean_east')
1237
1238        # add slide
1239        thisstagestep = domain.get_quantity('stage')
1240        if allclose(t, 60):
1241            slide = Quantity(domain)
1242            slide.set_values(tsunami_source)
1243            domain.set_quantity('stage', slide + thisstagestep)
1244
1245        for t in domain.evolve(yieldstep = 10, finaltime = 5000,
1246                               skip_initial_step = True):
1247            domain.write_time()
1248        domain.write_boundary_statistics(tags = 'ocean_east')
1249\end{verbatim}}
1250
1251For the fixed wave scenario, the simulation is run to 10000 seconds,
1252with the first half of the simulation stored at two minute intervals,
1253and the second half of the simulation stored at ten second intervals.
1254This functionality is especially convenient as it allows the detailed
1255parts of the simulation to be viewed at higher time resolution.
1256
1257
1258{\small \begin{verbatim}
1259
1260# save every two mins leading up to wave approaching land
1261    for t in domain.evolve(yieldstep = 120, finaltime = 5000):
1262        domain.write_time()
1263        domain.write_boundary_statistics(tags = 'ocean_east')
1264
1265    # save every 30 secs as wave starts inundating ashore
1266    for t in domain.evolve(yieldstep = 10, finaltime = 10000,
1267                           skip_initial_step = True):
1268        domain.write_time()
1269        domain.write_boundary_statistics(tags = 'ocean_east')
1270
1271\end{verbatim}}
1272
1273\section{Exploring the Model Output}
1274
1275Now that the scenario has been run, the user can view the output in a number of ways.
1276As described earlier, the user may run animate to view a three-dimensional representation
1277of the simulation.
1278
1279The user may also be interested in a maximum inundation map. This simply shows the
1280maximum water depth over the domain and is achieved with the function sww2dem (described in
1281Section \ref{sec:basicfileconversions}).
1282\file{ExportResults.py} demonstrates how this function can be used:
1283
1284\verbatiminput{demos/cairns/ExportResults.py}
1285
1286The script generates an maximum water depth ASCII grid at a defined
1287resolution (here 100 m$^2$) which can then be viewed in a GIS environment, for
1288example. The parameters used in the function are defined in \file{project.py}.
1289Figures \ref{fig:maxdepthcairnsslide} and \ref{fig:maxdepthcairnsfixedwave} show
1290the maximum water depth within the defined region for the slide and fixed wave scenario
1291respectively. {\bf Note, these inundation maps have been based on purely hypothetical
1292scenarios and were designed explicitly for demonstration purposes only.}
1293The user could develop a maximum absolute momentum or other expressions which can be
1294derived from the quantities.
1295It must be noted here that depth is more meaningful when the elevation is positive
1296(\code{depth} = \code{stage} $-$ \code{elevation}) as it describes the water height
1297above the available elevation. When the elevation is negative, depth is meauring the
1298water height from the sea floor. With this in mind, maximum inundation maps are
1299typically "clipped" to the coastline. However, the data input here did not contain a
1300coastline.
1301
1302\begin{figure}[hbt]
1303\centerline{\includegraphics[scale=0.5]{graphics/slidedepth.jpg}}
1304\caption{Maximum inundation map for the Cairns slide scenario. \bf Note, this
1305inundaiton map has been based on a purely hypothetical scenario which was
1306designed explictiy for demonstration purposes only.}
1307\label{fig:maxdepthcairnsslide}
1308\end{figure}
1309
1310\begin{figure}[hbt]
1311\centerline{\includegraphics[scale=0.5]{graphics/fixedwavedepth.jpg}}
1312\caption{Maximum inundation map for the Cairns fixed wave scenario.
1313\bf Note, this
1314inundaiton map has been based on a purely hypothetical scenario which was
1315designed explictiy for demonstration purposes only.}
1316\label{fig:maxdepthcairnsfixedwave}
1317\end{figure}
1318
1319The user may also be interested in interrogating the solution at a particular spatial
1320location to understand the behaviour of the system through time. To do this, the user
1321must first define the locations of interest. A number of locations have been
1322identified for the Cairns scenario, as shown in Figure \ref{fig:cairnsgauges}.
1323
1324\begin{figure}[hbt]
1325\centerline{\includegraphics[scale=0.5]{graphics/cairnsgauges.jpg}}
1326\caption{Point locations to show time series information for the Cairns scenario.}
1327\label{fig:cairnsgauges}
1328\end{figure}
1329
1330These locations
1331must be stored in either a .csv or .txt file. The corresponding .csv file for
1332the gauges shown in Figure \ref{fig:cairnsgauges} is \file{gauges.csv}
1333
1334\verbatiminput{demos/cairns/gauges.csv}
1335
1336Header information has been included to identify the location in terms of eastings and
1337northings, and each gauge is given a name. The elevation column can be zero here.
1338This information is then passed to the function \code{sww2csv_gauges} (shown in
1339\file{GetTimeseries.py} which generates the csv files for each point location. The csv files
1340can then be used in \code{csv2timeseries_graphs} to create the timeseries plot for each desired
1341quantity. \code{csv2timeseries_graphs} relies on \code{pylab} to be installed which is not part
1342of the standard \code{anuga} release, however it can be downloaded and installed from \code{http://matplotlib.sourceforge.net/}
1343
1344\verbatiminput{demos/cairns/GetTimeseries.py}
1345
1346Here, the time series for the quantities stage, depth and speed will be generated for
1347each gauge defined in the gauge file. As described earlier, depth is more meaningful
1348for onshore gauges, and stage is more appropriate for offshore gauges.
1349
1350As an example output,
1351Figure \ref{fig:reef} shows the time series for the quantity stage for the
1352Elford Reef location for each scenario (the elevation at this location is negative,
1353therefore stage is the more appropriate quantity to plot). Note the large negative stage value when the slide was
1354introduced. This is due to the double gaussian form of the initial surface
1355displacement of the slide. By contrast, the time series for depth is shown for the onshore location of the Cairns
1356Airport in Figure \ref{fig:airportboth}.
1357
1358\begin{figure}[hbt]
1359\centerline{\includegraphics[scale=0.5]{graphics/gaugeElfordReefstage.png}}
1360\caption{Time series information of the quantity stage for the Elford Reef location for the
1361fixed wave and slide scenario.}
1362\label{fig:reef}
1363\end{figure}
1364
1365\begin{figure}[hbt]
1366\centerline{\includegraphics[scale=0.5]{graphics/gaugeCairnsAirportdepth.png}}
1367\caption{Time series information of the quantity depth for the Cairns Airport
1368location for the slide and fixed wave scenario.}
1369\label{fig:airportboth}
1370\end{figure}
1371
1372
1373%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1374%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1375
1376\chapter{\anuga Public Interface}
1377\label{ch:interface}
1378
1379This chapter gives an overview of the features of \anuga available
1380to the user at the public interface. These are grouped under the
1381following headings, which correspond to the outline of the examples
1382described in Chapter \ref{ch:getstarted}:
1383
1384\begin{itemize}
1385    \item Establishing the Mesh
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  Example:
2327  {\scriptsize \begin{verbatim} 
2328        xmom = General_forcing(domain, 'xmomentum', polygon=P)
2329        ymom = General_forcing(domain, 'ymomentum', polygon=P)
2330
2331        xmom.rate = f
2332        ymom.rate = g
2333 
2334        domain.forcing_terms.append(xmom)
2335        domain.forcing_terms.append(ymom)       
2336  \end{itemize}}
2337  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.
2338  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]]}
2339 
2340\end{funcdesc} 
2341
2342
2343\begin{funcdesc}{Inflow}{}
2344  Module: \module{shallow\_water.shallow\_water\_domain}
2345
2346  This is a general class for infiltration and abstraction of water according to a given rate of change.
2347  This class will always modify the \code{stage} quantity.
2348 
2349  Inflow is based on the General_forcing class so the functionality is similar.
2350 
2351  The Inflow class takes as input:
2352  \begin{itemize} 
2353    \item \code{domain}: a reference to the domain being evolved
2354    \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
2355                function of time. Positive values indicate inflow,
2356                negative values indicate outflow.
2357               
2358                Note: The specified flow will be divided by the area of
2359                the inflow region and then applied to update the
2360                stage quantity.     
2361    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2362    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2363  \end{itemize}
2364 
2365  Example:
2366  {\scriptsize \begin{verbatim} 
2367    hydrograph = Inflow(center=(320, 300), radius=10,
2368                        rate=file_function('QPMF_Rot_Sub13.tms'))
2369
2370    domain.forcing_terms.append(hydrograph)
2371  \end{itemize}}
2372  Here, \code{'QPMF_Rot_Sub13.tms') is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for a hydrograph.
2373\end{funcdesc} 
2374
2375
2376\begin{funcdesc}{Rainfall}{}
2377  Module: \module{shallow\_water.shallow\_water\_domain}
2378
2379  This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon.
2380  This class will always modify the \code{stage} quantity.
2381 
2382  Rainfall is based on the General_forcing class so the functionality is similar.
2383 
2384  The Rainfall class takes as input:
2385  \begin{itemize} 
2386    \item \code{domain}: a reference to the domain being evolved
2387    \item \code{rate}: Total rain rate over the specified domain. 
2388                  Note: Raingauge Data needs to reflect the time step.
2389                  For example: if rain gauge is mm read every \code{dt} seconds, then the input
2390                  here is as \code{mm/dt} so 10 mm in 5 minutes becomes
2391                  10/(5x60) = 0.0333mm/s.
2392       
2393                  This parameter can be either a constant or a
2394                  function of time. Positive values indicate rain being added (or be used for general infiltration),
2395                  negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction).
2396    \item \code{center, radius}: Optionally restrict forcing to a circle with given center and radius.
2397    \item \code{polygon}: Optionally restrict forcing to an area enclosed by given polygon.             
2398  \end{itemize}
2399 
2400  Example:
2401  {\scriptsize \begin{verbatim} 
2402 
2403    catchmentrainfall = Rainfall(rain=file_function('Q100_2hr_Rain.tms')) 
2404    domain.forcing_terms.append(catchmentrainfall)
2405
2406  \end{itemize}}
2407  Here, \code{'Q100_2hr_Rain.tms') is assumed to be a NetCDF file in the format \code{tms} defining a timeseries for the rainfall.
2408\end{funcdesc} 
2409
2410
2411
2412\begin{funcdesc}{Culvert\_flow}{}
2413  Module: \module{culver\_flows.culvert\_class}
2414
2415  This is a general class for implementing flow through a culvert.
2416  This class modifies the quantities \code{stage, xmomentum, ymomentum} in areas at both ends of the culvert.
2417 
2418  The Culvert\_flow forcing term uses \code{Inflow} and {General\_forcing} to update the quantities. The flow direction is determined on-the-fly so
2419  openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow and Outflow.
2420 
2421  The Culvert\_flow class takes as input:
2422  \begin{itemize} 
2423    \item \code{domain}: a reference to the domain being evolved
2424    \item \code{label}: Short text naming the culvert
2425    \item \code{description}: Text describing it
2426    \item \code{end_point0}: Coordinates of one opening
2427    \item \code{end_point1}: Coordinates of other opening
2428    \item \code{width}:
2429    \item \code{height}:
2430    \item \code{diameter}:
2431    \item \code{manning}: Mannings Roughness for Culvert
2432    \item \code{invert_level0}: Invert level if not the same as the Elevation on the Domain
2433    \item \code{invert_level1}: Invert level if not the same as the Elevation on the Domain
2434    \item \code{culvert_routine}: Function specifying the calculation of flow based on energy difference between the two openings (see below)
2435  \end{itemize}
2436
2437  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.
