% Complete documentation on the extended LaTeX markup used for Python % documentation is available in ''Documenting Python'', which is part % of the standard documentation for Python. It may be found online % at: % % http://www.python.org/doc/current/doc/doc.html %labels %Sections and subsections \label{sec: } %Chapters \label{ch: } %Equations \label{eq: } %Figures \label{fig: } % Is latex failing with; % 'modanuga_user_manual.ind' not found? % try this command-line % makeindex modanuga_user_manual.idx % To produce the modanuga_user_manual.ind file. %%%%%%%%%%%%%% TODO %%%%%%%%%%%%%%%% % % ensure_geospatial % ensure_absolute % set_geo_reference \documentclass{manual} \usepackage{graphicx} \usepackage[english]{babel} \usepackage{datetime} \usepackage[hang,small,bf]{caption} \input{definitions} %%%%% % Set penalties for widows, etc, very high %%%%% \widowpenalty=10000 \clubpenalty=10000 \raggedbottom \title{\anuga User Manual} \author{Geoscience Australia and the Australian National University} % Please at least include a long-lived email address; % the rest is at your discretion. \authoraddress{Geoscience Australia \\ Email: \email{ole.nielsen@ga.gov.au} } %Draft date % update before release! % Use an explicit date so that reformatting % doesn't cause a new date to be used. Setting % the date to \today can be used during draft % stages to make it easier to handle versions. \longdate % Make date format long using datetime.sty %\settimeformat{xxivtime} % 24 hour Format \settimeformat{oclock} % Verbose \date{\today, \ \currenttime} %\hyphenation{set\_datadir} \ifhtml \date{\today} % latex2html does not know about datetime \fi \input{version} % Get version info - this file may be modified by % update_anuga_user_manual.py - if not a dummy % will be used. %\release{1.2} % release version; this is used to define the % % \version macro \makeindex % tell \index to actually write the .idx file \makemodindex % If this contains a lot of module sections. \setcounter{tocdepth}{3} \setcounter{secnumdepth}{3} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \maketitle % This makes the contents more accessible from the front page of the HTML. \ifhtml \chapter*{Front Matter\label{front}} \fi %Subversion keywords: % %$LastChangedDate: 2010-06-07 06:19:31 +0000 (Mon, 07 Jun 2010) $ %$LastChangedRevision: 7804 $ %$LastChangedBy: hudson $ \input{copyright} \begin{abstract} \label{def:anuga} \noindent \anuga\index{\anuga} is a hydrodynamic modelling tool that allows users to model realistic flow problems in complex 2D geometries. Examples include dam breaks or the effects of natural hazards such as riverine flooding, storm surges and tsunami. The user must specify a study area represented by a mesh of triangular cells, the topography and bathymetry, frictional resistance, initial values for water level (called \emph{stage}\index{stage} within \anuga), boundary conditions and forces such as rainfall, stream flows, windstress or pressure gradients if applicable. \anuga tracks the evolution of water depth and horizontal momentum within each cell over time by solving the shallow water wave equation governing equation using a finite-volume method. \anuga also incorporates a mesh generator that allows the user to set up the geometry of the problem interactively as well as tools for interpolation and surface fitting, and a number of auxiliary tools for visualising and interrogating the model output. Most \anuga components are written in the object-oriented programming language Python and most users will interact with \anuga by writing small Python programs based on the \anuga library functions. Computationally intensive components are written for efficiency in C routines working directly with Python numpy structures. \end{abstract} \tableofcontents %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Introduction} \section{Purpose} The purpose of this user manual is to introduce the new user to the inundation software system, describe what it can do and give step-by-step instructions for setting up and running hydrodynamic simulations. The stable release of \anuga and this manual are available on sourceforge ati \url{http://sourceforge.net/projects/anuga}. A snapshot of work in progress is available through the \anuga software repository at \url{https://datamining.anu.edu.au/svn/ga/anuga_core} where the more adventurous reader might like to go. This manual describes \anuga version 1.2. To check for later versions of this manual go to \url{https://datamining.anu.edu.au/anuga}. \section{Scope} This manual covers only what is needed to operate the software after installation and configuration. It does not includes instructions for installing the software or detailed API documentation, both of which will be covered in separate publications and by documentation in the source code. The latest installation instructions may be found at: \url{http://datamining.anu.edu.au/\~{}ole/anuga/user_manual/anuga_installation_guide.pdf}. \section{Audience} Readers are assumed to be familiar with the Python Programming language and its object oriented approach. Python tutorials include \url{http://docs.python.org/tut}, \url{http://www.sthurlow.com/python}, and %\url{http://datamining.anu.edu.au/\%7e ole/work/teaching/ctac2006/exercise1.pdf}. \url{http://datamining.anu.edu.au/\~{}ole/work/teaching/ctac2006/exercise1.pdf}. Readers also need to have a general understanding of scientific modelling, as well as enough programming experience to adapt the code to different requirements. \pagebreak %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Background} Modelling the effects on the built environment of natural hazards such as riverine flooding, storm surges and tsunami is critical for understanding their economic and social impact on our urban communities. Geoscience Australia and the Australian National University are developing a hydrodynamic inundation modelling tool called \anuga to help simulate the impact of these hazards. The core of \anuga is the fluid dynamics module, called \code{shallow\_water}, which is based on a finite-volume method for solving the Shallow Water Wave Equation. The study area is represented by a mesh of triangular cells. By solving the governing equation within each cell, water depth and horizontal momentum are tracked over time. A major capability of \anuga is that it can model the process of wetting and drying as water enters and leaves an area. This means that it is suitable for simulating water flow onto a beach or dry land and around structures such as buildings. \anuga is also capable of modelling hydraulic jumps due to the ability of the finite-volume method to accommodate discontinuities in the solution\footnote{ While \anuga works with discontinuities in the conserved quantities stage, xmomentum and ymomentum, it does not allow discontinuities in the bed elevation.}. To set up a particular scenario the user specifies the geometry (bathymetry and topography), the initial water level (stage), boundary conditions such as tide, and any forcing terms that may drive the system such as rainfall, abstraction of water, wind stress or atmospheric pressure gradients. Gravity and frictional resistance from the different terrains in the model are represented by predefined forcing terms. See section \ref{sec:forcing terms} for details on forcing terms available in \anuga. The built-in mesh generator, called \code{graphical\_mesh\_generator}, allows the user to set up the geometry of the problem interactively and to identify boundary segments and regions using symbolic tags. These tags may then be used to set the actual boundary conditions and attributes for different regions (e.g.\ the Manning friction coefficient) for each simulation. Most \anuga components are written in the object-oriented programming language Python. Software written in Python can be produced quickly and can be readily adapted to changing requirements throughout its lifetime. Computationally intensive components are written for efficiency in C routines working directly with Python numeric structures. The animation tool developed for \anuga is based on OpenSceneGraph, an Open Source Software (OSS) component allowing high level interaction with sophisticated graphics primitives. See \cite{nielsen2005} for more background on \anuga. \chapter{Restrictions and limitations on \anuga} \label{ch:limitations} Although a powerful and flexible tool for hydrodynamic modelling, \anuga has a number of limitations that any potential user needs to be aware of. They are: \begin{itemize} \item The mathematical model is the 2D shallow water wave equation. As such it cannot resolve vertical convection and consequently not breaking waves or 3D turbulence (e.g.\ vorticity). %\item The surface is assumed to be open, e.g.\ \anuga cannot model %flow under ceilings or in pipes \item All spatial coordinates are assumed to be UTM (meters). As such, \anuga is unsuitable for modelling flows in areas larger than one UTM zone (6 degrees wide). \item Fluid is assumed to be inviscid -- i.e.\ no kinematic viscosity included. \item The finite volume is a very robust and flexible numerical technique, but it is not the fastest method around. If the geometry is sufficiently simple and if there is no need for wetting or drying, a finite-difference method may be able to solve the problem faster than \anuga. %\item Mesh resolutions near coastlines with steep gradients need to be... \item Frictional resistance is implemented using Manning's formula, but \anuga has not yet been fully validated in regard to bottom roughness. %\item \anuga contains no tsunami-genic functionality relating to earthquakes. \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Getting Started} \label{ch:getstarted} This section is designed to assist the reader to get started with \anuga by working through some examples. Two examples are discussed; the first is a simple example to illustrate many of the concepts, and the second is a more realistic example. \section{A Simple Example} \label{sec:simpleexample} \subsection{Overview} What follows is a discussion of the structure and operation of a script called \file{runup.py}. This example carries out the solution of the shallow-water wave equation in the simple case of a configuration comprising a flat bed, sloping at a fixed angle in one direction and having a constant depth across each line in the perpendicular direction. The example demonstrates the basic ideas involved in setting up a complex scenario. In general the user specifies the geometry (bathymetry and topography), the initial water level, boundary conditions such as tide, and any forcing terms that may drive the system such as rainfall, abstraction of water, wind stress or atmospheric pressure gradients. Frictional resistance from the different terrains in the model is represented by predefined forcing terms. In this example, the boundary is reflective on three sides and a time dependent wave on one side. The present example represents a simple scenario and does not include any forcing terms, nor is the data taken from a file as it would typically be. The conserved quantities involved in the problem are stage (absolute height of water surface), $x$-momentum and $y$-momentum. Other quantities involved in the computation are the friction and elevation. Water depth can be obtained through the equation: \begin{verbatim} depth = stage - elevation \end{verbatim} \subsection{Outline of the Program} In outline, \file{runup.py} performs the following steps: \begin{enumerate} \item Sets up a triangular mesh. \item Sets certain parameters governing the mode of operation of the model, specifying, for instance, where to store the model output. \item Inputs various quantities describing physical measurements, such as the elevation, to be specified at each mesh point (vertex). \item Sets up the boundary conditions. \item Carries out the evolution of the model through a series of time steps and outputs the results, providing a results file that can be viewed. \end{enumerate} \subsection{The Code} For reference we include below the complete code listing for \file{runup.py}. Subsequent paragraphs provide a 'commentary' that describes each step of the program and explains it significance. \label{ref:runup_py_code} \verbatiminput{demos/runup.py} \subsection{Establishing the Mesh}\index{mesh, establishing} The first task is to set up the triangular mesh to be used for the scenario. This is carried out through the statement: \begin{verbatim} points, vertices, boundary = anuga.rectangular_cross(10, 10) \end{verbatim} The function \function{rectangular_cross} is imported from a module \module{mesh\_factory} defined elsewhere. (\anuga also contains several other schemes that can be used for setting up meshes, but we shall not discuss these.) The above assignment sets up a $10 \times 10$ rectangular mesh, triangulated in a regular way. The assignment: \begin{verbatim} points, vertices, boundary = anuga.rectangular_cross(m, n) \end{verbatim} returns: \begin{itemize} \item a list \code{points} giving the coordinates of each mesh point, \item a list \code{vertices} specifying the three vertices of each triangle, and \item a dictionary \code{boundary} that stores the edges on the boundary and associates each with one of the symbolic tags \code{'left'}, \code{'right'}, \code{'top'} or \code{'bottom'}. The edges are represented as pairs (i, j) where i refers to the triangle id and j to the edge id of that triangle. Edge ids are enumerated from 0 to 2 based on the id of the vertex opposite. \end{itemize} (For more details on symbolic tags, see page \pageref{ref:tagdescription}.) An example of a general unstructured mesh and the associated data structures \code{points}, \code{vertices} and \code{boundary} is given in Section \ref{sec:meshexample}. \subsection{Initialising the Domain} These variables are then used to set up a data structure \code{domain}, through the assignment: \begin{verbatim} domain = anuga.Domain(points, vertices, boundary) \end{verbatim} This creates an instance of the \class{Domain} class, which represents the domain of the simulation. Specific options are set at this point, including the basename for the output file and the directory to be used for data: \begin{verbatim} domain.set_name('runup') domain.set_datadir('.') \end{verbatim} In addition, the following statement could be used to state that quantities \code{stage}, \code{xmomentum} and \code{ymomentum} are to be stored at every timestep and \code{elevation} only once at the beginning of the simulation: \begin{verbatim} domain.set_quantities_to_be_stored({'stage': 2, 'xmomentum': 2, 'ymomentum': 2, 'elevation': 1}) \end{verbatim} However, this is not necessary, as the above is the default behaviour. \subsection{Initial Conditions} The next task is to specify a number of quantities that we wish to set for each mesh point. The class \class{Domain} has a method \method{set\_quantity}, used to specify these quantities. It is a flexible method that allows the user to set quantities in a variety of ways -- using constants, functions, numeric arrays, expressions involving other quantities, or arbitrary data points with associated values, all of which can be passed as arguments. All quantities can be initialised using \method{set\_quantity}. For a conserved quantity (such as \code{stage, xmomentum, ymomentum}) this is called an \emph{initial condition}. However, other quantities that aren't updated by the equation are also assigned values using the same interface. The code in the present example demonstrates a number of forms in which we can invoke \method{set\_quantity}. \subsubsection{Elevation} The elevation, or height of the bed, is set using a function defined through the statements below, which is specific to this example and specifies a particularly simple initial configuration for demonstration purposes: \begin{verbatim} def topography(x, y): return -x/2 \end{verbatim} This simply associates an elevation with each point \code{(x, y)} of the plane. It specifies that the bed slopes linearly in the \code{x} direction, with slope $-\frac{1}{2}$, and is constant in the \code{y} direction. Once the function \function{topography} is specified, the quantity \code{elevation} is assigned through the simple statement: \begin{verbatim} domain.set_quantity('elevation', topography) \end{verbatim} NOTE: If using function to set \code{elevation} it must be vector compatible. For example, using square root will not work. \subsubsection{Friction} The assignment of the friction quantity (a forcing term) demonstrates another way we can use \method{set\_quantity} to set quantities -- namely, assign them to a constant numerical value: \begin{verbatim} domain.set_quantity('friction', 0.1) \end{verbatim} This specifies that the Manning friction coefficient is set to 0.1 at every mesh point. \subsubsection{Stage} The stage (the height of the water surface) is related to the elevation and the depth at any time by the equation: \begin{verbatim} stage = elevation + depth \end{verbatim} For this example, we simply assign a constant value to \code{stage}, using the statement: \begin{verbatim} domain.set_quantity('stage', -0.4) \end{verbatim} which specifies that the surface level is set to a height of $-0.4$, i.e.\ 0.4 units (metres) below the zero level. Although it is not necessary for this example, it may be useful to digress here and mention a variant to this requirement, which allows us to illustrate another way to use \method{set\_quantity} -- namely, incorporating an expression involving other quantities. Suppose, instead of setting a constant value for the stage, we wished to specify a constant value for the \emph{depth}. For such a case we need to specify that \code{stage} is everywhere obtained by adding that value to the value already specified for \code{elevation}. We would do this by means of the statements: \begin{verbatim} h = 0.05 # Constant depth domain.set_quantity('stage', expression='elevation + %f' % h) \end{verbatim} That is, the value of \code{stage} is set to $\code{h} = 0.05$ plus the value of \code{elevation} already defined. The reader will probably appreciate that this capability to incorporate expressions into statements using \method{set\_quantity} greatly expands its power. See Section \ref{sec:initial conditions} for more details. \subsection{Boundary Conditions}\index{boundary conditions} The boundary conditions are specified as follows: \begin{verbatim} Br = anuga.Reflective_boundary(domain) Bt = anuga.Transmissive_boundary(domain) Bd = anuga.Dirichlet_boundary([0.2, 0.0, 0.0]) Bw = anuga.Time_boundary(domain=domain, f=lambda t: [(0.1*sin(t*2*pi)-0.3)*exp(-t), 0.0, 0.0]) \end{verbatim} The effect of these statements is to set up a selection of different alternative boundary conditions and store them in variables that can be assigned as needed. Each boundary condition specifies the behaviour at a boundary in terms of the behaviour in neighbouring elements. The boundary conditions introduced here may be briefly described as follows: \begin{itemize} \item \textbf{Reflective boundary}\label{def:reflective boundary} Returns same \code{stage} as in its neighbour volume but momentum vector reversed 180 degrees (reflected). Specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. A reflective boundary condition models a solid wall. \item \textbf{Transmissive boundary}\label{def:transmissive boundary} Returns same conserved quantities as those present in its neighbour volume. This is one way of modelling outflow from a domain, but it should be used with caution if flow is not steady state as replication of momentum at the boundary may cause numerical instabilities propagating into the domain and eventually causing \anuga to crash. If this occurs, consider using e.g.\ a Dirichlet boundary condition with a stage value less than the elevation at the boundary. \item \textbf{Dirichlet boundary}\label{def:dirichlet boundary} Specifies constant values for stage, $x$-momentum and $y$-momentum at the boundary. \item \textbf{Time boundary}\label{def:time boundary} Like a Dirichlet boundary but with behaviour varying with time. \end{itemize} \label{ref:tagdescription}Before describing how these boundary conditions are assigned, we recall that a mesh is specified using three variables \code{points}, \code{vertices} and \code{boundary}. In the code we are discussing, these three variables are returned by the function \code{rectangular}. The example given in Section \ref{sec:realdataexample} illustrates another way of assigning the values, by means of the function \code{create_mesh_from_regions}. These variables store the data determining the mesh as follows. (You may find that the example given in Section \ref{sec:meshexample} helps to clarify the following discussion, even though that example is a \emph{non-rectangular} mesh.) \begin{itemize} \item The variable \code{points} stores a list of 2-tuples giving the coordinates of the mesh points. \item The variable \code{vertices} stores a list of 3-tuples of numbers, representing vertices of triangles in the mesh. In this list, the triangle whose vertices are \code{points[i]}, \code{points[j]}, \code{points[k]} is represented by the 3-tuple \code{(i, j, k)}. \item The variable \code{boundary} is a Python dictionary that not only stores the edges that make up the boundary but also assigns symbolic tags to these edges to distinguish different parts of the boundary. An edge with endpoints \code{points[i]} and \code{points[j]} is represented by the 2-tuple \code{(i, j)}. The keys for the dictionary are the 2-tuples \code{(i, j)} corresponding to boundary edges in the mesh, and the values are the tags are used to label them. In the present example, the value \code{boundary[(i, j)]} assigned to \code{(i, j)]} is one of the four tags \code{'left'}, \code{'right'}, \code{'top'} or \code{'bottom'}, depending on whether the boundary edge represented by \code{(i, j)} occurs at the left, right, top or bottom of the rectangle bounding the mesh. The function \code{rectangular} automatically assigns these tags to the boundary edges when it generates the mesh. \end{itemize} The tags provide the means to assign different boundary conditions to an edge depending on which part of the boundary it belongs to. (In Section \ref{sec:realdataexample} we describe an example that uses different boundary tags -- in general, the possible tags are entirely selectable by the user when generating the mesh and not limited to 'left', 'right', 'top' and 'bottom' as in this example.) All segments in bounding polygon must be tagged. If a tag is not supplied, the default tag name 'exterior' will be assigned by \anuga. Using the boundary objects described above, we assign a boundary condition to each part of the boundary by means of a statement like: \begin{verbatim} domain.set_boundary({'left': Br, 'right': Bw, 'top': Br, 'bottom': Br}) \end{verbatim} It is critical that all tags are associated with a boundary condition in this statement. If not the program will halt with a statement like: \begin{verbatim} Traceback (most recent call last): File "mesh_test.py", line 114, in ? domain.set_boundary({'west': Bi, 'east': Bo, 'north': Br, 'south': Br}) File "X:\inundation\sandpits\onielsen\anuga_core\source\anuga\abstract_2d_finite_volumes\domain.py", line 505, in set_boundary raise msg ERROR (domain.py): Tag "exterior" has not been bound to a boundary object. All boundary tags defined in domain must appear in the supplied dictionary. The tags are: ['ocean', 'east', 'north', 'exterior', 'south'] \end{verbatim} The command \code{set_boundary} stipulates that, in the current example, the right boundary varies with time, as defined by the lambda function, while the other boundaries are all reflective. The reader may wish to experiment by varying the choice of boundary types for one or more of the boundaries. (In the case of \code{Bd} and \code{Bw}, the three arguments in each case represent the \code{stage}, $x$-momentum and $y$-momentum, respectively.) \begin{verbatim} Bw = anuga.Time_boundary(domain=domain, f=lambda t: [(0.1*sin(t*2*pi)-0.3), 0.0, 0.0]) \end{verbatim} \subsection{Evolution}\index{evolution} The final statement: \begin{verbatim} for t in domain.evolve(yieldstep=0.1, duration=10.0): print domain.timestepping_statistics() \end{verbatim} causes the configuration of the domain to 'evolve', over a series of steps indicated by the values of \code{yieldstep} and \code{duration}, which can be altered as required. The value of \code{yieldstep} controls the time interval between successive model outputs. Behind the scenes more time steps are generally taken. \subsection{Output} The output is a NetCDF file with the extension \code{.sww}. It contains stage and momentum information and can be used with the \anuga viewer \code{anuga\_viewer} to generate a visual display (see Section \ref{sec:animate}). See Section \ref{sec:file formats} (page \pageref{sec:file formats}) for more on NetCDF and other file formats. The following is a listing of the screen output seen by the user when this example is run: \verbatiminput{examples/runupoutput.txt} \section{How to Run the Code} The code can be run in various ways: \begin{itemize} \item{from a Windows or Unix command line} as in\ \code{python runup.py} \item{within the Python IDLE environment} \item{within emacs} \item{within Windows, by double-clicking the \code{runup.py} file.} \end{itemize} \section{Exploring the Model Output} The following figures are screenshots from the \anuga visualisation tool \code{animate}. Figure \ref{fig:runupstart} shows the domain with water surface as specified by the initial condition, $t=0$. Figure \ref{fig:runup2} shows later snapshots for $t=2.3$ and $t=4$ where the system has been evolved and the wave is encroaching on the previously dry bed. \code{animate} is described in more detail in Section \ref{sec:animate}. \begin{figure}[htp] \centerline{\includegraphics[width=75mm, height=75mm] {graphics/bedslopestart.jpg}} \caption{Runup example viewed with the \anuga viewer} \label{fig:runupstart} \end{figure} \begin{figure}[htp] \centerline{ \includegraphics[width=75mm, height=75mm]{graphics/bedslopeduring.jpg} \includegraphics[width=75mm, height=75mm]{graphics/bedslopeend.jpg} } \caption{Runup example viewed with ANGUA viewer} \label{fig:runup2} \end{figure} \clearpage \section{A slightly more complex example} \label{sec:channelexample} \subsection{Overview} The next example is about waterflow in a channel with varying boundary conditions and more complex topographies. These examples build on the concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}. The example will be built up through three progressively more complex scripts. \subsection{Overview} As in the case of \file{runup.py}, the actions carried out by the program can be organised according to this outline: \begin{enumerate} \item Set up a triangular mesh. \item Set certain parameters governing the mode of operation of the model -- specifying, for instance, where to store the model output. \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex). \item Set up the boundary conditions. \item Carry out the evolution of the model through a series of time steps and output the results, providing a results file that can be viewed. \end{enumerate} \subsection{The Code} Here is the code for the first version of the channel flow \file{channel1.py}: \verbatiminput{demos/channel1.py} In discussing the details of this example, we follow the outline given above, discussing each major step of the code in turn. \subsection{Establishing the Mesh}\index{mesh, establishing} In this example we use a similar simple structured triangular mesh as in \file{runup.py} for simplicity, but this time we will use a symmetric one and also change the physical extent of the domain. The assignment: \begin{verbatim} points, vertices, boundary = anuga.rectangular_cross(m, n, len1=length, len2=width) \end{verbatim} returns an \code{mxn} mesh similar to the one used in the previous example, except that now the extent in the x and y directions are given by the value of \code{length} and \code{width} respectively. Defining \code{m} and \code{n} in terms of the extent as in this example provides a convenient way of controlling the resolution: By defining \code{dx} and \code{dy} to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows: \begin{verbatim} length = 10.0 width = 5.0 dx = dy = 1 # Resolution: Length of subdivisions on both axes points, vertices, boundary = anuga.rectangular_cross(int(length/dx), int(width/dy), len1=length, len2=width) \end{verbatim} which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decreases the values of \code{dx} and \code{dy}. The rest of this script is similar to the previous example on page \pageref{ref:runup_py_code}. % 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}: %\begin{verbatim} % domain.set_quantity('stage', expression='elevation') %\end{verbatim} \section{Model Output} The following figure is a screenshot from the \anuga visualisation tool \code{animate} of output from this example. \begin{figure}[htp] \centerline{\includegraphics[height=75mm] {graphics/channel1.png}}% \caption{Simple channel example viewed with the \anuga viewer.} \label{fig:channel1} \end{figure} \subsection{Changing boundary conditions on the fly} \label{sec:change boundary} Here is the code for the second version of the channel flow \file{channel2.py}: \verbatiminput{demos/channel2.py} This example differs from the first version in that a constant outflow boundary condition has been defined: \begin{verbatim} Bo = anuga.Dirichlet_boundary([-5, 0, 0]) # Outflow \end{verbatim} and that it is applied to the right hand side boundary when the water level there exceeds 0m. \begin{verbatim} for t in domain.evolve(yieldstep=0.2, finaltime=40.0): domain.write_time() if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0: print 'Stage > 0: Changing to outflow boundary' domain.set_boundary({'right': Bo}) \end{verbatim} \label{sec:change boundary code} The \code{if} statement in the timestepping loop (\code{evolve}) gets the quantity \code{stage} and obtains the interpolated value at the point (10m, 2.5m) which is on the right boundary. If the stage exceeds 0m a message is printed and the old boundary condition at tag 'right' is replaced by the outflow boundary using the method: \begin{verbatim} domain.set_boundary({'right': Bo}) \end{verbatim} This type of dynamically varying boundary could for example be used to model the breakdown of a sluice door when water exceeds a certain level. \subsection{Output} The text output from this example looks like this: \begin{verbatim} ... Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6) Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6) Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6) Stage > 0: Changing to outflow boundary Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6) Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6) ... \end{verbatim} \subsection{Flow through more complex topograhies} Here is the code for the third version of the channel flow \file{channel3.py}: \verbatiminput{demos/channel3.py} This example differs from the first two versions in that the topography contains obstacles. This is accomplished here by defining the function \code{topography} as follows: \begin{verbatim} def topography(x,y): """Complex topography defined by a function of vectors x and y.""" z = -x/10 N = len(x) for i in range(N): # Step if 10 < x[i] < 12: z[i] += 0.4 - 0.05*y[i] # Constriction if 27 < x[i] < 29 and y[i] > 3: z[i] += 2 # Pole if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2: z[i] += 2 return z \end{verbatim} In addition, changing the resolution to \code{dx = dy = 0.1} creates a finer mesh resolving the new features better. A screenshot of this model at time 15s is: \begin{figure}[htp] \centerline{\includegraphics[height=75mm] {graphics/channel3.png}} \caption{More complex flow in a channel} \label{fig:channel3} \end{figure} \section{An Example with Real Data} \label{sec:realdataexample} The following discussion builds on the concepts introduced through the \file{runup.py} example and introduces a second example, \file{runcairns.py}. This refers to a {\bf hypothetical} scenario using real-life data, in which the domain of interest surrounds the Cairns region. Two scenarios are given; firstly, a hypothetical tsunami wave is generated by a submarine mass failure situated on the edge of the continental shelf, and secondly, a fixed wave of given amplitude and period is introduced through the boundary. {\bf Each scenario has been designed to generate a tsunami which will inundate the Cairns region. To achieve this, suitably large parameters were chosen and were not based on any known tsunami sources or realistic amplitudes. } \subsection{Overview} As in the case of \file{runup.py}, the actions carried out by the program can be organised according to this outline: \begin{enumerate} \item Set up a triangular mesh. \item Set certain parameters governing the mode of operation of the model -- specifying, for instance, where to store the model output. \item Input various quantities describing physical measurements, such as the elevation, to be specified at each mesh point (vertex). \item Set up the boundary conditions. \item Carry out the evolution of the model through a series of time steps and output the results, providing a results file that can be visualised. \end{enumerate} \subsection{The Code} Here is the code for \file{runcairns.py}: \verbatiminput{demos/cairns/runcairns.py} In discussing the details of this example, we follow the outline given above, discussing each major step of the code in turn. \subsection{Establishing the Mesh}\index{mesh, establishing} One obvious way that the present example differs from \file{runup.py} is in the use of a more complex method to create the mesh. Instead of imposing a mesh structure on a rectangular grid, the technique used for this example involves building mesh structures inside polygons specified by the user, using a mesh-generator. The mesh-generator creates the mesh within a single polygon whose vertices are at geographical locations specified by the user. The user specifies the \emph{resolution} -- that is, the maximal area of a triangle used for triangulation -- and a triangular mesh is created inside the polygon using a mesh generation engine. On any given platform, the same mesh will be returned each time the script is run. Boundary tags are not restricted to \code{'left'}, \code{'bottom'}, \code{'right'} and \code{'top'}, as in the case of \file{runup.py}. Instead the user specifies a list of tags appropriate to the configuration being modelled. In addition, the mesh-generator provides a way to adapt to geographic or other features in the landscape, whose presence may require an increase in resolution. This is done by allowing the user to specify a number of \emph{interior polygons}, each with a specified resolution. It is also possible to specify one or more 'holes' -- that is, areas bounded by polygons in which no triangulation is required. In its general form, the mesh-generator takes for its input a bounding polygon and (optionally) a list of interior polygons. The user specifies resolutions, both for the bounding polygon and for each of the interior polygons. Given this data, the mesh-generator first creates a triangular mesh with varying resolution. The function used to implement this process is \function{create\_domain\_from\_regions} which creates a Domain object as well as a mesh file. Its arguments include the bounding polygon and its resolution, a list of boundary tags, and a list of pairs \code{[polygon, resolution]} specifying the interior polygons and their resolutions. The resulting mesh is output to a \emph{mesh file}\index{mesh file}\label{def:mesh file}. This term is used to describe a file of a specific format used to store the data specifying a mesh. (There are in fact two possible formats for such a file: it can either be a binary file, with extension \code{.msh}, or an ASCII file, with extension \code{.tsh}. In the present case, the binary file format \code{.msh} is used. See Section \ref{sec:file formats} (page \pageref{sec:file formats}) for more on file formats. In practice, the details of the polygons used are read from a separate file \file{project.py}. Here is a complete listing of \file{project.py}: \verbatiminput{demos/cairns/project.py} Figure \ref{fig:cairns3d} illustrates the landscape of the region for the Cairns example. Understanding the landscape is important in determining the location and resolution of interior polygons. The supporting data is found in the ASCII grid, \code{cairns.asc}, which has been sourced from the publically available Australian Bathymetry and Topography Grid 2005, \cite{grid250}. The required resolution for inundation modelling will depend on the underlying topography and bathymetry; as the terrain becomes more complex, the desired resolution would decrease to the order of tens of metres. \clearpage \begin{figure}[htp] \centerline{\includegraphics[scale=0.5]{graphics/cairns3.jpg}} \caption{Landscape of the Cairns scenario.} \label{fig:cairns3d} \end{figure} The following statements are used to read in the specific polygons from \code{project.cairns} and assign a defined resolution to each polygon. \begin{verbatim} islands_res = 100000 cairns_res = 100000 shallow_res = 500000 interior_regions = [[project.poly_cairns, cairns_res], [project.poly_island0, islands_res], [project.poly_island1, islands_res], [project.poly_island2, islands_res], [project.poly_island3, islands_res], [project.poly_shallow, shallow_res]] \end{verbatim} Figure \ref{fig:cairnspolys} illustrates the polygons used for the Cairns scenario. \clearpage \begin{figure}[htp] \centerline{\includegraphics[scale=0.5] {graphics/cairnsmodel.jpg}} \caption{Interior and bounding polygons for the Cairns example.} \label{fig:cairnspolys} \end{figure} The statement: \begin{verbatim} remainder_res = 10000000 domain = anuga.create_domain_from_regions(project.bounding_polygon, boundary_tags={'top': [0], 'ocean_east': [1], 'bottom': [2], 'onshore': [3]}, maximum_triangle_area=project.default_res, mesh_filename=project.meshname, interior_regions=project.interior_regions, use_cache=True, verbose=True) \end{verbatim} is then used to create the mesh, taking the bounding polygon to be the polygon \code{bounding\_polygon} specified in \file{project.py}. The argument \code{boundary\_tags} assigns a dictionary, whose keys are the names of the boundary tags used for the bounding polygon -- \code{'top'}, \code{'ocean\_east'}, \code{'bottom'}, and \code{'onshore'} -- and whose values identify the indices of the segments associated with each of these tags. The polygon may be arranged either clock-wise or counter clock-wise and the indices 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. (Here, the values associated with each boundary tag are one-element lists, but they can have as many indices as there are edges) If polygons intersect, or edges coincide (or are even very close) the resolution may be undefined in some regions. Use the underlying mesh interface for such cases (see Chapter \ref{sec:mesh interface}). If a segment is omitted in the tags definition an Exception is raised. Note that every point on each polygon defining the mesh will be used as vertices in triangles. Consequently, polygons with points very close together will cause triangles with very small areas to be generated irrespective of the requested resolution. Make sure points on polygons are spaced to be no closer than the smallest resolution requested. \subsection{Initialising the Domain} Since we used \code{create_domain_from_regions} to create the mesh file, we do not need to create the domain explicitly, as the above function does both mesh and domain creation. The following statements specify a basename and data directory, and sets a minimum storable height, which helps with visualisation and post-processing if one wants to remove water less than 1cm deep (for instance). \begin{verbatim} domain.set_name('cairns_' + project.scenario) # Name of SWW file domain.set_datadir('.') # Store SWW output here domain.set_minimum_storable_height(0.01) # Store only depth > 1cm \end{verbatim} \subsection{Initial Conditions} Quantities for \file{runcairns.py} are set using similar methods to those in \file{runup.py}. However, in this case, many of the values are read from the auxiliary file \file{project.py} or, in the case of \code{elevation}, from an auxiliary points file. \subsubsection{Stage} The stage is initially set to 0.0 (i.e.