2438     
2439  Example:
2440  {\scriptsize \begin{verbatim} 
2441    from anuga.culvert_flows.culvert_class import Culvert_flow
2442    from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model 
2443
2444    culvert1 = Culvert_flow(domain,
2445                           label='Culvert No. 1',
2446                           description='This culvert is a test unit 1.2m Wide by 0.75m High',   
2447                           end_point0=[9.0, 2.5],
2448                           end_point1=[13.0, 2.5],
2449                           width=1.20,height=0.75,
2450                           culvert_routine=boyd_generalised_culvert_model,       
2451                           verbose=True)
2452
2453    culvert2 = Culvert_flow(domain,
2454                           label='Culvert No. 2',
2455                           description='This culvert is a circular test with d=1.2m',   
2456                           end_point0=[9.0, 1.5],
2457                           end_point1=[30.0, 3.5],
2458                           diameter=1.20,
2459                           invert_level0=7,
2460                           culvert_routine=boyd_generalised_culvert_model,       
2461                           verbose=True)
2462                           
2463    domain.forcing_terms.append(culvert1)
2464    domain.forcing_terms.append(culvert2)
2465
2466   
2467  \end{itemize}}
2468\end{funcdesc} 
2469
2470
2471
2472
2473
2474
2475\section{Evolution}\index{evolution}
2476
2477  \begin{methoddesc}{evolve}{yieldstep = None, finaltime = None, duration = None, skip_initial_step = False}
2478
2479  Module: \module{abstract\_2d\_finite\_volumes.domain}
2480
2481  This function (a method of \class{domain}) is invoked once all the
2482  preliminaries have been completed, and causes the model to progress
2483  through successive steps in its evolution, storing results and
2484  outputting statistics whenever a user-specified period
2485  \code{yieldstep} is completed (generally during this period the
2486  model will evolve through several steps internally
2487  as the method forces the water speed to be calculated
2488  on successive new cells). The user
2489  specifies the total time period over which the evolution is to take
2490  place, by specifying values (in seconds) for either \code{duration}
2491  or \code{finaltime}, as well as the interval in seconds after which
2492  results are to be stored and statistics output.
2493
2494  You can include \method{evolve} in a statement of the type:
2495
2496  {\small \begin{verbatim}
2497      for t in domain.evolve(yieldstep, finaltime):
2498          <Do something with domain and t>
2499  \end{verbatim}}
2500
2501  \end{methoddesc}
2502
2503
2504
2505\subsection{Diagnostics}
2506\label{sec:diagnostics}
2507
2508
2509  \begin{funcdesc}{statistics}{}
2510  Module: \module{abstract\_2d\_finite\_volumes.domain}
2511
2512  \end{funcdesc}
2513
2514  \begin{funcdesc}{timestepping\_statistics}{}
2515  Module: \module{abstract\_2d\_finite\_volumes.domain}
2516
2517  Returns a string of the following type for each
2518  timestep:
2519
2520  \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12
2521  (12)}
2522
2523  Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and
2524  the number of first-order steps, respectively.\\
2525
2526  The optional keyword argument \code{track_speeds=True} will
2527  generate a histogram of speeds generated by each triangle. The
2528  speeds relate to the size of the timesteps used by ANUGA and
2529  this diagnostics may help pinpoint problem areas where excessive speeds
2530  are generated.
2531
2532  \end{funcdesc}
2533
2534
2535  \begin{funcdesc}{boundary\_statistics}{quantities = None, tags = None}
2536  Module: \module{abstract\_2d\_finite\_volumes.domain}
2537
2538  Returns a string of the following type when \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']}:
2539
2540  {\small \begin{verbatim}
2541 Boundary values at time 0.5000:
2542    top:
2543        stage in [ -0.25821218,  -0.02499998]
2544    bottom:
2545        stage in [ -0.27098821,  -0.02499974]
2546  \end{verbatim}}
2547
2548  \end{funcdesc}
2549
2550
2551  \begin{funcdesc}{get\_quantity}{name, location='vertices', indices = None}
2552  Module: \module{abstract\_2d\_finite\_volumes.domain}
2553
2554  Allow access to individual quantities and their methods
2555
2556  \end{funcdesc}
2557
2558
2559  \begin{funcdesc}{set\_quantities\_to\_be\_monitored}{}
2560  Module: \module{abstract\_2d\_finite\_volumes.domain}
2561
2562  Selects quantities and derived quantities for which extrema attained at internal timesteps
2563  will be collected.
2564
2565  Information can be tracked in the evolve loop by printing \code{quantity\_statistics} and
2566  collected data will be stored in the sww file.
2567
2568  Optional parameters \code{polygon} and \code{time\_interval} may be specified to restrict the
2569  extremum computation.
2570  \end{funcdesc}
2571
2572  \begin{funcdesc}{quantity\_statistics}{}
2573  Module: \module{abstract\_2d\_finite\_volumes.domain}
2574
2575  Reports on extrema attained by selected quantities.
2576
2577  Returns a string of the following type for each
2578  timestep:
2579
2580  \begin{verbatim}
2581  Monitored quantities at time 1.0000:
2582    stage-elevation:
2583      values since time = 0.00 in [0.00000000, 0.30000000]
2584      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2585      maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667)
2586    ymomentum:
2587      values since time = 0.00 in [0.00000000, 0.06241221]
2588      minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667)
2589      maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667)
2590    xmomentum:
2591      values since time = 0.00 in [-0.06062178, 0.47886313]
2592      minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333)
2593      maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667)
2594  \end{verbatim}
2595
2596  The quantities (and derived quantities) listed here must be selected at model
2597  initialisation using the method \code{domain.set_quantities_to_be_monitored}.\\
2598
2599  The optional keyword argument \code{precision='\%.4f'} will
2600  determine the precision used for floating point values in the output.
2601  This diagnostics helps track extrema attained by the selected quantities
2602  at every internal timestep.
2603
2604  These values are also stored in the sww file for post processing.
2605
2606  \end{funcdesc}
2607
2608
2609
2610  \begin{funcdesc}{get\_values}{location='vertices', indices = None}
2611  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2612
2613  Extract values for quantity as an array
2614
2615  \end{funcdesc}
2616
2617
2618  \begin{funcdesc}{get\_integral}{}
2619  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2620
2621  Return computed integral over entire domain for this quantity
2622
2623  \end{funcdesc}
2624
2625
2626
2627
2628  \begin{funcdesc}{get\_maximum\_value}{indices = None}
2629  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2630
2631  Return maximum value of quantity (on centroids)
2632
2633  Optional argument indices is the set of element ids that
2634  the operation applies to. If omitted all elements are considered.
2635
2636  We do not seek the maximum at vertices as each vertex can
2637  have multiple values - one for each triangle sharing it.
2638  \end{funcdesc}
2639
2640
2641
2642  \begin{funcdesc}{get\_maximum\_location}{indices = None}
2643  Module: \module{abstract\_2d\_finite\_volumes.quantity}
2644
2645  Return location of maximum value of quantity (on centroids)
2646
2647  Optional argument indices is the set of element ids that
2648  the operation applies to.
2649
2650  We do not seek the maximum at vertices as each vertex can
2651  have multiple values - one for each triangle sharing it.
2652
2653  If there are multiple cells with same maximum value, the
2654  first cell encountered in the triangle array is returned.
2655  \end{funcdesc}
2656
2657
2658
2659  \begin{funcdesc}{get\_wet\_elements}{indices=None}
2660  Module: \module{shallow\_water.shallow\_water\_domain}
2661
2662  Return indices for elements where h $>$ minimum_allowed_height
2663  Optional argument indices is the set of element ids that the operation applies to.
2664  \end{funcdesc}
2665
2666
2667  \begin{funcdesc}{get\_maximum\_inundation\_elevation}{indices=None}
2668  Module: \module{shallow\_water.shallow\_water\_domain}
2669
2670  Return highest elevation where h $>$ 0.\\
2671  Optional argument indices is the set of element ids that the operation applies to.\\
2672
2673  Example to find maximum runup elevation:\\
2674     z = domain.get_maximum_inundation_elevation()
2675  \end{funcdesc}
2676
2677
2678  \begin{funcdesc}{get\_maximum\_inundation\_location}{indices=None}
2679  Module: \module{shallow\_water.shallow\_water\_domain}
2680
2681  Return location (x,y) of highest elevation where h $>$ 0.\\
2682  Optional argument indices is the set of element ids that the operation applies to.\\
2683
2684  Example to find maximum runup location:\\
2685     x, y = domain.get_maximum_inundation_location()
2686  \end{funcdesc}
2687
2688
2689\section{Queries of SWW model output files}
2690After a model has been run, it is often useful to extract various information from the sww
2691output file (see Section \ref{sec:sww format}). This is typically more convenient than using the
2692diagnostics described in Section \ref{sec:diagnostics} which rely on the model running - something
2693that can be very time consuming. The sww files are easy and quick to read and offer much information
2694about the model results such as runup heights, time histories of selected quantities,
2695flow through cross sections and much more.
2696
2697\begin{funcdesc}{get\_maximum\_inundation\_elevation}{filename, polygon=None,
2698    time_interval=None, verbose=False}
2699  Module: \module{shallow\_water.data\_manager}
2700
2701  Return highest elevation where depth is positive ($h > 0$)
2702
2703  Example to find maximum runup elevation:\\
2704  max_runup = get_maximum_inundation_elevation(filename,
2705  polygon=None,
2706  time_interval=None,
2707  verbose=False)
2708
2709
2710  filename is a NetCDF sww file containing ANUGA model output.
2711  Optional arguments polygon and time_interval restricts the maximum runup calculation
2712  to a points that lie within the specified polygon and time interval.
2713
2714  If no inundation is found within polygon and time_interval the return value
2715  is None signifying "No Runup" or "Everything is dry".
2716
2717  See doc string for general function get_maximum_inundation_data for details.
2718\end{funcdesc}
2719
2720
2721\begin{funcdesc}{get\_maximum\_inundation\_location}{filename, polygon=None,
2722    time_interval=None, verbose=False}
2723  Module: \module{shallow\_water.data\_manager}
2724
2725  Return location (x,y) of highest elevation where depth is positive ($h > 0$)
2726
2727  Example to find maximum runup location:\\
2728  max_runup_location = get_maximum_inundation_location(filename,
2729  polygon=None,
2730  time_interval=None,
2731  verbose=False)
2732
2733
2734  filename is a NetCDF sww file containing ANUGA model output.
2735  Optional arguments polygon and time_interval restricts the maximum runup calculation
2736  to a points that lie within the specified polygon and time interval.
2737
2738  If no inundation is found within polygon and time_interval the return value
2739  is None signifying "No Runup" or "Everything is dry".
2740
2741  See doc string for general function get_maximum_inundation_data for details.
2742\end{funcdesc}
2743
2744
2745\begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report = None, reportname = None,
2746plot_quantity = None, generate_fig = False, surface = None, time_min = None, time_max = None, time_thinning = 1,
2747time_unit = None, title_on = None, use_cache = False, verbose = False}
2748
2749  Module: \module{anuga.abstract\_2d\_finite\_volumes.util}
2750
2751  Return csv files for the location in the \code{gauge_filename} and can also return plots of them
2752
2753  See doc string for general function sww2timeseries for details.
2754
2755\end{funcdesc}
2756
2757
2758\begin{funcdesc}{get\_flow\_through\_cross\_section}{filename, cross\_section, verbose=False}
2759  Module: \module{shallow\_water.data\_manager}
2760
2761  Obtain flow $[m^2]$ perpendicular to specified cross section.
2762
2763  Inputs:
2764  \begin{itemize} 
2765        \item filename: Name of sww file containing ANUGA model output.