\ Mean Sea Level) by the following statements: \begin{verbatim} tide = 0.0 domain.set_quantity('stage', tide) \end{verbatim} It could also take the value of the highest astronomical tide. %For the scenario we are modelling in this case, we use a callable %object \code{tsunami_source}, assigned by means of a function %\function{slide\_tsunami}. This is similar to how we set elevation in %\file{runup.py} using a function -- however, in this case the %function is both more complex and more interesting. %The function returns the water displacement for all \code{x} and %\code{y} in the domain. The water displacement is a double Gaussian %function that depends on the characteristics of the slide (length, %width, thickness, slope, etc), its location (origin) and the depth at that %location. For this example, we choose to apply the slide function %at a specified time into the simulation. {\bf Note, the parameters used %in this example have been deliberately chosen to generate a suitably %large amplitude tsunami which would inundate the Cairns region.} \subsubsection{Friction} We assign the friction exactly as we did for \file{runup.py}: \begin{verbatim} domain.set_quantity('friction', 0.0) \end{verbatim} \subsubsection{Elevation} The elevation is specified by reading data from a file with a name derived from \code{project.demname} with the \code{.pts} extension: \begin{verbatim} domain.set_quantity('elevation', filename=project.demname + '.pts', use_cache=True, verbose=True, alpha=0.1) \end{verbatim} The \code{alpha} parameter controls how smooth the elevation surface should be. See section \ref{class:alpha_shape}, page \pageref{class:alpha_shape}. Setting \code{cache=True} allows \anuga to save the result in order to make subsequent runs faster. Using \code{verbose=True} tells the function to write diagnostics to the screen. \subsection{Boundary Conditions}\index{boundary conditions} Setting boundaries follows a similar pattern to the one used for \file{runup.py}, except that in this case we need to associate a boundary type with each of the boundary tag names introduced when we established the mesh. In place of the four boundary types introduced for \file{runup.py}, we use the reflective boundary for each of the tagged segments defined by \code{create_domain_from_regions}: \begin{verbatim} Bd = anuga.Dirichlet_boundary([tide,0,0]) # Mean water level Bs = anuga.Transmissive_stage_zero_momentum_boundary(domain) # Neutral boundary if project.scenario == 'fixed_wave': # Huge 50m wave starting after 60 seconds and lasting 1 hour. Bw = anuga.Time_boundary(domain=domain, function=lambda t: [(60}.add_hole}{x, y, geo_reference=None} Module: \module{pmesh.mesh} This method adds a hole to the mesh outline. \code{x} and \code{y} define a point on the already defined hole boundary. If \code{geo_reference} is not supplied the points are assumed to be absolute. \end{methoddesc} \begin{methoddesc}{\emph{}.add_hole_from_polygon}{polygon, segment_tags=None, geo_reference=None} Module: \module{pmesh.mesh} This method is used to add a 'hole' within a region -- that is, to define a interior region where the triangular mesh will not be generated -- to a \class{Mesh} instance. The region boundary is described by the polygon passed in. Additionally, the user specifies a list of boundary tags, one for each edge of the bounding polygon. \code{polygon} is the polygon that defines the hole to be added to the \code{}. \code{segment_tags} -- ?? If \code{geo_reference} is \code{None} then the default \code{geo_reference} is used. \end{methoddesc} \begin{methoddesc}{\emph{}.add_points_and_segments}{points, segments=None, segment_tags=None} Module: \module{pmesh.mesh} This adds points and segments connecting the points to a mesh. \code{points} is a list of points. \code{segments} is a list of segments. Each segment is defined by the start and end of the line by its point index, e.g.\ use \code{segments = [[0,1],[1,2]]} to make a polyline between points 0, 1 and 2. \code{segment_tags} may be used to optionally define a tag for each segment. \end{methoddesc} \begin{methoddesc}{\emph{}.add_region}{x,y, geo_reference=None, tag=None} Module: \module{pmesh.mesh} This method adds a region to a mesh outline. \code{x} and \code{y} define a point on the already-defined region that is to be added to the mesh. If \code{geo_reference} is not supplied the points data is assumed to be absolute. \code{tag} -- ?? A region instance is returned. This can be used to set the resolution of the added region. \end{methoddesc} \begin{methoddesc}{\emph{}.add_region_from_polygon}{polygon, segment_tags=None, max_triangle_area=None, geo_reference=None, region_tag=None} Module: \module{pmesh.mesh} This method adds a region to a \class{Mesh} instance. Regions are commonly used to describe an area with an increased density of triangles by setting \code{max_triangle_area}. \code{polygon} describes the region boundary to add to the \code{}. \code{segment_tags} specifies a list of segment tags, one for each edge of the bounding polygon. If \code{geo_reference} is not supplied the points data is assumed to be absolute. \code{region_tag} sets the region tag. \end{methoddesc} \begin{methoddesc}{\emph{}.add_vertices}{point_data} Module: \module{pmesh.mesh} Add user vertices to a mesh. \code{point_data} is the list of point data, and can be a list of (x,y) values, a numeric array or a geospatial_data instance. \end{methoddesc} \begin{methoddesc}{\emph{}.auto_segment}{alpha=None, raw_boundary=True, remove_holes=False, smooth_indents=False, expand_pinch=False} Module: \module{pmesh.mesh} Add segments between some of the user vertices to give the vertices an outline. The outline is an alpha shape. This method is useful since a set of user vertices need to be outlined by segments before generate_mesh is called. \code{alpha} determines the $smoothness$ of the alpha shape. \code{raw_boundary}, if \code{True} instructs the function to return the raw boundary, i.e.\ the regular edges of the alpha shape. \code{remove_holes}, if \code{True} enables a filter to remove small holes (small is defined by boundary_points_fraction). \code{smooth_indents}, if \code{True} removes sharp triangular indents in the boundary. \code{expand_pinch}, if \code{True} tests for pinch-off and corrects (i.e.\ a boundary vertex with more than two edges). \end{methoddesc} \begin{methoddesc}{\emph{}.export_mesh_file}{ofile} Module: \module{pmesh.mesh} This method is used to save a mesh to a file. \code{ofile} is the name of the mesh file to be written, including the extension. Use the extension \code{.msh} for the file to be in NetCDF format and \code{.tsh} for the file to be ASCII format. \end{methoddesc} \begin{methoddesc}{\emph{}.generate_mesh}{maximum_triangle_area="", minimum_triangle_angle=28.0, verbose=True} Module: \module{pmesh.mesh} This method is used to generate the triangular mesh. \code{maximum_triangle_area} sets the maximum area of any triangle in the mesh. \code{minimum_triangle_angle} sets the minimum area of any triangle in the mesh. These two parameters can be used to control the triangle density. \end{methoddesc} \begin{methoddesc}{\emph{}.import_ungenerate_file}{ofile, tag=None, region_tag=None} Module: \module{pmesh.mesh} This method is used to import a polygon file in the ungenerate format, which is used by arcGIS. The polygons from the file are converted to vertices and segments. \code{ofile} is the name of the polygon file. \code{tag} is the tag given to all the polygon's segments. If \code{tag} is not supplied then the segment will not effect the water flow, it will only effect the mesh generation. \code{region_tag} is the tag given to all the polygon's segments. If it is a string the tag will be assigned to all regions. If it is a list the first value in the list will be applied to the first polygon etc. This function can be used to import building footprints. \end{methoddesc} \section{Initialising the Domain}\index{Initialising the Domain} \label{sec:initialising the domain} \begin{classdesc}{Domain}{source=None, triangles=None, boundary=None, conserved_quantities=None, other_quantities=None, tagged_elements=None, geo_reference=None, use_inscribed_circle=False, mesh_filename=None, use_cache=False, verbose=False, full_send_dict=None, ghost_recv_dict=None, processor=0, numproc=1, number_of_full_nodes=None, number_of_full_triangles=None} Module: \refmodule{abstract_2d_finite_volumes.domain} This class is used to create an instance of a structure used to store and manipulate data associated with a mesh. The mesh is specified either by assigning the name of a mesh file to \code{source} or by specifying the points, triangle and boundary of the mesh. \end{classdesc} \subsection{Key Methods of Domain} \begin{methoddesc}{\emph{}.set_name}{name} Module: \refmodule{abstract_2d_finite_volumes.domain}, page \pageref{mod:domain} \code{name} is used to name the domain. The \code{name} is also used to identify the output SWW file. If no name is assigned to a domain, the assumed name is \code{'domain'}. \end{methoddesc} \begin{methoddesc}{\emph{}.get_name}{} Module: \module{abstract_2d_finite_volumes.domain} Returns the name assigned to the domain by \code{set_name()}. If no name has been assigned, returns \code{'domain'}. \end{methoddesc} \begin{methoddesc}{\emph{}.set_datadir}{path} Module: \module{abstract_2d_finite_volumes.domain} \code{path} specifies the path to the directory used to store SWW files. Before this method is used to set the SWW directory path, the assumed directory path is \code{default_datadir} specified in \code{config.py}. Since different operating systems use different formats for specifying pathnames it is necessary to specify path separators using the Python code \code{os.sep} rather than the operating-specific ones such as '$\slash$' or '$\backslash$'. For this to work you will need to include the statement \code{import os} in your code, before the first use of \code{set_datadir()}. For example, to set the data directory to a subdirectory \code{data} of the directory \code{project}, you could use the statements: \begin{verbatim} import os domain.set_datadir{'project' + os.sep + 'data'} \end{verbatim} \end{methoddesc} \begin{methoddesc}{\emph{}.get_datadir}{} Module: \module{abstract_2d_finite_volumes.domain} Returns the path to the directory where SWW files will be stored. If the path has not previously been set with \code{set_datadir()} this method will return the value \code{default_datadir} specified in \code{config.py}. \end{methoddesc} \begin{methoddesc}{\emph{}.set_minimum_allowed_height}{minimum_allowed_height} Module: \module{shallow_water.shallow_water_domain} Set the minimum depth (in metres) that will be recognised in the numerical scheme (including limiters and flux computations) \code{minimum_allowed_height} is the new minimum allowed height value. Default value is $10^{-3}$ metre, but by setting this to a greater value, e.g.\ for large scale simulations, the computation time can be significantly reduced. \end{methoddesc} \begin{methoddesc}{\emph{}.set_minimum_storable_height}{minimum_storable_height} Module: \module{shallow_water.shallow_water_domain} Sets the minimum depth that will be recognised when writing to an SWW file. This is useful for removing thin water layers that seems to be caused by friction creep. \code{minimum_storable_height} is the new minimum storable height value. \end{methoddesc} \begin{methoddesc}{\emph{}.set_maximum_allowed_speed}{maximum_allowed_speed} Module: \module{shallow_water.shallow_water_domain} Set the maximum particle speed that is allowed in water shallower than \code{minimum_allowed_height}. This is useful for controlling speeds in very thin layers of water and at the same time allow some movement avoiding pooling of water. \code{maximum_allowed_speed} sets the maximum allowed speed value. \end{methoddesc} \begin{methoddesc}{\emph{}.set_time}{time=0.0} Module: \module{abstract_2d_finite_volumes.domain} \code{time} sets the initial time, in seconds, for the simulation. The default is 0.0. \end{methoddesc} \begin{methoddesc}{\emph{}.set_default_order}{n} Module: \module{abstract_2d_finite_volumes.domain} Sets the default (spatial) order to the value specified by \code{n}, which must be either 1 or 2. (Assigning any other value to \code{n} will cause an error.) \end{methoddesc} \begin{methoddesc}{\emph{}.set_store_vertices_uniquely}{flag, reduction=None} Module: \module{shallow_water.shallow_water_domain} Decide whether vertex values should be stored uniquely as computed in the model or whether they should be reduced to one value per vertex using averaging. \code{flag} may be \code{True} (meaning allow surface to be discontinuous) or \code{False} (meaning smooth vertex values). \code{reduction} defines the smoothing operation if \code{flag} is \code{False}. If not supplied, \code{reduction} is assumed to be \code{mean}. Triangles stored in the SWW file can be discontinuous reflecting the internal representation of the finite-volume scheme (this is a feature allowing for arbitrary steepness of the water surface gradient as well as the momentum gradients). However, for visual purposes and also for use with \code{Field_boundary} (and \code{File_boundary}), it is often desirable to store triangles with values at each vertex point as the average of the potentially discontinuous numbers found at vertices of different triangles sharing the same vertex location. Storing one way or the other is controlled in \anuga through the method \code{.store_vertices_uniquely()}. Options are: \begin{itemize} \item \code{.store_vertices_uniquely(True)}: Allow discontinuities in the SWW file \item \code{.store_vertices_uniquely(False)}: (Default). Average values to ensure continuity in SWW file. The latter also makes for smaller SWW files. \end{itemize} Note that when model data in the SWW file are averaged (i.e.\ not stored uniquely), then there will most likely be a small discrepancy between values extracted from the SWW file and the same data stored in the model domain. This must be borne in mind when comparing data from the SWW files with that of the model internally. \end{methoddesc} \begin{methoddesc}{\emph{}.set_quantities_to_be_stored}{quantity_dictionary} Module: \module{shallow_water.shallow_water_domain} Selects quantities that is to be stored in the sww files. The argument can be None, in which case nothing is stored. Otherwise, the argument must be a dictionary where the keys are names of quantities already defined within ANUGA and the values are either 1 or 2. If the value is 1, the quantity will be stored once at the beginning of the simulation, if the value is 2 it will be stored at each timestep. The ANUGA default is equivalent to the call \begin{verbatim} domain.set_quantities_to_be_stored({'elevation': 1, 'stage': 2, 'xmomentum': 2, 'ymomentum': 2}) \end{verbatim} \end{methoddesc} % Structural methods \begin{methoddesc}{\emph{}.get_nodes}{absolute=False} Module: \module{abstract_2d_finite_volumes.domain} Return x,y coordinates of all nodes in the domain mesh. The nodes are ordered in an \code{Nx2} array where N is the number of nodes. This is the same format they were provided in the constructor i.e.\ without any duplication. \code{absolute} is a boolean which determines whether coordinates are to be made absolute by taking georeference into account. Default is \code{False} as many parts of \anuga expect relative coordinates. \end{methoddesc} \begin{methoddesc}{\emph{}.get_vertex_coordinates}{absolute=False} Module: \module{abstract_2d_finite_volumes.domain} \label{pg:get vertex coordinates} Return vertex coordinates for all triangles as a \code{3*Mx2} array where the jth vertex of the ith triangle is located in row 3*i+j and M is the number of triangles in the mesh. \code{absolute} is a boolean which determines whether coordinates are to be made absolute by taking georeference into account. Default is \code{False} as many parts of \anuga expect relative coordinates. \end{methoddesc} \begin{methoddesc}{\emph{}.get_centroid_coordinates}{absolute=False} Module: \module{abstract_2d_finite_volumes.domain} Return centroid coordinates for all triangles as an \code{Mx2} array. \code{absolute} is a boolean which determines whether coordinates are to be made absolute by taking georeference into account. Default is \code{False} as many parts of \anuga expect relative coordinates. \end{methoddesc} \begin{methoddesc}{\emph{}.get_triangles}{indices=None} Module: \module{abstract_2d_finite_volumes.domain} Return an \code{Mx3} integer array where M is the number of triangles. Each row corresponds to one triangle and the three entries are indices into the mesh nodes which can be obtained using the method \code{get_nodes()}. \code{indices}, if specified, is the set of triangle \code{id}s of interest. \end{methoddesc} \begin{methoddesc}{\emph{}.get_disconnected_triangles}{} Module: \module{abstract_2d_finite_volumes.domain} Get the domain mesh based on nodes obtained from \code{get_vertex_coordinates()}. Returns an \code{Mx3} array of integers where each row corresponds to a triangle. A triangle is a triplet of indices into point coordinates obtained from \code{get_vertex_coordinates()} and each index appears only once. This provides a mesh where no triangles share nodes (hence the name disconnected triangles) and different nodes may have the same coordinates. This version of the mesh is useful for storing meshes with discontinuities at each node and is e.g.\ used for storing data in SWW files. The triangles created will have the format: \begin{verbatim} [[0,1,2], [3,4,5], [6,7,8], ... [3*M-3 3*M-2 3*M-1]] \end{verbatim} \end{methoddesc} \section{Initial Conditions}\index{Initial Conditions} \label{sec:initial conditions} In standard usage of partial differential equations, initial conditions refers to the values associated to the system variables (the conserved quantities here) for \code{time = 0}. In setting up a scenario script as described in Sections \ref{sec:simpleexample} and \ref{sec:realdataexample}, \code{set_quantity} is used to define the initial conditions of variables other than the conserved quantities, such as friction. Here, we use the terminology of initial conditions to refer to initial values for variables which need prescription to solve the shallow water wave equation. Further, it must be noted that \code{set_quantity()} does not necessarily have to be used in the initial condition setting; it can be used at any time throughout the simulation. \begin{methoddesc}{\emph{}.set_quantity}{numeric=None, quantity=None, function=None, geospatial_data=None, filename=None, attribute_name=None, alpha=None, location='vertices', polygon=None, indices=None, smooth=False, verbose=False, use_cache=False} Module: \module{abstract_2d_finite_volumes.domain} \\ (This method passes off to \module{abstract_2d_finite_volumes.quantity.set_values()}) This function is used to assign values to individual quantities for a domain. It is very flexible and can be used with many data types: a statement of the form \code{\emph{}.set_quantity(name, x)} can be used to define a quantity having the name \code{name}, where the other argument \code{x} can be any of the following: \begin{itemize} \item a number, in which case all vertices in the mesh gets that for the quantity in question \item a list of numbers or a numeric array ordered the same way as the mesh vertices \item a function (e.g.\ see the samples introduced in Chapter 2) \item an expression composed of other quantities and numbers, arrays, lists (for example, a linear combination of quantities, such as \code{\emph{}.set_quantity('stage','elevation'+x))} \item the name of a file from which the data can be read. In this case, the optional argument \code{attribute_name} will select which attribute to use from the file. If left out, \code{set_quantity()} will pick one. This is useful in cases where there is only one attribute \item a geospatial dataset (See Section \ref{sec:geospatial}). Optional argument \code{attribute_name} applies here as with files \end{itemize} Exactly one of the arguments \code{numeric}, \code{quantity}, \code{function}, \code{geospatial_data} and \code{filename} must be present. \code{set_quantity()} will look at the type of the \code{numeric} and determine what action to take. Values can also be set using the appropriate keyword arguments. If \code{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)} are all equivalent. Other optional arguments are: \begin{itemize} \item \code{indices} which is a list of ids of triangles to which \code{set_quantity()} should apply its assignment of values. \item \code{location} determines which part of the triangles to assign to. Options are 'vertices' (the default), 'edges', 'unique vertices', and 'centroids'. If 'vertices' is used, edge and centroid values are automatically computed as the appropriate averages. This option ensures continuity of the surface. If, on the other hand, 'centroids' is used, vertex and edge values will be set to the same value effectively creating a piecewise constant surface with possible discontinuities at the edges. \end{itemize} \anuga provides a number of predefined initial conditions to be used with \code{set_quantity()}. See for example callable object \code{slump_tsunami} below. \end{methoddesc} \begin{methoddesc}{\emph{}.add_quantity}{numeric=None, quantity=None, function=None, geospatial_data=None, filename=None, attribute_name=None, alpha=None, location='vertices', polygon=None, indices=None, smooth=False, verbose=False, use_cache=False} Module: \module{abstract_2d_finite_volumes.domain} \\ (passes off to \module{abstract_2d_finite_volumes.domain.set_quantity()}) \label{add quantity} This function is used to \emph{add} values to individual quantities for a domain. It has the same syntax as \code{\emph{}.set_quantity(name, x)}. A typical use of this function is to add structures to an existing elevation model: \begin{verbatim} # Create digital elevation model from points file domain.set_quantity('elevation', filename='elevation_file.pts, verbose=True) # Add buildings from file building_polygons, building_heights = csv2building_polygons(building_file) B = [] for key in building_polygons: poly = building_polygons[key] elev = building_heights[key] B.append((poly, elev)) domain.add_quantity('elevation', Polygon_function(B, default=0.0)) \end{verbatim} \end{methoddesc} \begin{methoddesc}{\emph{}.set_region}{tag, quantity, X, location='vertices'} Module: \module{abstract_2d_finite_volumes.domain} \\ (see also \module{abstract_2d_finite_volumes.quantity.set_values}) This function is used to assign values to individual quantities given a regional tag. It is similar to \code{set_quantity()}. For example, if in the mesh-generator a regional tag of 'ditch' was used, \code{set_region()} can be used to set elevation of this region to -10m. \code{X} is the constant or function to be applied to the \code{quantity}, over the tagged region. \code{location} describes how the values will be applied. Options are 'vertices' (the default), 'edges', 'unique vertices', and 'centroids'. This method can also be called with a list of region objects. This is useful for adding quantities in regions, and having one quantity value based on another quantity. See \module{abstract_2d_finite_volumes.region} for more details. \end{methoddesc} \begin{funcdesc}{slump_tsunami}{length, depth, slope, width=None, thickness=None, radius=None, dphi=0.48, x0=0.0, y0=0.0, alpha=0.0, gravity=9.8, gamma=1.85, massco=1, dragco=1, frictionco=0, dx=None, kappa=3.0, kappad=1.0, zsmall=0.01, scale=None, domain=None, verbose=False} Module: \module{shallow\_water.smf} This function returns a callable object representing an initial water displacement generated by a submarine sediment failure. These failures can take the form of a submarine slump or slide. In the case of a slide, use \code{slide_tsunami} instead. \code{length} is the length of the slide or slump. \code{depth} is the water depth to the centre of the sediment mass. \code{slope} is the bathymetric slope. Other slump or slide parameters can be included if they are known. \end{funcdesc} \begin{funcdesc}{\emph{} = file_function}{filename, domain=None, quantities=None, interpolation_points=None, time_thinning=1, time_limit=None, verbose=False, use_cache=False, boundary_polygon=None} Module: \module{abstract_2d_finite_volumes.util} Reads the time history of spatial data for specified interpolation points from a NetCDF file and returns a callable object. Values returned from the \code{\emph{}} are interpolated values based on the input file using the underlying \code{interpolation_function}. \code{filename} is the name of the input file. This would be either an SWW, TMS or STS file. \code{quantities} is either the name of a single quantity to be interpolated or a list of such quantity names. In the second case, the resulting function will return a tuple of values -- one for each quantity. If the NetCDF file uses names other than 'stage', 'xmomentum', and 'ymomentum' the name(s) appearing in the file must be explicitly stated using the quantities keyword. This is for example be the case if a 'tms' file is used to specify time dependent precipitation. In this case the keyword might be called 'rainfall' both in the call to file\_function and in the 'tms' file. \code{interpolation_points} is a list of absolute coordinates or a geospatial object for points at which values are sought. \code{boundary_polygon} is a list of coordinates specifying the vertices of the boundary. This must be the same polygon as used when calling \code{create_mesh_from_regions()}. This argument can only be used when reading boundary data from an STS format file. The model time stored within the file function can be accessed using the method \code{\emph{}.get_time()} The underlying algorithm used is as follows:\\ Given a time series (i.e.