2766        \item polyline: Representation of desired cross section - it may contain multiple
2767          sections allowing for complex shapes. Assume absolute UTM coordinates.
2768  \end{itemize} 
2769
2770  Output:
2771  \begin{itemize}
2772    \item time: All stored times in sww file
2773    \item Q: Hydrograph of total flow across given segments for all stored times.
2774  \end{itemize} 
2775 
2776  The normal flow is computed for each triangle intersected by the polyline and
2777  added up.  Multiple segments at different angles are specified the normal flows
2778  may partially cancel each other.
2779 
2780  Example to find flow through cross section:
2781 
2782  \begin{verbatim} 
2783  cross_section = [[x, 0], [x, width]]
2784  time, Q = get_flow_through_cross_section(filename,
2785                                           cross_section,
2786                                           verbose=False)
2787  \end{verbatim} 
2788
2789
2790  See doc string for general function get_maximum_inundation_data for details.
2791 
2792\end{funcdesc}
2793
2794
2795
2796\section{Other}
2797
2798  \begin{funcdesc}{domain.create\_quantity\_from\_expression}{string}
2799
2800  Handy for creating derived quantities on-the-fly as for example
2801  \begin{verbatim}
2802  Depth = domain.create_quantity_from_expression('stage-elevation')
2803
2804  exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5')
2805  Absolute_momentum = domain.create_quantity_from_expression(exp)
2806  \end{verbatim}
2807
2808  %See also \file{Analytical\_solution\_circular\_hydraulic\_jump.py} for an example of use.
2809  \end{funcdesc}
2810
2811
2812
2813
2814
2815%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2816%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2817
2818\chapter{\anuga System Architecture}
2819
2820
2821\section{File Formats}
2822\label{sec:file formats}
2823
2824\anuga makes use of a number of different file formats. The
2825following table lists all these formats, which are described in more
2826detail in the paragraphs below.
2827
2828\bigskip
2829
2830\begin{center}
2831
2832\begin{tabular}{|ll|}  \hline
2833
2834\textbf{Extension} & \textbf{Description} \\
2835\hline\hline
2836
2837\code{.sww} & NetCDF format for storing model output
2838\code{f(t,x,y)}\\
2839
2840\code{.tms} & NetCDF format for storing time series \code{f(t)}\\
2841
2842\code{.csv/.txt} & ASCII format called points csv for storing
2843arbitrary points and associated attributes\\
2844
2845\code{.pts} & NetCDF format for storing arbitrary points and
2846associated attributes\\
2847
2848\code{.asc} & ASCII format of regular DEMs as output from ArcView\\
2849
2850\code{.prj} & Associated ArcView file giving more metadata for
2851\code{.asc} format\\
2852
2853\code{.ers} & ERMapper header format of regular DEMs for ArcView\\
2854
2855\code{.dem} & NetCDF representation of regular DEM data\\
2856
2857\code{.tsh} & ASCII format for storing meshes and associated
2858boundary and region info\\
2859
2860\code{.msh} & NetCDF format for storing meshes and associated
2861boundary and region info\\
2862
2863\code{.nc} & Native ferret NetCDF format\\
2864
2865\code{.geo} & Houdinis ASCII geometry format (?) \\  \par \hline
2866%\caption{File formats used by \anuga}
2867\end{tabular}
2868
2869
2870\end{center}
2871
2872The above table shows the file extensions used to identify the
2873formats of files. However, typically, in referring to a format we
2874capitalise the extension and omit the initial full stop---thus, we
2875refer, for example, to `SWW files' or `PRJ files'.
2876
2877\bigskip
2878
2879A typical dataflow can be described as follows:
2880
2881\subsection{Manually Created Files}
2882
2883\begin{tabular}{ll}
2884ASC, PRJ & Digital elevation models (gridded)\\
2885NC & Model outputs for use as boundary conditions (e.g. from MOST)
2886\end{tabular}
2887
2888\subsection{Automatically Created Files}
2889
2890\begin{tabular}{ll}
2891ASC, PRJ  $\rightarrow$  DEM  $\rightarrow$  PTS & Convert
2892DEMs to native \code{.pts} file\\
2893
2894NC $\rightarrow$ SWW & Convert MOST boundary files to
2895boundary \code{.sww}\\
2896
2897PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\
2898
2899TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using
2900\code{animate}\\
2901
2902TSH + Boundary SWW $\rightarrow$ SWW & Simulation using
2903\code{\anuga}\\
2904
2905Polygonal mesh outline $\rightarrow$ & TSH or MSH
2906\end{tabular}
2907
2908
2909
2910
2911\bigskip
2912
2913\subsection{SWW and TMS Formats}
2914\label{sec:sww format}
2915
2916The SWW and TMS formats are both NetCDF formats, and are of key
2917importance for \anuga.
2918
2919An SWW file is used for storing \anuga output and therefore pertains
2920to a set of points and a set of times at which a model is evaluated.
2921It contains, in addition to dimension information, the following
2922variables:
2923
2924\begin{itemize}
2925    \item \code{x} and \code{y}: coordinates of the points, represented as Numeric arrays
2926    \item \code{elevation}, a Numeric array storing bed-elevations
2927    \item \code{volumes}, a list specifying the points at the vertices of each of the
2928    triangles
2929    % Refer here to the example to be provided in describing the simple example
2930    \item \code{time}, a Numeric array containing times for model
2931    evaluation
2932\end{itemize}
2933
2934
2935The contents of an SWW file may be viewed using the anuga viewer
2936\code{animate}, which creates an on-screen geometric
2937representation. See section \ref{sec:animate} (page
2938\pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more
2939on \code{animate}.
2940
2941Alternatively, there are tools, such as \code{ncdump}, that allow
2942you to convert an NetCDF file into a readable format such as the
2943Class Definition Language (CDL). The following is an excerpt from a
2944CDL representation of the output file \file{runup.sww} generated
2945from running the simple example \file{runup.py} of
2946Chapter \ref{ch:getstarted}:
2947
2948\verbatiminput{examples/bedslopeexcerpt.cdl}
2949
2950The SWW format is used not only for output but also serves as input
2951for functions such as \function{file\_boundary} and
2952\function{file\_function}, described in Chapter \ref{ch:interface}.
2953
2954A TMS file is used to store time series data that is independent of
2955position.
2956
2957
2958\subsection{Mesh File Formats}
2959
2960A mesh file is a file that has a specific format suited to
2961triangular meshes and their outlines. A mesh file can have one of
2962two formats: it can be either a TSH file, which is an ASCII file, or
2963an MSH file, which is a NetCDF file. A mesh file can be generated
2964from the function \function{create\_mesh\_from\_regions} (see
2965Section \ref{sec:meshgeneration}) and used to initialise a domain.
2966
2967A mesh file can define the outline of the mesh---the vertices and
2968line segments that enclose the region in which the mesh is
2969created---and the triangular mesh itself, which is specified by
2970listing the triangles and their vertices, and the segments, which
2971are those sides of the triangles that are associated with boundary
2972conditions.
2973
2974In addition, a mesh file may contain `holes' and/or `regions'. A
2975hole represents an area where no mesh is to be created, while a
2976region is a labelled area used for defining properties of a mesh,
2977such as friction values.  A hole or region is specified by a point
2978and bounded by a number of segments that enclose that point.
2979
2980A mesh file can also contain a georeference, which describes an
2981offset to be applied to $x$ and $y$ values---eg to the vertices.
2982
2983
2984\subsection{Formats for Storing Arbitrary Points and Attributes}
2985
2986
2987A CSV/TXT file is used to store data representing
2988arbitrary numerical attributes associated with a set of points.
2989
2990The format for an CSV/TXT file is:\\
2991%\begin{verbatim}
2992
2993            first line:     \code{[column names]}\\
2994            other lines:  \code{[x value], [y value], [attributes]}\\
2995
2996            for example:\\
2997            \code{x, y, elevation, friction}\\
2998            \code{0.6, 0.7, 4.9, 0.3}\\
2999            \code{1.9, 2.8, 5, 0.3}\\
3000            \code{2.7, 2.4, 5.2, 0.3}
3001
3002        The delimiter is a comma. The first two columns are assumed to
3003        be x, y coordinates.
3004       
3005
3006A PTS file is a NetCDF representation of the data held in an points CSV
3007file. If the data is associated with a set of $N$ points, then the
3008data is stored using an $N \times 2$ Numeric array of float
3009variables for the points and an $N \times 1$ Numeric array for each
3010attribute.
3011
3012%\end{verbatim}
3013
3014\subsection{ArcView Formats}
3015
3016Files of the three formats ASC, PRJ and ERS are all associated with
3017data from ArcView.
3018
3019An ASC file is an ASCII representation of DEM output from ArcView.
3020It contains a header with the following format:
3021
3022\begin{tabular}{l l}
3023\code{ncols}      &   \code{753}\\
3024\code{nrows}      &   \code{766}\\
3025\code{xllcorner}  &   \code{314036.58727982}\\
3026\code{yllcorner}  & \code{6224951.2960092}\\
3027\code{cellsize}   & \code{100}\\
3028\code{NODATA_value} & \code{-9999}
3029\end{tabular}
3030
3031The remainder of the file contains the elevation data for each grid point
3032in the grid defined by the above information.
3033
3034A PRJ file is an ArcView file used in conjunction with an ASC file
3035to represent metadata for a DEM.
3036
3037
3038\subsection{DEM Format}
3039
3040A DEM file is a NetCDF representation of regular DEM data.
3041
3042
3043\subsection{Other Formats}
3044
3045
3046
3047
3048\subsection{Basic File Conversions}
3049\label{sec:basicfileconversions}
3050
3051  \begin{funcdesc}{sww2dem}{basename_in, basename_out = None,
3052            quantity = None,
3053            timestep = None,
3054            reduction = None,
3055            cellsize = 10,
3056            NODATA_value = -9999,
3057            easting_min = None,
3058            easting_max = None,
3059            northing_min = None,
3060            northing_max = None,
3061            expand_search = False,
3062            verbose = False,
3063            origin = None,
3064            datum = 'WGS84',
3065            format = 'ers'}
3066  Module: \module{shallow\_water.data\_manager}
3067
3068  Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or
3069  ERS) of a desired grid size \code{cellsize} in metres.
3070  The easting and northing values are used if the user wished to clip the output
3071  file to a specified rectangular area. The \code{reduction} input refers to a function
3072  to reduce the quantities over all time step of the SWW file, example, maximum.
3073  \end{funcdesc}
3074
3075
3076  \begin{funcdesc}{dem2pts}{basename_in, basename_out=None,
3077            easting_min=None, easting_max=None,
3078            northing_min=None, northing_max=None,
3079            use_cache=False, verbose=False}
3080  Module: \module{shallow\_water.data\_manager}
3081
3082  Takes DEM data (a NetCDF file representation of data from a regular Digital
3083  Elevation Model) and converts it to PTS format.
3084  \end{funcdesc}
3085
3086
3087
3088%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3089%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3090
3091\chapter{\anuga mathematical background}
3092\label{cd:mathematical background}
3093
3094\section{Introduction}
3095
3096This chapter outlines the mathematics underpinning \anuga.