\ a series of values associated with different times), whose values are either just numbers, a set of numbers defined at the vertices of a triangular mesh (such as those stored in SWW files) or a set of numbers defined at a number of points on the boundary (such as those stored in STS files), \code{Interpolation_function()} is used to create a callable object that interpolates a value for an arbitrary time \code{t} within the model limits and possibly a point \code{(x, y)} within a mesh region. The actual time series at which data is available is specified by means of an array \code{time} of monotonically increasing times. The quantities containing the values to be interpolated are specified in an array -- or dictionary of arrays (used in conjunction with the optional argument \code{quantity_names}) -- called \code{quantities}. The optional arguments \code{vertex_coordinates} and \code{triangles} represent the spatial mesh associated with the quantity arrays. If omitted the function must be created using an STS file or a TMS file. Since, in practice, values need to be computed at specified points, the syntax allows the user to specify, once and for all, a list \code{interpolation_points} of points at which values are required. In this case, the function may be called using the form \code{\emph{}(t, id)}, where \code{id} is an index for the list \code{interpolation_points}. \end{funcdesc} \begin{classdesc}{\emph{} = Interpolation_function}{time, quantities, quantity_names=None, vertex_coordinates=None, triangles=None, interpolation_points=None, time_thinning=1, verbose=False, gauge_neighbour_id=None} Module: \module{fit_interpolate.interpolate} Given a time series (i.e.\ a series of values associated with different times) whose values are either just numbers or a set of numbers defined at the vertices of a triangular mesh (such as those stored in SWW files), \code{Interpolation_function} is used to create a callable object that interpolates a value for an arbitrary time \code{t} within the model limits and possibly a point \code{(x, y)} within a mesh region. The actual time series at which data is available is specified by means of an array \code{time} of monotonically increasing times. The quantities containing the values to be interpolated are specified in an array -- or dictionary of arrays (used in conjunction with the optional argument \code{quantity\_names}) -- called \code{quantities}. The optional arguments \code{vertex_coordinates} and \code{triangles} represent the spatial mesh associated with the quantity arrays. If omitted the function created by \code{Interpolation_function} will be a function of \code{t} only. Since, in practice, values need to be computed at specified points, the syntax allows the user to specify, once and for all, a list \code{interpolation_points} of points at which values are required. In this case, the function may be called using the form \code{f(t, id)}, where \code{id} is an index for the list \code{interpolation_points}. \end{classdesc} \section{Boundary Conditions}\index{boundary conditions} \label{sec:boundary conditions} \anuga provides a large number of predefined boundary conditions, represented by objects such as \code{Reflective_boundary(domain)} and \code{Dirichlet_boundary([0.2, 0.0, 0.0])}, described in the examples in Chapter 2. Alternatively, you may prefer to ''roll your own'', following the method explained in Section \ref{sec:roll your own}. These boundary objects may be used with the function \code{set_boundary} described below to assign boundary conditions according to the tags used to label boundary segments. \begin{methoddesc}{\emph{}.set_boundary}{boundary_map} Module: \module{abstract_2d_finite_volumes.domain} This function allows you to assign a boundary object (corresponding to a pre-defined or user-specified boundary condition) to every boundary segment that has been assigned a particular tag. \code{boundary_map} is a dictionary of boundary objects keyed by symbolic tags. \end{methoddesc} \begin{methoddesc} {\emph{}.get_boundary_tags}{} Module: \module{abstract\_2d\_finite\_volumes.domain} Returns a list of the available boundary tags. \end{methoddesc} \subsection{Predefined boundary conditions} \begin{classdesc}{Reflective_boundary}{domain=None} Module: \module{shallow_water} Reflective boundary returns same conserved quantities as those present in the neighbouring volume but reflected. This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. \end{classdesc} \begin{classdesc}{Transmissive_boundary}{domain=None} \label{pg: transmissive boundary} Module: \module{abstract_2d_finite_volumes.generic_boundary_conditions} A transmissive boundary returns the same conserved quantities as those present in the neighbouring volume. The underlying domain must be specified when the boundary is instantiated. \end{classdesc} \begin{classdesc}{Dirichlet_boundary}{conserved_quantities=None} Module: \module{abstract_2d_finite_volumes.generic_boundary_conditions} A Dirichlet boundary returns constant values for each of conserved quantities. In the example of \code{Dirichlet_boundary([0.2, 0.0, 0.0])}, the \code{stage} value at the boundary is 0.2 and the \code{xmomentum} and \code{ymomentum} at the boundary are set to 0.0. The list must contain a value for each conserved quantity. \end{classdesc} \begin{classdesc}{Time_boundary}{domain=None, function=None, default_boundary=None, verbose=False} Module: \module{abstract_2d_finite_volumes.generic_boundary_conditions} A time-dependent boundary returns values for the conserved quantities as a function of time \code{function(t)}. The user must specify the domain to get access to the model time. Optional argument \code{default_boundary} can be used to specify another boundary object to be used in case model time exceeds the time available in the file used by \code{File_boundary}. The \code{default_boundary} could be a simple Dirichlet condition or even another \code{Time_boundary} typically using data pertaining to another time interval. \end{classdesc} \begin{classdesc}{File_boundary}{filename, domain, time_thinning=1, time_limit=None, boundary_polygon=None, default_boundary=None, use_cache=False, verbose=False} Module: \module{abstract_2d_finite_volumes.generic_boundary_conditions} This method may be used if the user wishes to apply a SWW file, STS file or a time series file (TMS) to a boundary segment or segments. The boundary values are obtained from a file and interpolated to the appropriate segments for each conserved quantity. Optional argument \code{default_boundary} can be used to specify another boundary object to be used in case model time exceeds the time available in the file used by \code{File_boundary}. The \code{default_boundary} could be a simple Dirichlet condition or even another \code{File_boundary} typically using data pertaining to another time interval. \end{classdesc} \begin{classdesc}{Field_boundary}{filename, domain, mean_stage=0.0, time_thinning=1, time_limit=None, boundary_polygon=None, default_boundary=None, use_cache=False, verbose=False} Module: \module{shallow_water.shallow_water_domain} This method works in the same way as \code{File_boundary} except that it allows for the value of stage to be offset by a constant specified in the keyword argument \code{mean_stage}. This functionality allows for models to be run for a range of tides using the same boundary information (from STS, SWW or TMS files). The tidal value for each run would then be specified in the keyword argument \code{mean_stage}. If \code{mean_stage} = 0.0, \code{Field_boundary} and \code{File_boundary} behave identically. Note that if the optional argument \code{default_boundary} is specified its stage value will be adjusted by \code{mean_stage} just like the values obtained from the file. See \code{File_boundary} for further details. \end{classdesc} \begin{classdesc}{Transmissive_momentum_set_stage_boundary}{domain=None, function=None} Module: \module{shallow_water.shallow_water_domain} \label{pg: transmissive momentum set stage boundary} This boundary returns the same momentum conserved quantities as those present in its neighbour volume but sets stage as in a \code{Time_boundary}. The underlying domain must be specified when boundary is instantiated. This type of boundary is useful when stage is known at the boundary as a function of time, but momenta (or speeds) aren't. This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. In some circumstances, this boundary condition may cause numerical instabilities for similar reasons as what has been observed with the simple fully transmissive boundary condition (see Page \pageref{pg: transmissive boundary}). This could for example be the case if a planar wave is reflected out through this boundary. \end{classdesc} \begin{classdesc}{Transmissive_stage_zero_momentum_boundary}{domain=None} Module: \module{shallow_water} \label{pg: transmissive stage zero momentum boundary} This boundary returns same stage conserved quantities as those present in its neighbour volume but sets momentum to zero. The underlying domain must be specified when boundary is instantiated This type of boundary is useful when stage is known at the boundary as a function of time, but momentum should be set to zero. This is for example the case where a boundary is needed in the ocean on the two sides perpendicular to the coast to maintain the wave height of the incoming wave. This class is specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. This boundary condition should not cause the numerical instabilities seen with the transmissive momentum boundary conditions (see Page \pageref{pg: transmissive boundary} and Page \pageref{pg: transmissive momentum set stage boundary}). \end{classdesc} \begin{classdesc}{Dirichlet_discharge_boundary}{domain=None, stage0=None, wh0=None} Module: \module{shallow_water.shallow_water_domain} \code{stage0} sets the stage. \code{wh0} sets momentum in the inward normal direction. \end{classdesc} \subsection{User-defined boundary conditions} \label{sec:roll your own} All boundary classes must inherit from the generic boundary class \code{Boundary} and have a method called \code{evaluate()} which must take as inputs \code{self}, \code{vol_id} and \code{edge_id} where \code{self} refers to the object itself and \code{vol_id} and \code{edge_id} are integers referring to particular edges. The method must return a list of three floating point numbers representing values for \code{stage}, \code{xmomentum} and \code{ymomentum}, respectively. The constructor of a particular boundary class may be used to specify particular values or flags to be used by the \code{evaluate()} method. Please refer to the source code for the existing boundary conditions for examples of how to implement boundary conditions. \section{Forcing Terms}\index{Forcing terms} \label{sec:forcing terms} \anuga provides a number of predefined forcing functions to be used with simulations. Gravity and friction are always calculated using the elevation and friction quantities, but the user may additionally add forcing terms to the list \code{domain.forcing_terms} and have them affect the model. Currently, predefined forcing terms are: \\ \begin{classdesc}{General_forcing}{domain, quantity_name, rate=0.0, center=None, radius=None, polygon=None, default_rate=None, verbose=False} Module: \module{shallow_water.shallow_water_domain} This is a general class to modify any quantity according to a given rate of change. Other specific forcing terms are based on this class but it can be used by itself as well (e.g.\ to modify momentum). \code{domain} is the domain being evolved. \code{quantity_name} is the name of the quantity that will be affected by this forcing term. \code{rate} is the rate at which the quantity should change. This can be either a constant or a function of time. Positive values indicate increases, negative values indicate decreases. The parameter \code{rate} can be \code{None} at initialisation but must be specified before a forcing term is applied (i.e.\ simulation has started). The default value is 0.0 -- i.e.