3097
3098
3099
3100\section{Model}
3101\label{sec:model}
3102
3103The shallow water wave equations are a system of differential
3104conservation equations which describe the flow of a thin layer of
3105fluid over terrain. The form of the equations are:
3106\[
3107\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
3108x}+\frac{\partial \GG}{\partial y}=\SSS
3109\]
3110where $\UU=\left[ {{\begin{array}{*{20}c}
3111 h & {uh} & {vh} \\
3112\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
3113$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
3114entering the system are bed elevation $z$ and stage (absolute water
3115level) $w$, where the relation $w = z + h$ holds true at all times.
3116The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
3117by
3118\[
3119\EE=\left[ {{\begin{array}{*{20}c}
3120 {uh} \hfill \\
3121 {u^2h+gh^2/2} \hfill \\
3122 {uvh} \hfill \\
3123\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
3124 {vh} \hfill \\
3125 {vuh} \hfill \\
3126 {v^2h+gh^2/2} \hfill \\
3127\end{array} }} \right]
3128\]
3129and the source term (which includes gravity and friction) is given
3130by
3131\[
3132\SSS=\left[ {{\begin{array}{*{20}c}
3133 0 \hfill \\
3134 -{gh(z_{x} + S_{fx} )} \hfill \\
3135 -{gh(z_{y} + S_{fy} )} \hfill \\
3136\end{array} }} \right]
3137\]
3138where $S_f$ is the bed friction. The friction term is modelled using
3139Manning's resistance law
3140\[
3141S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
3142=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
3143\]
3144in which $\eta$ is the Manning resistance coefficient.
3145
3146As demonstrated in our papers, \cite{ZR1999,nielsen2005} these
3147equations provide an excellent model of flows associated with
3148inundation such as dam breaks and tsunamis.
3149
3150\section{Finite Volume Method}
3151\label{sec:fvm}
3152
3153We use a finite-volume method for solving the shallow water wave
3154equations \cite{ZR1999}. The study area is represented by a mesh of
3155triangular cells as in Figure~\ref{fig:mesh} in which the conserved
3156quantities of  water depth $h$, and horizontal momentum $(uh, vh)$,
3157in each volume are to be determined. The size of the triangles may
3158be varied within the mesh to allow greater resolution in regions of
3159particular interest.
3160
3161\begin{figure}
3162\begin{center}
3163\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five}
3164\caption{Triangular mesh used in our finite volume method. Conserved
3165quantities $h$, $uh$ and $vh$ are associated with the centroid of
3166each triangular cell.} \label{fig:mesh}
3167\end{center}
3168\end{figure}
3169
3170The equations constituting the finite-volume method are obtained by
3171integrating the differential conservation equations over each
3172triangular cell of the mesh. Introducing some notation we use $i$ to
3173refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the
3174set of indices referring to the cells neighbouring the $i$th cell.
3175Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is
3176the length of the edge between the $i$th and $j$th cells.
3177
3178By applying the divergence theorem we obtain for each volume an
3179equation which describes the rate of change of the average of the
3180conserved quantities within each cell, in terms of the fluxes across
3181the edges of the cells and the effect of the source terms. In
3182particular, rate equations associated with each cell have the form
3183$$
3184 \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i
3185$$
3186where
3187\begin{itemize}
3188\item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell,
3189\item $\SSS_i$ is the source term associated with the $i$th cell,
3190and
3191\item $\HH_{ij}$ is the outward normal flux of
3192material across the \textit{ij}th edge.
3193\end{itemize}
3194
3195
3196%\item $l_{ij}$ is the length of the edge between the $i$th and $j$th
3197%cells
3198%\item $m_{ij}$ is the midpoint of
3199%the \textit{ij}th edge,
3200%\item
3201%$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing
3202%normal along the \textit{ij}th edge, and The
3203
3204The flux $\HH_{ij}$ is evaluated using a numerical flux function
3205$\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow
3206water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$
3207$$
3208H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 .
3209$$
3210
3211Then
3212$$
3213\HH_{ij}  = \HH(\UU_i(m_{ij}),
3214\UU_j(m_{ij}); \mathbf{n}_{ij})
3215$$
3216where $m_{ij}$ is the midpoint of the \textit{ij}th edge and
3217$\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the
3218\textit{ij}th edge. The function $\UU_i(x)$ for $x \in
3219T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and
3220neighbouring  cells.
3221
3222We use a second order reconstruction to produce a piece-wise linear
3223function construction of the conserved quantities for  all $x \in
3224T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This
3225function is allowed to be discontinuous across the edges of the
3226cells, but the slope of this function is limited to avoid
3227artificially introduced oscillations.
3228
3229Godunov's method (see \cite{Toro1992}) involves calculating the
3230numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly
3231solving the corresponding one dimensional Riemann problem normal to
3232the edge. We use the central-upwind scheme of \cite{KurNP2001} to
3233calculate an approximation of the flux across each edge.
3234
3235\begin{figure}
3236\begin{center}
3237\includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct}
3238\caption{From the values of the conserved quantities at the centroid
3239of the cell and its neighbouring cells, a discontinuous piecewise
3240linear reconstruction of the conserved quantities is obtained.}
3241\label{fig:mesh:reconstruct}
3242\end{center}
3243\end{figure}
3244
3245In the computations presented in this paper we use an explicit Euler
3246time stepping method with variable timestepping adapted to the
3247observed CFL condition.
3248
3249
3250\section{Flux limiting}
3251
3252The shallow water equations are solved numerically using a
3253finite volume method on unstructured triangular grid.
3254The upwind central scheme due to Kurganov and Petrova is used as an
3255approximate Riemann solver for the computation of inviscid flux functions.
3256This makes it possible to handle discontinuous solutions.
3257
3258To alleviate the problems associated with numerical instabilities due to
3259small water depths near a wet/dry boundary we employ a new flux limiter that
3260ensures that unphysical fluxes are never encounted.
3261
3262
3263Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction,
3264$w$ the absolute water level (stage) and
3265$z$ the bed elevation. The latter are assumed to be relative to the
3266same height datum.
3267The conserved quantities tracked by ANUGA are momentum in the
3268$x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$)
3269and depth ($h = w-z$).
3270
3271The flux calculation requires access to the velocity vector $(u, v)$
3272where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively.
3273In the presence of very small water depths, these calculations become
3274numerically unreliable and will typically cause unphysical speeds.
3275
3276We have employed a flux limiter which replaces the calculations above with
3277the limited approximations.
3278\begin{equation}
3279  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
3280\end{equation}
3281where $h_0$ is a regularisation parameter that controls the minimal
3282magnitude of the denominator. Taking the limits we have for $\hat{u}$
3283\[
3284  \lim_{h \rightarrow 0} \hat{u} =
3285  \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0
3286\]
3287and
3288\[
3289  \lim_{h \rightarrow \infty} \hat{u} =
3290  \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u
3291\]
3292with similar results for $\hat{v}$.
3293
3294The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator)
3295\[
3296  1 - h_0/h^2 = 0
3297\]
3298or
3299\[
3300  h_0 = h^2
3301\]
3302
3303
3304ANUGA has a global parameter $H_0$ that controls the minimal depth which
3305is considered in the various equations. This parameter is typically set to
3306$10^{-3}$. Setting
3307\[
3308  h_0 = H_0^2
3309\]
3310provides a reasonable balance between accurracy and stability. In fact,
3311setting $h=H_0$ will scale the predicted speed by a factor of $0.5$:
3312\[
3313  \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \frac{\mu}{2 H_0}
3314\]
3315In general, for multiples of the minimal depth $N H_0$ one obtains
3316\[
3317  \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
3318  \frac{\mu}{H_0 (1 + 1/N^2)}
3319\]
3320which converges quadratically to the true value with the multiple N.
3321
3322
3323%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.
3324
3325
3326
3327
3328
3329\section{Slope limiting}
3330A 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.
3331
3332However 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.
3333
3334
3335Let $w, z, h$  be the stage, bed elevation and depth at the centroid and
3336let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$.
3337Define the minimal depth across all vertices as $\hmin$ as
3338\[
3339  \hmin = \min_i h_i
3340\]
3341
3342Let $\tilde{w_i}$ be the stage obtained from a gradient limiter
3343limiting on stage only. The corresponding depth is then defined as
3344\[
3345  \tilde{h_i} = \tilde{w_i} - z_i
3346\]
3347We would use this limiter in deep water which we will define (somewhat boldly)
3348as
3349\[
3350  \hmin \ge \epsilon
3351\]
3352
3353
3354Similarly, let $\bar{w_i}$ be the stage obtained from a gradient
3355limiter limiting on depth respecting the bed slope.
3356The corresponding depth is defined as
3357\[
3358  \bar{h_i} = \bar{w_i} - z_i
3359\]
3360
3361
3362We introduce the concept of a balanced stage $w_i$ which is obtained as
3363the linear combination
3364
3365\[
3366  w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i}
3367\]
3368or
3369\[
3370  w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i}
3371\]
3372where $\alpha \in [0, 1]$.
3373
3374Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope
3375is ignored we have immediately that
3376\[
3377  \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0
3378\]
3379%where the maximal bed elevation range $dz$ is defined as
3380%\[
3381%  dz = \max_i |z_i - z|
3382%\]
3383
3384If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that
3385no negative depths occur. Formally, we will require that
3386\[
3387  \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i
3388\]
3389or
3390\begin{equation}
3391  \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i
3392  \label{eq:limiter bound}
3393\end{equation}
3394
3395There are two cases:
3396\begin{enumerate}
3397  \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage)
3398  vertex is at least as far away from the bed than the shallow water
3399  (limited using depth). In this case we won't need any contribution from
3400  $\bar{h_i}$ and can accept any $\alpha$.
3401
3402  E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to
3403  \[
3404    \tilde{h_i} > \epsilon
3405  \]
3406  whereas $\alpha=0$ yields
3407  \[
3408    \bar{h_i} > \epsilon
3409  \]
3410  all well and good.
3411  \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is
3412  closer to the bed than the shallow water vertex or even below the bed.
3413  In this case we need to find an $\alpha$ that will ensure a positive depth.
3414  Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one
3415  obtains the bound
3416  \[
3417    \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i
3418  \]
3419\end{enumerate}
3420
3421Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one
3422arrives at the definition
3423\[
3424  \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}}
3425\]
3426which will guarantee that no vertex 'cuts' through the bed. Finally, should
3427$\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting
3428$\alpha=0$ and similarly capping $\alpha$ at 1 just in case.
3429
3430%Furthermore,
3431%dropping the $\epsilon$ ensures that alpha is always positive and also
3432%provides a numerical safety {??)
3433
3434
3435
3436
3437
3438%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3439%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3440
3441\chapter{Basic \anuga Assumptions}
3442
3443
3444Physical model time cannot be earlier than 1 Jan 1970 00:00:00.
3445If one wished to recreate scenarios prior to that date it must be done
3446using some relative time (e.g. 0).
3447
3448
3449All spatial data relates to the WGS84 datum (or GDA94) and has been
3450projected into UTM with false easting of 500000 and false northing of
34511000000 on the southern hemisphere (0 on the northern).
3452
3453It is assumed that all computations take place within one UTM zone and
3454all locations must consequently be specified in Cartesian coordinates
3455(eastings, northings) or (x,y) where the unit is metres.
3456
3457DEMs, meshes and boundary conditions can have different origins within
3458one UTM zone. However, the computation will use that of the mesh for
3459numerical stability.
3460
3461When generating a mesh it is assumed that polygons do not cross.
3462Having polygons tht cross can cause the mesh generation to fail or bad
3463meshes being produced.
3464
3465
3466%OLD
3467%The dataflow is: (See data_manager.py and from scenarios)
3468%
3469%
3470%Simulation scenarios
3471%--------------------%
3472%%
3473%
3474%Sub directories contain scrips and derived files for each simulation.
3475%The directory ../source_data contains large source files such as
3476%DEMs provided externally as well as MOST tsunami simulations to be used
3477%as boundary conditions.
3478%
3479%Manual steps are:
3480%  Creation of DEMs from argcview (.asc + .prj)
3481%  Creation of mesh from pmesh (.tsh)
3482%  Creation of tsunami simulations from MOST (.nc)
3483%%
3484%
3485%Typical scripted steps are%
3486%
3487%  prepare_dem.py:  Convert asc and prj files supplied by arcview to
3488%                   native dem and pts formats%
3489%
3490%  prepare_pts.py: Convert netcdf output from MOST to an sww file suitable
3491%                  as boundary condition%
3492%
3493%  prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares
3494%                   smoothing. The outputs are tsh files with elevation data.%
3495%
3496%  run_simulation.py: Use the above together with various parameters to
3497%                     run inundation simulation.
3498
3499
3500%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3501%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3502
3503\appendix
3504
3505\chapter{Supporting Tools}
3506\label{ch:supportingtools}
3507
3508This section describes a number of supporting tools, supplied with \anuga, that offer a
3509variety of types of functionality and enhance the basic capabilities of \anuga.
3510
3511\section{caching}
3512\label{sec:caching}
3513
3514The \code{cache} function is used to provide supervised caching of function
3515results. A Python function call of the form
3516
3517      {\small \begin{verbatim}
3518      result = func(arg1,...,argn)
3519      \end{verbatim}}
3520
3521  can be replaced by
3522
3523      {\small \begin{verbatim}
3524      from caching import cache
3525      result = cache(func,(arg1,...,argn))
3526      \end{verbatim}}
3527
3528  which returns the same output but reuses cached
3529  results if the function has been computed previously in the same context.
3530  \code{result} and the arguments can be simple types, tuples, list, dictionaries or
3531  objects, but not unhashable types such as functions or open file objects.
3532  The function \code{func} may be a member function of an object or a module.
3533
3534  This type of caching is particularly useful for computationally intensive
3535  functions with few frequently used combinations of input arguments. Note that
3536  if the inputs or output are very large caching may not save time because
3537  disc access may dominate the execution time.
3538
3539  If the function definition changes after a result has been cached, this will be
3540  detected by examining the functions \code{bytecode (co\_code, co\_consts,
3541  func\_defaults, co\_argcount)} and the function will be recomputed.
3542  However, caching will not detect changes in modules used by \code{func}.
3543  In this case cache must be cleared manually.
3544
3545  Options are set by means of the function \code{set\_option(key, value)},
3546  where \code{key} is a key associated with a
3547  Python dictionary \code{options}. This dictionary stores settings such as the name of
3548  the directory used, the maximum
3549  number of cached files allowed, and so on.
3550
3551  The \code{cache} function allows the user also to specify a list of dependent files. If any of these
3552  have been changed, the function is recomputed and the results stored again.
3553
3554  %Other features include support for compression and a capability to \ldots
3555
3556
3557   \textbf{USAGE:} \nopagebreak
3558
3559    {\small \begin{verbatim}
3560    result = cache(func, args, kwargs, dependencies, cachedir, verbose,
3561                   compression, evaluate, test, return_filename)
3562    \end{verbatim}}
3563
3564
3565\section{ANUGA viewer - animate}
3566\label{sec:animate}
3567 The output generated by \anuga may be viewed by
3568means of the visualisation tool \code{animate}, which takes the
3569\code{SWW} file output by \anuga and creates a visual representation
3570of the data. Examples may be seen in Figures \ref{fig:runupstart}
3571and \ref{fig:runup2}. To view an \code{SWW} file with
3572\code{animate} in the Windows environment, you can simply drag the
3573icon representing the file over an icon on the desktop for the
3574\code{animate} executable file (or a shortcut to it), or set up a
3575file association to make files with the extension \code{.sww} open
3576with \code{animate}. Alternatively, you can operate \code{animate}
3577from the command line, in both Windows and Linux environments.
3578
3579On successful operation, you will see an interactive moving-picture
3580display. You can use keys and the mouse to slow down, speed up or
3581stop the display, change the viewing position or carry out a number
3582of other simple operations. Help is also displayed when you press
3583the \code{h} key.
3584
3585The main keys operating the interactive screen are:\\
3586
3587\begin{center}
3588\begin{tabular}{|ll|}   \hline
3589
3590\code{w} & toggle wireframe \\
3591
3592space bar & start/stop\\
3593
3594up/down arrows & increase/decrease speed\\
3595
3596left/right arrows & direction in time \emph{(when running)}\\
3597& step through simulation \emph{(when stopped)}\\
3598
3599left mouse button & rotate\\
3600
3601middle mouse button & pan\\
3602
3603right mouse button & zoom\\  \hline
3604
3605\end{tabular}
3606\end{center}
3607
3608\vfill
3609
3610The following table describes how to operate animate from the command line:
3611
3612Usage: \code{animate [options] swwfile \ldots}\\  \nopagebreak
3613Options:\\  \nopagebreak
3614\begin{tabular}{ll}
3615  \code{--display <type>} & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\
3616                                    & \code{HEAD\_MOUNTED\_DISPLAY}\\
3617  \code{--rgba} & Request a RGBA colour buffer visual\\
3618  \code{--stencil} & Request a stencil buffer visual\\
3619  \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\
3620                                    & overridden by environmental variable\\
3621  \code{--stereo <mode>} & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\
3622                                    & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\
3623                                     & \code{ON | OFF} \\
3624  \code{-alphamax <float 0-1>} & Maximum transparency clamp value\\
3625  \code{-alphamin <float 0-1>} & Transparency value at \code{hmin}\\
3626\end{tabular}
3627
3628\begin{tabular}{ll}
3629  \code{-cullangle <float angle 0-90>} & Cull triangles steeper than this value\\
3630  \code{-help} & Display this information\\
3631  \code{-hmax <float>} & Height above which transparency is set to
3632                                     \code{alphamax}\\
3633\end{tabular}
3634
3635\begin{tabular}{ll}
3636
3637  \code{-hmin <float>} & Height below which transparency is set to
3638                                     zero\\
3639\end{tabular}
3640
3641\begin{tabular}{ll}
3642  \code{-lightpos <float>,<float>,<float>} & $x,y,z$ of bedslope directional light ($z$ is
3643                                     up, default is overhead)\\
3644\end{tabular}
3645
3646\begin{tabular}{ll}
3647  \code{-loop}  & Repeated (looped) playback of \code{.swm} files\\
3648
3649\end{tabular}
3650
3651\begin{tabular}{ll}
3652  \code{-movie <dirname>} & Save numbered images to named directory and
3653                                     quit\\
3654
3655  \code{-nosky} & Omit background sky\\
3656
3657
3658  \code{-scale <float>} & Vertical scale factor\\
3659  \code{-texture <file>} & Image to use for bedslope topography\\
3660  \code{-tps <rate>} & Timesteps per second\\
3661  \code{-version} & Revision number and creation (not compile)
3662                                     date\\
3663\end{tabular}
3664
3665\section{utilities/polygons}
3666
3667  \declaremodule{standard}{utilities.polygon}
3668  \refmodindex{utilities.polygon}
3669
3670  \begin{classdesc}{Polygon\_function}{regions, default=0.0, geo_reference=None}
3671  Module: \code{utilities.polygon}
3672
3673  Creates a callable object that returns one of a specified list of values when
3674  evaluated at a point \code{x, y}, depending on which polygon, from a specified list of polygons, the
3675  point belongs to. The parameter \code{regions} is a list of pairs
3676  \code{(P, v)}, where each \code{P} is a polygon and each \code{v}
3677  is either a constant value or a function of coordinates \code{x}
3678  and \code{y}, specifying the return value for a point inside \code{P}. The
3679  optional parameter \code{default} may be used to specify a value
3680  (or a function)
3681  for a point not lying inside any of the specified polygons. When a
3682  point lies in more than one polygon, the return value is taken to
3683  be the value for whichever of these polygon appears later in the
3684  list.
3685  %FIXME (Howard): CAN x, y BE VECTORS?
3686  The optional parameter geo\_reference refers to the status of points
3687  that are passed into the function. Typically they will be relative to
3688  some origin. In ANUGA, a typical call will take the form:
3689  {\small \begin{verbatim}
3690     set_quantity('elevation',
3691                  Polygon_function([(P1, v1), (P2, v2)],
3692                                   default=v3,
3693                                   geo_reference=domain.geo_reference))
3694  \end{verbatim}}
3695 
3696
3697  \end{classdesc}
3698
3699  \begin{funcdesc}{read\_polygon}{filename}
3700  Module: \code{utilities.polygon}
3701
3702  Reads the specified file and returns a polygon. Each
3703  line of the file must contain exactly two numbers, separated by a comma, which are interpreted
3704  as coordinates of one vertex of the polygon.
3705  \end{funcdesc}
3706
3707  \begin{funcdesc}{populate\_polygon}{polygon, number_of_points, seed = None, exclude = None}
3708  Module: \code{utilities.polygon}
3709
3710  Populates the interior of the specified polygon with the specified number of points,
3711  selected by means of a uniform distribution function.
3712  \end{funcdesc}
3713
3714  \begin{funcdesc}{point\_in\_polygon}{polygon, delta=1e-8}
3715  Module: \code{utilities.polygon}
3716
3717  Returns a point inside the specified polygon and close to the edge. The distance between
3718  the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the
3719  second argument \code{delta}, which is taken as $10^{-8}$ by default.
3720  \end{funcdesc}
3721
3722  \begin{funcdesc}{inside\_polygon}{points, polygon, closed = True, verbose = False}
3723  Module: \code{utilities.polygon}
3724
3725  Used to test whether the members of a list of points
3726  are inside the specified polygon. Returns a Numeric
3727  array comprising the indices of the points in the list that lie inside the polygon.
3728  (If none of the points are inside, returns \code{zeros((0,), 'l')}.)
3729  Points on the edges of the polygon are regarded as inside if
3730  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3731  \end{funcdesc}
3732
3733  \begin{funcdesc}{outside\_polygon}{points, polygon, closed = True, verbose = False}
3734  Module: \code{utilities.polygon}
3735
3736  Exactly like \code{inside\_polygon}, but with the words `inside' and `outside' interchanged.
3737  \end{funcdesc}
3738
3739  \begin{funcdesc}{is\_inside\_polygon}{point, polygon, closed=True, verbose=False}
3740  Module: \code{utilities.polygon}
3741
3742  Returns \code{True} if \code{point} is inside \code{polygon} or
3743  \code{False} otherwise. Points on the edges of the polygon are regarded as inside if
3744  \code{closed} is set to \code{True} or omitted; otherwise they are regarded as outside.