\ no forcing. \code{center} and \code{ radius} optionally restrict forcing to a circle with given center and radius. \code{polygon} optionally restricts forcing to an area enclosed by the given polygon. Note: specifying \code{center}, \code{radius} and \code{polygon} will cause an exception to be thrown. Moreover, if the specified polygon or circle does not lie fully within the mesh boundary an Exception will be thrown. Example: \begin{verbatim} P = [[x0, y0], [x1, y0], [x1, y1], [x0, y1]] # Square polygon xmom = General_forcing(domain, 'xmomentum', polygon=P) ymom = General_forcing(domain, 'ymomentum', polygon=P) xmom.rate = f ymom.rate = g domain.forcing_terms.append(xmom) domain.forcing_terms.append(ymom) \end{verbatim} Here, \code{f} and \code{g} are assumed to be defined as functions of time providing a time dependent rate of change for xmomentum and ymomentum respectively. \code{P} is assumed to be the polygon, specified as a list of points. \end{classdesc} \begin{classdesc}{Inflow}{domain, rate=0.0, center=None, radius=None, polygon=None, default_rate=None, verbose=False} Module: \module{shallow_water.shallow_water_domain} This is a general class for inflow and abstraction of water according to a given rate of change. This class will always modify the \code{stage} quantity. Inflow is based on the \code{General_forcing} class so the functionality is similar. \code{domain} is the domain being evolved. \code{rate} is the flow rate ($m^3/s$) at which the quantity should change. This can be either a constant or a function of time. Positive values indicate inflow, negative values indicate outflow. Note: The specified flow will be divided by the area of the inflow region and then applied to update the stage quantity. \code{center} and \code{ radius} optionally restrict forcing to a circle with given center and radius. \code{polygon} optionally restricts forcing to an area enclosed by the given polygon. Example: \begin{verbatim} hydrograph = Inflow(center=(320, 300), radius=10, rate=file_function('QPMF_Rot_Sub13.tms')) domain.forcing_terms.append(hydrograph) \end{verbatim} Here, \code{'QPMF_Rot_Sub13.tms'} is assumed to be a NetCDF file in the TMS format defining a timeseries for a hydrograph. \end{classdesc} \begin{classdesc}{Rainfall}{domain, rate=0.0, center=None, radius=None, polygon=None, default_rate=None, verbose=False} Module: \module{shallow_water.shallow_water_domain} This is a general class for implementing rainfall over the domain, possibly restricted to a given circle or polygon. This class will always modify the \code{stage} quantity. Rainfall is based on the \code{General_forcing} class so the functionality is similar. \code{domain} is the domain being evolved. \code{rate} is the total rain rate over the specified domain. Note: Raingauge Data needs to reflect the time step. For example, if rain gauge is \code{mm} read every \code{dt} seconds, then the input here is as \code{mm/dt} so 10 mm in 5 minutes becomes 10/(5x60) = 0.0333mm/s. This parameter can be either a constant or a function of time. Positive values indicate rain being added (or be used for general infiltration), negative values indicate outflow at the specified rate (presumably this could model evaporation or abstraction). \code{center} and \code{ radius} optionally restrict forcing to a circle with given center and radius. \code{polygon} optionally restricts forcing to an area enclosed by the given polygon. Example: \begin{verbatim} catchmentrainfall = Rainfall(rate=file_function('Q100_2hr_Rain.tms')) domain.forcing_terms.append(catchmentrainfall) \end{verbatim} Here, \code{'Q100_2hr_Rain.tms'} is assumed to be a NetCDF file in the TMS format defining a timeseries for the rainfall. \end{classdesc} \begin{classdesc}{Culvert_flow}{domain, culvert_description_filename=None, culvert_routine=None, end_point0=None, end_point1=None, enquiry_point0=None, enquiry_point1=None, type='box', width=None, height=None, length=None, number_of_barrels=1, trigger_depth=0.01, manning=None, sum_loss=None, use_velocity_head=False, use_momentum_jet=False, label=None, description=None, update_interval=None, log_file=False, discharge_hydrograph=False, verbose=False} Module: \module{culvert_flows.culvert_class} This is a general class for implementing flow through a culvert. This class modifies the quantities \code{stage}, \code{xmomentum} and \code{ymomentum} in areas at both ends of the culvert. The \code{Culvert_flow} forcing term uses \code{Inflow} and \code{General_forcing} to update the quantities. The flow direction is determined on-the-fly so openings are referenced simple as opening0 and opening1 with either being able to take the role as Inflow or Outflow. The \code{Culvert_flow} class takes as input: \begin{itemize} \item \code{domain}: a reference to the domain being evolved \item \code{culvert_description_filename}: \item \code{culvert_routine}: \item \code{end_point0}: Coordinates of one opening \item \code{end_point1}: Coordinates of other opening \item \code{enquiry_point0}: \item \code{enquiry_point1}: \item \code{type}: (default is 'box') \item \code{width}: \item \code{height}: \item \code{length}: \item \code{number_of_barrels}: Number of identical pipes in the culvert (default is 1) \item \code{trigger_depth}: (default is 0.01) \item \code{manning}: Mannings Roughness for Culvert \item \code{sum_loss}: \item \code{use_velocity_head}: \item \code{use_momentum_jet}: \item \code{label}: Short text naming the culvert \item \code{description}: Text describing the culvert \item \code{update_interval}: \item \code{log_file}: \item \code{discharge_hydrograph}: \end{itemize} The user can specify different culvert routines. Hower \anuga currently provides only one, namely the \code{boyd_generalised_culvert_model} as used in the example below: \begin{verbatim} from anuga.culvert_flows.culvert_class import Culvert_flow from anuga.culvert_flows.culvert_routines import boyd_generalised_culvert_model culvert1 = Culvert_flow(domain, label='Culvert No. 1', description='This culvert is a test unit 1.2m Wide by 0.75m High', end_point0=[9.0, 2.5], end_point1=[13.0, 2.5], width=1.20, height=0.75, culvert_routine=boyd_generalised_culvert_model, number_of_barrels=1, verbose=True) culvert2 = Culvert_flow(domain, label='Culvert No. 2', description='This culvert is a circular test with d=1.2m', end_point0=[9.0, 1.5], end_point1=[30.0, 3.5], diameter=1.20, invert_level0=7, culvert_routine=boyd_generalised_culvert_model, number_of_barrels=1, verbose=True) domain.forcing_terms.append(culvert1) domain.forcing_terms.append(culvert2) \end{verbatim} \end{classdesc} \section{Evolution}\index{evolution} \label{sec:evolution} \begin{methoddesc}{\emph{}.evolve}{yieldstep=None, finaltime=None, duration=None, skip_initial_step=False} Module: \module{abstract_2d_finite_volumes.domain} This method is invoked once all the preliminaries have been completed, and causes the model to progress through successive steps in its evolution, storing results and outputting statistics whenever a user-specified period \code{yieldstep} is completed. Generally during this period the model will evolve through several steps internally as the method forces the water speed to be calculated on successive new cells. \code{yieldstep} is the interval in seconds between yields where results are stored, statistics written and the domain is inspected or possibly modified. If omitted an internal predefined \code{yieldstep} is used. Internally, smaller timesteps may be taken. \code{duration} is the duration of the simulation in seconds. \code{finaltime} is the time in seconds where simulation should end. This is currently relative time, so it's the same as \code{duration}. If both \code{duration} and \code{finaltime} are given an exception is thrown. \code{skip_initial_step} is a boolean flag that decides whether the first yield step is skipped or not. This is useful for example to avoid duplicate steps when multiple evolve processes are dove tailed. The code specified by the user in the block following the evolve statement is only executed once every \code{yieldstep} even though \anuga typically will take many more internal steps behind the scenes. You can include \method{evolve} in a statement of the type: \begin{verbatim} for t in domain.evolve(yieldstep, finaltime): \end{verbatim} \end{methoddesc} \subsection{Diagnostics} \label{sec:diagnostics} \begin{methoddesc}{\emph{}.statistics}{} Module: \module{abstract\_2d\_finite\_volumes.domain} Outputs statistics about the mesh within the \code{Domain}. \end{methoddesc} \begin{methoddesc}{\emph{}.timestepping_statistics}{track_speeds=False, triangle_id=None} Module: \module{abstract_2d_finite_volumes.domain} Returns a string of the following type for each timestep:\\ \code{Time = 0.9000, delta t in [0.00598964, 0.01177388], steps=12 (12)} Here the numbers in \code{steps=12 (12)} indicate the number of steps taken and the number of first-order steps, respectively. The optional keyword argument \code{track_speeds} will generate a histogram of speeds generated by each triangle if set to \code{True}. The speeds relate to the size of the timesteps used by \anuga and this diagnostics may help pinpoint problem areas where excessive speeds are generated. The optional keyword argument \code{triangle_id} can be used to specify a particular triangle rather than the one with the largest speed. \end{methoddesc} \begin{methoddesc}{\emph{}.boundary_statistics}{quantities=None, tags=None} Module: \module{abstract_2d_finite_volumes.domain} Generates output about boundary forcing at each timestep. \code{quantities} names the quantities to be reported -- may be \code{None}, a string or a list of strings. \code{tags} names the tags to be reported -- may be either None, a string or a list of strings. When \code{quantities = 'stage'} and \code{tags = ['top', 'bottom']} will return a string like: \begin{verbatim} Boundary values at time 0.5000: top: stage in [ -0.25821218, -0.02499998] bottom: stage in [ -0.27098821, -0.02499974] \end{verbatim} \end{methoddesc} \begin{methoddesc}{Q = \emph{}.get_quantity}{name, location='vertices', indices=None} Module: \module{abstract_2d_finite_volumes.domain} This function returns a Quantity object Q. Access to its values should be done through \code{Q.get_values()} documented on Page \pageref{pg:get values}. \code{name} is the name of the quantity to retrieve. \code{location} is \code{indices} is \end{methoddesc} \begin{methoddesc}{\emph{}.set_quantities_to_be_monitored}{quantity, polygon=None, time_interval=None} Module: \module{abstract\_2d\_finite\_volumes.domain} Selects quantities and derived quantities for which extrema attained at internal timesteps will be collected. \code{quantity} specifies the quantity or quantities to be monitored and must be either: \begin{itemize} \item the name of a quantity or derived quantity such as 'stage-elevation', \item a list of quantity names, or \item \code{None}. \end{itemize} \code{polygon} can be used to monitor only triangles inside the polygon. Otherwise all triangles will be included. \code{time_interval} will restrict monitoring to time steps in the interval. Otherwise all timesteps will be included. Information can be tracked in the evolve loop by printing \code{quantity_statistics} and collected data will be stored in the SWW file. \end{methoddesc} \begin{methoddesc}{\emph{}.quantity_statistics}{precision='\%.4f'} Module: \module{abstract_2d_finite_volumes.domain} Reports on extrema attained by selected quantities. Returns a string of the following type for each timestep: \begin{verbatim} Monitored quantities at time 1.0000: stage-elevation: values since time = 0.00 in [0.00000000, 0.30000000] minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333) maximum attained at time = 0.00000000, location = (0.83333333, 0.16666667) ymomentum: values since time = 0.00 in [0.00000000, 0.06241221] minimum attained at time = 0.00000000, location = (0.33333333, 0.16666667) maximum attained at time = 0.22472667, location = (0.83333333, 0.66666667) xmomentum: values since time = 0.00 in [-0.06062178, 0.47886313] minimum attained at time = 0.00000000, location = (0.16666667, 0.33333333) maximum attained at time = 0.35103646, location = (0.83333333, 0.16666667) \end{verbatim} The quantities (and derived quantities) listed here must be selected at model initialisation time using the method \code{domain.set_quantities_to_be_monitored()}. The optional keyword argument \code{precision='\%.4f'} will determine the precision used for floating point values in the output. This diagnostics helps track extrema attained by the selected quantities at every internal timestep. These values are also stored in the SWW file for post-processing. \end{methoddesc} \begin{methoddesc}{\emph{}.get_values}{interpolation_points=None, location='vertices', indices=None, use_cache=False, verbose=False} \label{pg:get values} Module: \module{abstract_2d_finite_volumes.quantity} Extract values for quantity as a numeric array. \code{interpolation_points} is a list of (x, y) coordinates where the value is sought (using interpolation). If \code{interpolation_points} is given, values for \code{location} and \code{indices} are ignored. Assume