3745  \end{funcdesc}
3746
3747  \begin{funcdesc}{is\_outside\_polygon}{point, polygon, closed=True, verbose=False}
3748  Module: \code{utilities.polygon}
3749
3750  Exactly like \code{is\_outside\_polygon}, but with the words `inside' and `outside' interchanged.
3751  \end{funcdesc}
3752
3753  \begin{funcdesc}{point\_on\_line}{x, y, x0, y0, x1, y1}
3754  Module: \code{utilities.polygon}
3755
3756  Returns \code{True} or \code{False}, depending on whether the point with coordinates
3757  \code{x, y} is on the line passing through the points with coordinates \code{x0, y0}
3758  and \code{x1, y1} (extended if necessary at either end).
3759  \end{funcdesc}
3760
3761  \begin{funcdesc}{separate\_points\_by\_polygon}{points, polygon, closed = True, verbose = False}
3762    \indexedcode{separate\_points\_by\_polygon}
3763  Module: \code{utilities.polygon}
3764
3765  \end{funcdesc}
3766
3767  \begin{funcdesc}{polygon\_area}{polygon}
3768  Module: \code{utilities.polygon}
3769
3770  Returns area of arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html)
3771  \end{funcdesc}
3772
3773  \begin{funcdesc}{plot\_polygons}{polygons, style, figname, verbose = False}
3774    Module: \code{utilities.polygon}
3775 
3776    Plots each polygon contained in input polygon list, e.g.
3777   \code{polygons = [poly1, poly2, poly3]} where \code{poly1 = [[x11,y11],[x12,y12],[x13,y13]]}
3778   etc.  Each polygon can be closed for plotting purposes by assigning the style type to each
3779   polygon in the list, e.g. \code{style = ['line','line','line']}. The default will be a line
3780   type when \code{style = None}.
3781   The subsequent plot will be saved to \code{figname} or defaulted to \code{test_image.png}.
3782    The function returns a list containing the minimum and maximum of \code{x} and \code{y},
3783    i.e. \code{[x_{min}, x_{max}, y_{min}, y_{max}]}.
3784  \end{funcdesc}
3785
3786\section{coordinate\_transforms}
3787
3788\section{geospatial\_data}
3789\label{sec:geospatial}
3790
3791This describes a class that represents arbitrary point data in UTM
3792coordinates along with named attribute values.
3793
3794%FIXME (Ole): This gives a LaTeX error
3795%\declaremodule{standard}{geospatial_data}
3796%\refmodindex{geospatial_data}
3797
3798
3799
3800\begin{classdesc}{Geospatial\_data}
3801  {data_points = None,
3802    attributes = None,
3803    geo_reference = None,
3804    default_attribute_name = None,
3805    file_name = None}
3806Module: \code{geospatial\_data}
3807
3808This class is used to store a set of data points and associated
3809attributes, allowing these to be manipulated by methods defined for
3810the class.
3811
3812The data points are specified either by reading them from a NetCDF
3813or CSV file, identified through the parameter \code{file\_name}, or
3814by providing their \code{x}- and \code{y}-coordinates in metres,
3815either as a sequence of 2-tuples of floats or as an $M \times 2$
3816Numeric array of floats, where $M$ is the number of points.
3817Coordinates are interpreted relative to the origin specified by the
3818object \code{geo\_reference}, which contains data indicating the UTM
3819zone, easting and northing. If \code{geo\_reference} is not
3820specified, a default is used.
3821
3822Attributes are specified through the parameter \code{attributes},
3823set either to a list or array of length $M$ or to a dictionary whose
3824keys are the attribute names and whose values are lists or arrays of
3825length $M$. One of the attributes may be specified as the default
3826attribute, by assigning its name to \code{default\_attribute\_name}.
3827If no value is specified, the default attribute is taken to be the
3828first one.
3829\end{classdesc}
3830
3831
3832\begin{methoddesc}{import\_points\_file}{delimiter = None, verbose = False}
3833
3834\end{methoddesc}
3835
3836
3837\begin{methoddesc}{export\_points\_file}{ofile, absolute=False}
3838
3839\end{methoddesc}
3840
3841
3842\begin{methoddesc}{get\_data\_points}{absolute = True, as\_lat\_long =
3843    False}
3844    If \code{as\_lat\_long} is\code{True} the point information
3845    returned will be in Latitudes and Longitudes.
3846
3847\end{methoddesc}
3848
3849
3850\begin{methoddesc}{set\_attributes}{attributes}
3851
3852\end{methoddesc}
3853
3854
3855\begin{methoddesc}{get\_attributes}{attribute_name = None}
3856
3857\end{methoddesc}
3858
3859
3860\begin{methoddesc}{get\_all\_attributes}{}
3861
3862\end{methoddesc}
3863
3864
3865\begin{methoddesc}{set\_default\_attribute\_name}{default_attribute_name}
3866
3867\end{methoddesc}
3868
3869
3870\begin{methoddesc}{set\_geo\_reference}{geo_reference}
3871
3872\end{methoddesc}
3873
3874
3875\begin{methoddesc}{add}{}
3876
3877\end{methoddesc}
3878
3879
3880\begin{methoddesc}{clip}{}
3881Clip geospatial data by a polygon
3882
3883Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3884a Geospatial data object and \code{closed}(optional) which determines
3885whether points on boundary should be regarded as belonging to the polygon
3886(\code{closed=True}) or not (\code{closed=False}).
3887Default is \code{closed=True}.
3888
3889Returns new Geospatial data object representing points
3890inside specified polygon.
3891\end{methoddesc}
3892
3893
3894\begin{methoddesc}{clip_outside}{}
3895Clip geospatial data by a polygon
3896
3897Inputs are \code{polygon} which is either a list of points, an Nx2 array or
3898a Geospatial data object and \code{closed}(optional) which determines
3899whether points on boundary should be regarded as belonging to the polygon
3900(\code{closed=True}) or not (\code{closed=False}).
3901Default is \code{closed=True}.
3902
3903Returns new Geospatial data object representing points
3904\emph{out}side specified polygon.
3905\end{methoddesc}
3906
3907\begin{methoddesc}{split}{factor=0.5, seed_num=None, verbose=False}
3908Returns two geospatial_data object, first is the size of the 'factor'
3909smaller the original and the second is the remainder. The two
3910new object are disjoin set of each other.
3911       
3912Points of the two new geospatial_data object are selected RANDOMLY.
3913       
3914Input - the (\code{factor}) which to split the object, if 0.1 then 10% of the
3915together object will be returned
3916       
3917Output - two geospatial_data objects that are disjoint sets of the original
3918\end{methoddesc}
3919
3920\begin{methoddesc}{find_optimal_smoothing_parameter}{data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000,
3921north_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}
3922
3923Removes a small random sample of points from 'data_file'. Creates
3924models from resulting points in 'data_file' with different alpha values from 'alpha_list' and cross validates
3925the predicted value to the previously removed point data. Returns the
3926alpha value which has the smallest covariance.
3927
3928data_file: must not contain points outside the boundaries defined
3929and it either a pts, txt or csv file.
3930   
3931alpha_list: the alpha values to test in a single list
3932   
3933mesh_file: name of the created mesh file or if passed in will read it.
3934NOTE, if there is a mesh file mesh_resolution, north_boundary, south... etc will be ignored.
3935   
3936mesh_resolution: the maximum area size for a triangle
3937   
3938north_boundary... west_boundary: the value of the boundary
3939   
3940plot_name: the name for the plot contain the results
3941   
3942seed_num: the seed to the random number generator
3943   
3944USAGE:
3945convariance_value, alpha = find_optimal_smoothing_parameter(data_file=fileName,
3946                                             alpha_list=[0.0001, 0.01, 1],
3947                                             mesh_file=None,
3948                                             mesh_resolution=3,
3949                                             north_boundary=5,
3950                                             south_boundary=-5,
3951                                             east_boundary=5,
3952                                             west_boundary=-5,
3953                                             plot_name='all_alphas',
3954                                             seed_num=100000,
3955                                             verbose=False)
3956   
3957OUTPUT: returns the minumum normalised covalance calculate AND the
3958alpha that created it. PLUS writes a plot of the results
3959           
3960NOTE: code will not work if the data_file extent is greater than the
3961boundary_polygon or any of the boundaries, eg north_boundary...west_boundary
3962\end{methoddesc}
3963
3964
3965
3966\section{Graphical Mesh Generator GUI}
3967The program \code{graphical\_mesh\_generator.py} in the pmesh module
3968allows the user to set up the mesh of the problem interactively.
3969It can be used to build the outline of a mesh or to visualise a mesh
3970automatically generated.
3971
3972Graphical Mesh Generator will let the user select various modes. The
3973current allowable modes are vertex, segment, hole or region.  The mode
3974describes what sort of object is added or selected in response to
3975mouse clicks.  When changing modes any prior selected objects become
3976deselected.
3977
3978In general the left mouse button will add an object and the right
3979mouse button will select an object.  A selected object can de deleted
3980by pressing the the middle mouse button (scroll bar).
3981
3982\section{alpha\_shape}
3983\emph{Alpha shapes} are used to generate close-fitting boundaries
3984around sets of points. The alpha shape algorithm produces a shape
3985that approximates to the `shape formed by the points'---or the shape
3986that would be seen by viewing the points from a coarse enough
3987resolution. For the simplest types of point sets, the alpha shape
3988reduces to the more precise notion of the convex hull. However, for
3989many sets of points the convex hull does not provide a close fit and
3990the alpha shape usually fits more closely to the original point set,
3991offering a better approximation to the shape being sought.
3992
3993In \anuga, an alpha shape is used to generate a polygonal boundary
3994around a set of points before mesh generation. The algorithm uses a
3995parameter $\alpha$ that can be adjusted to make the resultant shape
3996resemble the shape suggested by intuition more closely. An alpha
3997shape can serve as an initial boundary approximation that the user
3998can adjust as needed.
3999
4000The following paragraphs describe the class used to model an alpha
4001shape and some of the important methods and attributes associated
4002with instances of this class.
4003
4004\begin{classdesc}{Alpha\_Shape}{points, alpha = None}
4005Module: \code{alpha\_shape}
4006
4007To instantiate this class the user supplies the points from which
4008the alpha shape is to be created (in the form of a list of 2-tuples
4009\code{[[x1, y1],[x2, y2]}\ldots\code{]}, assigned to the parameter
4010\code{points}) and, optionally, a value for the parameter
4011\code{alpha}. The alpha shape is then computed and the user can then
4012retrieve details of the boundary through the attributes defined for
4013the class.
4014\end{classdesc}
4015
4016
4017\begin{funcdesc}{alpha\_shape\_via\_files}{point_file, boundary_file, alpha= None}
4018Module: \code{alpha\_shape}
4019
4020This function reads points from the specified point file
4021\code{point\_file}, computes the associated alpha shape (either
4022using the specified value for \code{alpha} or, if no value is
4023specified, automatically setting it to an optimal value) and outputs
4024the boundary to a file named \code{boundary\_file}. This output file
4025lists the coordinates \code{x, y} of each point in the boundary,
4026using one line per point.
4027\end{funcdesc}
4028
4029
4030\begin{methoddesc}{set\_boundary\_type}{self,raw_boundary=True,
4031                          remove_holes=False,
4032                          smooth_indents=False,
4033                          expand_pinch=False,
4034                          boundary_points_fraction=0.2}
4035Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4036
4037This function sets flags that govern the operation of the algorithm
4038that computes the boundary, as follows:
4039
4040\code{raw\_boundary = True} returns raw boundary, i.e. the regular edges of the
4041                alpha shape.\\
4042\code{remove\_holes = True} removes small holes (`small' is defined by
4043\code{boundary\_points\_fraction})\\
4044\code{smooth\_indents = True} removes sharp triangular indents in
4045boundary\\
4046\code{expand\_pinch = True} tests for pinch-off and
4047corrects---preventing a boundary vertex from having more than two edges.
4048\end{methoddesc}
4049
4050
4051\begin{methoddesc}{get\_boundary}{}
4052Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4053
4054Returns a list of tuples representing the boundary of the alpha
4055shape. Each tuple represents a segment in the boundary by providing
4056the indices of its two endpoints.
4057\end{methoddesc}
4058
4059
4060\begin{methoddesc}{write\_boundary}{file_name}
4061Module: \code{alpha\_shape},  Class: \class{Alpha\_Shape}
4062
4063Writes the list of 2-tuples returned by \code{get\_boundary} to the
4064file \code{file\_name}, using one line per tuple.
4065\end{methoddesc}
4066
4067\section{Numerical Tools}
4068
4069The following table describes some useful numerical functions that
4070may be found in the module \module{utilities.numerical\_tools}:
4071
4072\begin{tabular}{|p{8cm} p{8cm}|}  \hline
4073\code{angle(v1, v2=None)} & Angle between two-dimensional vectors
4074\code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if
4075\code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\
4076
4077\code{normal\_vector(v)} & Normal vector to \code{v}.\\
4078
4079\code{mean(x)} & Mean value of a vector \code{x}.\\
4080
4081\code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}.
4082If \code{y} is \code{None}, returns \code{cov(x, x)}.\\
4083
4084\code{err(x, y=0, n=2, relative=True)} & Relative error of
4085$\parallel$\code{x}$-$\code{y}$\parallel$ to
4086$\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm
4087if \code{n} = \code{None}). If denominator evaluates to zero or if
4088\code{y}
4089is omitted or if \code{relative = False}, absolute error is returned.\\
4090
4091\code{norm(x)} & 2-norm of \code{x}.\\
4092
4093\code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If
4094\code{y} is \code{None} returns autocorrelation of \code{x}.\\
4095
4096\code{ensure\_numeric(A, typecode = None)} & Returns a Numeric array
4097for any sequence \code{A}. If \code{A} is already a Numeric array it
4098will be returned unaltered. Otherwise, an attempt is made to convert
4099it to a Numeric array. (Needed because \code{array(A)} can
4100cause memory overflow.)\\
4101
4102\code{histogram(a, bins, relative=False)} & Standard histogram. If
4103\code{relative} is \code{True}, values will be normalised against
4104the total and thus represent frequencies rather than counts.\\
4105
4106\code{create\_bins(data, number\_of\_bins = None)} & Safely create
4107bins for use with histogram. If \code{data} contains only one point
4108or is constant, one bin will be created. If \code{number\_of\_bins}
4109is omitted, 10 bins will be created.\\  \hline
4110
4111\section{Finding the Optimal Alpha Value}
4112
4113The function ????
4114more to come very soon
4115
4116\end{tabular}
4117
4118
4119\chapter{Modules available in \anuga}
4120
4121
4122\section{\module{abstract\_2d\_finite\_volumes.general\_mesh} }
4123\declaremodule[generalmesh]{}{general\_mesh}
4124\label{mod:generalmesh}
4125
4126\section{\module{abstract\_2d\_finite\_volumes.neighbour\_mesh} }
4127\declaremodule[neighbourmesh]{}{neighbour\_mesh}
4128\label{mod:neighbourmesh}
4129
4130\section{\module{abstract\_2d\_finite\_volumes.domain} --- Generic module for 2D triangular domains for finite-volume computations of conservation laws}
4131\declaremodule{}{domain}
4132\label{mod:domain}
4133
4134
4135\section{\module{abstract\_2d\_finite\_volumes.quantity}}
4136\declaremodule{}{quantity}
4137\label{mod:quantity}
4138
4139\begin{verbatim}
4140Class Quantity - Implements values at each triangular element
4141
4142To create:
4143
4144   Quantity(domain, vertex_values)
4145
4146   domain: Associated domain structure. Required.
4147
4148   vertex_values: N x 3 array of values at each vertex for each element.
4149                  Default None
4150
4151   If vertex_values are None Create array of zeros compatible with domain.
4152   Otherwise check that it is compatible with dimenions of domain.
4153   Otherwise raise an exception
4154
4155\end{verbatim}
4156
4157
4158
4159
4160\section{\module{shallow\_water} --- 2D triangular domains for finite-volume
4161computations of the shallow water wave equation. This module contains a specialisation
4162of class Domain from module domain.py consisting of methods specific to the Shallow Water
4163Wave Equation
4164}
4165\declaremodule[shallowwater]{}{shallow\_water}
4166\label{mod:shallowwater}
4167
4168
4169
4170
4171%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4172
4173\chapter{Frequently Asked Questions}
4174
4175
4176\section{General Questions}
4177
4178\subsubsection{What is \anuga?}
4179It is a software package suitable for simulating 2D water flows in
4180complex geometries.
4181
4182\subsubsection{Why is it called \anuga?}
4183The software was developed in collaboration between the
4184Australian National University (ANU) and Geoscience Australia (GA).
4185
4186\subsubsection{How do I obtain a copy of \anuga?}
4187See \url{https://datamining.anu.edu.au/anuga} for all things ANUGA.
4188
4189%\subsubsection{What developments are expected for \anuga in the future?}
4190%This
4191
4192\subsubsection{Are there any published articles about \anuga that I can reference?}
4193See \url{https://datamining.anu.edu.au/anuga} for links.
4194
4195
4196\subsubsection{How do I find out what version of \anuga I am running?}
4197Use the following code snippet
4198\begin{verbatim}
4199from anuga.utilities.system_tools import get_revision_number
4200print get_revision_number()
4201\end{verbatim}
4202This should work both for installations from SourceForge as well as when working off the repository.
4203
4204
4205
4206
4207\section{Modelling Questions}
4208
4209\subsubsection{Which type of problems are \anuga good for?}
4210General 2D waterflows in complex geometries such as
4211dam breaks, flows amoung structurs, coastal inundation etc.
4212
4213\subsubsection{Which type of problems are beyond the scope of \anuga?}
4214See Chapter \ref{ch:limitations}.
4215
4216\subsubsection{Can I start the simulation at an arbitrary time?}
4217Yes, using \code{domain.set\_time()} you can specify an arbitrary
4218starting time. This is for example useful in conjunction with a
4219file\_boundary, which may start hours before anything hits the model
4220boundary. By assigning a later time for the model to start,
4221computational resources aren't wasted.
4222
4223\subsubsection{Can I change values for any quantity during the simulation?}
4224Yes, using \code{domain.set\_quantity()} inside the domain.evolve
4225loop you can change values of any quantity. This is for example
4226useful if you wish to let the system settle for a while before
4227assigning an initial condition. Another example would be changing
4228the values for elevation to model e.g. erosion.
4229
4230\subsubsection{Can I change boundary conditions during the simulation?}
4231Yes - see example on page \pageref{sec:change boundary code} in Section
4232\ref{sec:change boundary}.
4233
4234\subsubsection{How do I access model time during the simulation?}
4235The variable \code{t} in the evolve for loop is the model time.
4236For 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})
4237one would write something like
4238{\small \begin{verbatim}
4239    for t in domain.evolve(yieldstep = 0.2, duration = 40.0):
4240
4241        if Numeric.allclose(t, 15):
4242            print 'Changing boundary to outflow'
4243            domain.set_boundary({'right': Bo})
4244
4245\end{verbatim}}
4246The 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()}.
4247
4248
4249\subsubsection{Why does a file\_function return a list of numbers when evaluated?}
4250Currently, file\_function works by returning values for the conserved
4251quantities \code{stage}, \code{xmomentum} and \code{ymomentum} at a given point in time
4252and space as a triplet. To access e.g.\ \code{stage} one must specify element 0 of the
4253triplet returned by file\_function.
4254
4255\subsubsection{Which diagnostics are available to troubleshoot a simulation?}
4256
4257\subsubsection{How do I use a DEM in my simulation?}
4258You use \code{dem2pts} to convert your DEM to the required .pts format. This .pts file is then called
4259when setting the elevation data to the mesh in \code{domain.set_quantity}
4260
4261\subsubsection{What sort of DEM resolution should I use?}
4262Try and work with the \emph{best} you have available. Onshore DEMs
4263are typically available in 25m, 100m and 250m grids. Note, offshore
4264data is often sparse, or non-existent.
4265
4266\subsubsection{What sort of mesh resolution should I use?}
4267The 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,
4268if 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,
4269you need a fine mesh over regions where the DEM changes rapidly, and other areas of significant interest, such as the coast.
4270If 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.
4271
4272
4273\subsubsection{How do I tag interior polygons?}
4274At the moment create_mesh_from_regions does not allow interior
4275polygons with symbolic tags. If tags are needed, the interior
4276polygons must be created subsequently. For example, given a filename
4277of polygons representing solid walls (in Arc Ungenerate format) can
4278be tagged as such using the code snippet:
4279\begin{verbatim}
4280  # Create mesh outline with tags
4281  mesh = create_mesh_from_regions(bounding_polygon,
4282                                  boundary_tags=boundary_tags)
4283  # Add buildings outlines with tags set to 'wall'. This would typically
4284  # bind to a Reflective boundary
4285  mesh.import_ungenerate_file(buildings_filename, tag='wall')
4286
4287  # Generate and write mesh to file
4288  mesh.generate_mesh(maximum_triangle_area=max_area)
4289  mesh.export_mesh_file(mesh_filename)
4290\end{verbatim}
4291
4292Note that a mesh object is returned from \code{create_mesh_from_regions}
4293when file name is omitted.
4294
4295\subsubsection{How often should I store the output?}
4296This 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
4297to look in detail at the evolution, then you will need to balance your storage requirements and the duration of the simulation.
4298If 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
4299quantities on a mesh with approximately 300000 triangles on a 2 min interval for 5 hours will result in approximately 350Mb SWW file
4300(as for the \file{run\_sydney\_smf.py} example).
4301
4302\subsubsection{How can I set the friction in different areas in the domain?}
4303The model area will typically be estimating the water height and momentum over varying
4304topographies which will have different friction values. One way of assigning
4305different friction values is to create polygons (say \code{poly1, poly2 and poly3}) describing each
4306area and then set the corresponding friction values in the following way
4307
4308\code{domain.set_quantity('friction',Polygon_function([(poly1,f1),(poly2,f2),
4309(poly3,f3))]))}
4310
4311The values of \code{f1,f2} and \code{f3} could be constant or functions
4312as determined by the user.
4313
4314\subsubsection{How can I combine data sets?}
4315
4316A user may have access to a range of different resolution DEMs and raw data points (such
4317as beach profiles, spot heights, single or multi-beam data etc) and will need
4318to combine them to create an overall elevation data set.
4319
4320If there are multiple DEMs, say of 10m and 25m resolution, then the technique is similar to
4321that defined in the Cairns example described earlier, that is
4322
4323{\small \begin{verbatim}
4324convert_dem_from_ascii2netcdf(10m_dem_name, use_cache=True, verbose=True)
4325convert_dem_from_ascii2netcdf(25m_dem_name, use_cache=True, verbose=True)
4326\end{verbatim}}
4327followed by
4328{\small \begin{verbatim}
4329dem2pts(10m_dem_name, use_cache=True, verbose=True)
4330dem2pts(25m_dem_name, use_cache=True, verbose=True)
4331\end{verbatim}}
4332These data sets can now be combined by
4333{\small \begin{verbatim}
4334from anuga.geospatial_data.geospatial_data import *
4335G1 = Geospatial_data(file_name = 10m_dem_name + '.pts')
4336G2 = Geospatial_data(file_name = 25m_dem_name + '.pts')
4337G = G1 + G2
4338G.export_points_file(combined_dem_name + ‘.pts’)
4339\end{verbatim}}
4340this is the basic way of combining data sets, however, the user will need to
4341assess the boundaries of each data set and whether they overlap. For example, consider
4342if the 10m DEM is describing by \code{poly1} and the 25m DEM is described by \code{poly2}
4343with \code{poly1} completely enclosed in \code{poly2} as shown in Figure \ref{fig:polydata}
4344\begin{figure}[hbt]
4345  \centerline{\includegraphics{graphics/polyanddata.jpg}}
4346  \caption{Polygons describing the extent of the 10m and 25m DEM.}
4347  \label{fig:polydata}
4348\end{figure}
4349To combine the data sets, the geospatial addition is updated to
4350{\small \begin{verbatim}
4351G = G1 + G2.clip_outside(Geospatial_data(poly1))
4352\end{verbatim}}
4353For this example, we assume that \code{poly2} is the domain, otherwise an additional dataset
4354would be required for the remainder of the domain.
4355
4356This technique can be expanded to handle point data sets as well. In the case
4357of a bathymetry data set available in text format in an \code{.csv} file, then
4358the geospatial addition is updated to
4359{\small \begin{verbatim}
4360G3 = Geospatial_data(file_name = bathy_data_name + '.csv')
4361G = G1 + G2.clip_outside(Geospatial_data(poly1)) + G3
4362\end{verbatim}}
4363The \code{.csv} file has the data stored as \code{x,y,elevation} with the text \code{elevation}
4364on the first line.
4365
4366The coastline could be included
4367as part of the clipping polygon to separate the offshore and onshore datasets if required.
4368Assume that \code{poly1} crosses the coastline
4369In this case, two new polygons could be created out of \code{poly1} which uses the coastline
4370as the divider. As shown in Figure \ref{fig:polycoast}, \code{poly3} describes the
4371onshore data and \code{poly4} describes the offshore data.
4372\begin{figure}[hbt]
4373  \centerline{\includegraphics{graphics/polyanddata2.jpg}}
4374  \caption{Inclusion of new polygons separating the 10m DEM area into an
4375  onshore (poly3) and offshore (poly4) data set.}
4376  \label{fig:polycoast}
4377\end{figure}
4378Let's include the bathymetry
4379data described above, so to combine the datasets in this case,
4380{\small \begin{verbatim}
4381G = G1.clip(Geospatial_data(poly3)) + G2.clip_outside(Geospatial_data(poly1)) + G3
4382\end{verbatim}}
4383
4384Finally, to fit the elevation data to the mesh, the script is adjusted in this way
4385{\small \begin{verbatim}
4386    domain.set_quantity('elevation',
4387                        filename = combined_dem_name + '.pts',
4388                        use_cache = True,
4389                        verbose = True)
4390\end{verbatim}}
4391\subsection{Boundary Conditions}
4392
4393\subsubsection{How do I create a Dirichlet boundary condition?}
4394
4395A Dirichlet boundary condition sets a constant value for the
4396conserved quantities at the boundaries. A list containing
4397the constant values for stage, xmomentum and ymomentum is constructed
4398and used in the function call, e.g. \code{Dirichlet_boundary([0.2,0.,0.])}
4399
4400\subsubsection{How do I know which boundary tags are available?}
4401The method \code{domain.get\_boundary\_tags()} will return a list of
4402available tags for use with
4403\code{domain.set\_boundary\_condition()}.
4404
4405\subsubsection{What is the difference between file_boundary and field_boundary?}
4406The only difference is field_boundary will allow you to change the level of the stage height when you read in the boundary condition.
4407This is very useful when running different tide heights in the same area as you need only to convert
4408one boundary condition to a SWW file, ideally for tide height of 0 m (saving disk space). Then you can
4409use field_boundary to read this SWW file and change the stage height (tide) on the fly depending on the scenario.
4410
4411
4412
4413
4414\subsection{Analysing Results}
4415
4416\subsubsection{How do I easily plot "tide gauges" timeseries graphs from a SWW file?}
4417
4418There is two ways to do this.
4419
44201) Create csv files from the sww file using \code{anuga.abstract_2d_finite_volumes.util sww2csv_gauges}
4421and then use \code{anuga.abstract_2d_finite_volumes.util csv2timeseries_graphs} to
4422create the plots. This code is newer, has unit tests and might be easier to use. Read doc strings for more information and
4423review section 4.7 of this manual.
4424
4425Or
4426
44272) Use \code{anuga.abstract_2d_finite_volumes.util sww2timeseries} to do the whole thing
4428however this doesn't have a much control on the file name and plots. Plus there is no unit tests yet.
4429
4430Read the doc string for more information.
4431
4432\subsubsection{How do I extract elevation and other quantities from a SWW file?}
4433
4434The function \code{sww2dem} can extract any quantity, or expression using
4435quantities, from a SWW file as used in
4436the Cairns example described earlier. This function is used in \code{ExportResults.py}
4437in the Cairns demo folder where stage, absolute momentum, depth, speed and elevation
4438can be exported from the input sww file. Note that depth, absolute momentum and speed
4439are expressions and stage and elevation are quantities. In addition to extracting a particular
4440quantity or expression, the user can define a region to extract these values by
4441defining the minimum and maximum of both the easting and northing coordinates. The function
4442also calls for a grid resolution, or cell size, to extract these values at. It is
4443recommended to align this resolution with the mesh resolution in the desired region and to not
4444generate a fine grid where the model output cannot support that resolution.
4445
4446 
4447
4448\chapter{Glossary}
4449
4450\begin{tabular}{|lp{10cm}|c|}  \hline
4451%\begin{tabular}{|llll|}  \hline
4452    \emph{Term} & \emph{Definition} & \emph{Page}\\  \hline
4453
4454    \indexedbold{\anuga} & Name of software (joint development between ANU and
4455    GA) & \pageref{def:anuga}\\
4456
4457    \indexedbold{bathymetry} & offshore elevation &\\
4458
4459    \indexedbold{conserved quantity} & conserved (stage, x and y
4460    momentum) & \\
4461
4462%    \indexedbold{domain} & The domain of a function is the set of all input values to the
4463%    function.&\\
4464
4465    \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations,
4466sampled systematically at equally spaced intervals.& \\
4467
4468    \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation
4469 that specifies the values the solution is to take on the boundary of the
4470 domain. & \pageref{def:dirichlet boundary}\\
4471
4472    \indexedbold{edge} & A triangular cell within the computational mesh can be depicted
4473    as a set of vertices joined by lines (the edges). & \\
4474
4475    \indexedbold{elevation} & refers to bathymetry and topography &\\
4476
4477    \indexedbold{evolution} & integration of the shallow water wave equations
4478    over time &\\
4479
4480    \indexedbold{finite volume method} & The method evaluates the terms in the shallow water
4481    wave equation as fluxes at the surfaces of each finite volume. Because the
4482    flux entering a given volume is identical to that leaving the adjacent volume,
4483    these methods are conservative. Another advantage of the finite volume method is
4484    that it is easily formulated to allow for unstructured meshes. The method is used
4485    in many computational fluid dynamics packages. & \\
4486
4487    \indexedbold{forcing term} & &\\
4488
4489    \indexedbold{flux} & the amount of flow through the volume per unit
4490    time & \\
4491
4492    \indexedbold{grid} & Evenly spaced mesh & \\
4493
4494    \indexedbold{latitude} & The angular distance on a mericlear north and south of the
4495    equator, expressed in degrees and minutes. & \\
4496
4497    \indexedbold{longitude} & The angular distance east or west, between the meridian
4498    of a particular place on Earth and that of the Prime Meridian (located in Greenwich,
4499    England) expressed in degrees or time.& \\
4500
4501    \indexedbold{Manning friction coefficient} & &\\
4502
4503    \indexedbold{mesh} & Triangulation of domain &\\
4504
4505    \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\
4506
4507    \indexedbold{NetCDF} & &\\
4508
4509    \indexedbold{node} & A point at which edges meet & \\
4510
4511    \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance
4512    north from a north-south reference line, usually a meridian used as the axis of
4513    origin within a map zone or projection. Northing is a UTM (Universal Transverse
4514    Mercator) coordinate. & \\
4515
4516
4517    \indexedbold{points file} & A PTS or CSV file & \\  \hline
4518
4519    \end{tabular}
4520
4521    \begin{tabular}{|lp{10cm}|c|}  \hline
4522
4523    \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon
4524    either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$
4525    Numeric array, where $N$ is the number of points.
4526
4527    The unit square, for example, would be represented either as
4528    \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1],
4529    [0,1] )}.
4530
4531    NOTE: For details refer to the module \module{utilities/polygon.py}. &
4532    \\     \indexedbold{resolution} &  The maximal area of a triangular cell in a
4533    mesh & \\
4534
4535
4536    \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved
4537    quantities as those present in the neighbouring volume but reflected. Specific to the
4538    shallow water equation as it works with the momentum quantities assumed to be the
4539    second and third conserved quantities. & \pageref{def:reflective boundary}\\
4540
4541    \indexedbold{stage} & &\\
4542
4543%    \indexedbold{try this}
4544
4545    \indexedbold{animate} & visualisation tool used with \anuga &
4546    \pageref{sec:animate}\\
4547
4548    \indexedbold{time boundary} & Returns values for the conserved
4549quantities as a function of time. The user must specify
4550the domain to get access to the model time. & \pageref{def:time boundary}\\
4551
4552    \indexedbold{topography} & onshore elevation &\\
4553
4554    \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\
4555
4556    \indexedbold{vertex} & A point at which edges meet. & \\
4557
4558    \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say
4559    only \code{x} and \code{y} and NOT \code{z}) &\\
4560
4561    \indexedbold{ymomentum}  & conserved quantity & \\  \hline
4562
4563    \end{tabular}
4564
4565
4566%The \code{\e appendix} markup need not be repeated for additional
4567%appendices.
4568
4569
4570%
4571%  The ugly "%begin{latexonly}" pseudo-environments are really just to
4572%  keep LaTeX2HTML quiet during the \renewcommand{} macros; they're
4573%  not really valuable.
4574%
4575%  If you don't want the Module Index, you can remove all of this up
4576%  until the second \input line.
4577%
4578
4579%begin{latexonly}
4580%\renewcommand{\indexname}{Module Index}
4581%end{latexonly}
4582\input{mod\jobname.ind}        % Module Index
4583%
4584%begin{latexonly}
4585%\renewcommand{\indexname}{Index}
4586%end{latexonly}
4587\input{\jobname.ind}            % Index
4588
4589
4590
4591\begin{thebibliography}{99}
4592\bibitem[nielsen2005]{nielsen2005}
4593{\it Hydrodynamic modelling of coastal inundation}.
4594Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman.
4595In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on
4596Modelling and Simulation. Modelling and Simulation Society of Australia and
4597New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\
4598http://www.mssanz.org.au/modsim05/papers/nielsen.pdf
4599
4600\bibitem[grid250]{grid250}
4601Australian Bathymetry and Topography Grid, June 2005.
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4624
4625\end{document}
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