either an absolute UTM coordinates or geospatial data object. \code{location} specifies where values are to be stored. Permissible options are 'vertices', 'edges', 'centroids' or 'unique vertices'. The returned values will have the leading dimension equal to length of the \code{indices} list or N (all values) if \code{indices} is \code{None}. If \code{location} is 'centroids' the dimension of returned values will be a list or a numeric array of length N, N being the number of elements. If \code{location} is 'vertices' or 'edges' the dimension of returned values will be of dimension \code{Nx3}. If \code{location} is 'unique vertices' the average value at each vertex will be returned and the dimension of returned values will be a 1d array of length "number of vertices" \code{indices} is the set of element ids that the operation applies to. The values will be stored in elements following their internal ordering. \end{methoddesc} \begin{methoddesc}{\emph{}.set_values}{numeric=None, quantity=None, function=None, geospatial_data=None, filename=None, attribute_name=None, alpha=None, location='vertices', polygon=None, indices=None, smooth=False, verbose=False, use_cache=False} Module: \module{abstract_2d_finite_volumes.quantity} Assign values to a quantity object. This method works the same way as \code{set_quantity()} except that it doesn't take a quantity name as the first argument since it is applied directly to the quantity. Use \code{set_values} is used to assign values to a new quantity that has been created but which is not part of the domain's predefined quantities. \code{location} is ?? \code{indices} is ?? The method \code{set_values()} is always called by \code{set_quantity()} behind the scenes. \end{methoddesc} \begin{methoddesc}{\emph{}.get_integral}{} Module: \module{abstract_2d_finite_volumes.quantity} Return the computed integral over the entire domain for the quantity. \end{methoddesc} \begin{methoddesc}{\emph{}.get_maximum_value}{indices=None} Module: \module{abstract_2d_finite_volumes.quantity} Return the maximum value of a quantity (on centroids). \code{indices} is the optional set of element \code{id}s that the operation applies to. We do not seek the maximum at vertices as each vertex can have multiple values -- one for each triangle sharing it. \end{methoddesc} \begin{methoddesc}{\emph{}.get_maximum_location}{indices=None} Module: \module{abstract_2d_finite_volumes.quantity} Return the location of the maximum value of a quantity (on centroids). \code{indices} is the optional set of element \code{id}s that the operation applies to. We do not seek the maximum at vertices as each vertex can have multiple values -- one for each triangle sharing it. If there are multiple cells with the same maximum value, the first cell encountered in the triangle array is returned. \end{methoddesc} \begin{methoddesc}{\emph{}.get_wet_elements}{indices=None} Module: \module{shallow_water.shallow_water_domain} Returns the indices for elements where h $>$ minimum_allowed_height \code{indices} is the optional set of element \code{id}s that the operation applies to. \end{methoddesc} \begin{methoddesc}{\emph{}.get_maximum_inundation_elevation}{indices=None} Module: \module{shallow_water.shallow_water_domain} Return highest elevation where h $>$ 0. \code{indices} is the optional set of element \code{id}s that the operation applies to. Example to find maximum runup elevation: \begin{verbatim} z = domain.get_maximum_inundation_elevation() \end{verbatim} \end{methoddesc} \begin{methoddesc}{\emph{}.get_maximum_inundation_location}{indices=None} Module: \module{shallow_water.shallow_water_domain} Return location (x,y) of highest elevation where h $>$ 0. \code{indices} is the optional set of element \code{id}s that the operation applies to. Example to find maximum runup location: \begin{verbatim} x, y = domain.get_maximum_inundation_location() \end{verbatim} \end{methoddesc} \section{Queries of SWW model output files} After a model has been run, it is often useful to extract various information from the SWW output file (see Section \ref{sec:sww format}). This is typically more convenient than using the diagnostics described in Section \ref{sec:diagnostics} which rely on the model running -- something that can be very time consuming. The SWW files are easy and quick to read and offer information about the model results such as runup heights, time histories of selected quantities, flow through cross sections and much more. \begin{funcdesc}{elevation = get_maximum_inundation_elevation}{filename, polygon=None, time_interval=None, verbose=False} Module: \module{shallow_water.data_manager} Return the highest elevation where depth is positive ($h > 0$). \code{filename} is the path to a NetCDF SWW file containing \anuga model output. \code{polygon} restricts the query to the points that lie within the polygon. \code {time_interval} restricts the query to within the time interval. Example to find maximum runup elevation: \begin{verbatim} max_runup = get_maximum_inundation_elevation(filename) \end{verbatim} If no inundation is found (within the \code{polygon} and \code{time_interval}, if specified) the return value is \code{None}. This indicates "No Runup" or "Everything is dry". \end{funcdesc} \begin{funcdesc}{(x, y) = get_maximum_inundation_location}{filename, polygon=None, time_interval=None, verbose=False} Module: \module{shallow_water.data_manager} Return location (x,y) of the highest elevation where depth is positive ($h > 0$). \code{filename} is the path to a NetCDF SWW file containing \anuga model output. \code{polygon} restricts the query to the points that lie within the polygon. \code {time_interval} restricts the query to within the time interval. Example to find maximum runup location: \begin{verbatim} max_runup_location = get_maximum_inundation_location(filename) \end{verbatim} If no inundation is found (within the \code{polygon} and \code{time_interval}, if specified) the return value is \code{None}. This indicates "No Runup" or "Everything is dry". is \code{None}. This indicates "No Runup" or "Everything is dry". \end{funcdesc} \begin{funcdesc}{sww2timeseries}{swwfiles, gauge_filename, production_dirs, report=None, reportname=None, plot_quantity=None, generate_fig=False, surface=None, time_min=None, time_max=None, time_thinning=1, time_unit=None, title_on=None, use_cache=False, verbose=False} Module: \module{abstract_2d_finite_volumes.util} Read a set of SWW files and plot the time series for the prescribed quantities at defined gauge locations and prescribed time range. \code{swwfiles} is a dictionary of SWW files with keys of \code{label_id}. \code{gauge_filename} is the path to a file containing gauge data. THIS NEEDS MORE WORK. WORK ON FUNCTION __DOC__ STRING, IF NOTHING ELSE! \end{funcdesc} \begin{funcdesc}{(time, Q) = get_flow_through_cross_section}{filename, polyline, verbose=False} Module: \module{shallow_water.data_manager} Obtain flow ($m^3/s$) perpendicular to specified cross section. \code{filename} is the path to the SWW file. \code{polyline} is the representation of the desired cross section -- it may contain multiple sections allowing for complex shapes. Assumes absolute UTM coordinates. Returns a tuple \code{time, Q} where: \code{time} is all the stored times in the SWW file. \code{Q} is a hydrograph of total flow across the given segments for all stored times. The normal flow is computed for each triangle intersected by the \code{polyline} and added up. If multiple segments at different angles are specified the normal flows may partially cancel each other. Example to find flow through cross section: \begin{verbatim} cross_section = [[x, 0], [x, width]] time, Q = get_flow_through_cross_section(filename, cross_section) \end{verbatim} \end{funcdesc} \section{Other} \begin{methoddesc}{quantity = \emph{}.create_quantity_from_expression}{string} Module: \module{abstract_2d_finite_volumes.domain} Create a new quantity from other quantities in the domain using an arbitrary expression. \code{string} is a string containing an arbitrary quantity expression. Returns the new \code{Quantity} object. Handy for creating derived quantities on-the-fly: \begin{verbatim} Depth = domain.create_quantity_from_expression('stage-elevation') exp = '(xmomentum*xmomentum + ymomentum*ymomentum)**0.5' Absolute_momentum = domain.create_quantity_from_expression(exp) \end{verbatim} %See also \file{Analytical_solution_circular_hydraulic_jump.py} for an example. \end{methoddesc} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{\anuga System Architecture} \section{File Formats} \label{sec:file formats} \anuga makes use of a number of different file formats. The following table lists all these formats, which are described in more detail in the paragraphs below. \begin{center} \begin{tabular}{|ll|} \hline \textbf{Extension} & \textbf{Description} \\ \hline\hline \code{.sww} & NetCDF format for storing model output with mesh information \code{f(t,x,y)}\\ \code{.sts} & NetCDF format for storing model ouput \code{f(t,x,y)} without mesh information\\ \code{.tms} & NetCDF format for storing time series \code{f(t)}\\ \code{.csv/.txt} & ASCII format for storing arbitrary points and associated attributes\\ \code{.pts} & NetCDF format for storing arbitrary points and associated attributes\\ \code{.asc} & ASCII format of regular DEMs as output from ArcView\\ \code{.prj} & Associated ArcView file giving more metadata for \code{.asc} format\\ \code{.ers} & ERMapper header format of regular DEMs for ArcView\\ \code{.dem} & NetCDF representation of regular DEM data\\ \code{.tsh} & ASCII format for storing meshes and associated boundary and region info\\ \code{.msh} & NetCDF format for storing meshes and associated boundary and region info\\ \code{.nc} & Native ferret NetCDF format\\ \code{.geo} & Houdinis ASCII geometry format (?) \\ \par \hline \end{tabular} \end{center} The above table shows the file extensions used to identify the formats of files. However, typically, in referring to a format we capitalise the extension and omit the initial full stop -- thus, we refer to 'SWW files' or 'PRJ files', not 'sww files' or '.prj files'. \bigskip A typical dataflow can be described as follows: SOMETHING MISSING HERE!? \subsection{Manually Created Files} \begin{tabular}{ll} ASC, PRJ & Digital elevation models (gridded)\\ NC & Model outputs for use as boundary conditions (e.g.\ from MOST) \end{tabular} \subsection{Automatically Created Files} \begin{tabular}{ll} ASC, PRJ $\rightarrow$ DEM $\rightarrow$ PTS & Convert DEMs to native \code{.pts} file\\ NC $\rightarrow$ SWW & Convert MOST boundary files to boundary \code{.sww}\\ PTS + TSH $\rightarrow$ TSH with elevation & Least squares fit\\ TSH $\rightarrow$ SWW & Convert TSH to \code{.sww}-viewable using \code{animate}\\ TSH + Boundary SWW $\rightarrow$ SWW & Simulation using \code{\anuga}\\ Polygonal mesh outline $\rightarrow$ & TSH or MSH \end{tabular} \bigskip \subsection{SWW, STS and TMS Formats} \label{sec:sww format} The SWW, STS and TMS formats are all NetCDF formats and are of key importance for \anuga. An SWW file is used for storing \anuga output and therefore pertains to a set of points and a set of times at which a model is evaluated. It contains, in addition to dimension information, the following variables: \begin{itemize} \item \code{x} and \code{y}: coordinates of the points, represented as numeric arrays \item \code{elevation}: a numeric array storing bed-elevations \item \code{volumes}: a list specifying the points at the vertices of each of the triangles % Refer here to the example to be provided in describing the simple example \item \code{time}: a numeric array containing times for model evaluation \end{itemize} The contents of an SWW file may be viewed using the anuga viewer \code{animate}, which creates an on-screen visialisation. See section \ref{sec:animate} (page \pageref{sec:animate}) in Appendix \ref{ch:supportingtools} for more on \code{animate}. Alternatively, there are tools, such as \code{ncdump}, that allow you to convert a NetCDF file into a readable format such as the Class Definition Language (CDL). The following is an excerpt from a CDL representation of the output file \file{runup.sww} generated from running the simple example \file{runup.py} of Chapter \ref{ch:getstarted}: %FIXME (Ole): Should put in example with nonzero xllcorner, yllcorner \verbatiminput{examples/bedslopeexcerpt.cdl} The SWW format is used not only for output but also serves as input for functions such as \function{file\_boundary} and \function{file\_function}, described in Chapter \ref{ch:interface}. An STS file is used for storing a set of points and associated times. It contains, in addition to dimension information, the following variables: \begin{itemize} \item \code{x} and \code{y}: coordinates of the points, represented as numeric arrays \item \code{permutation}: Original indices of the points as specified by the optional \code{ordering_file} (see the function \code{urs2sts()} in Section \ref{sec:basicfileconversions}) \item \code{elevation}: a numeric array storing bed-elevations % Refer here to the example to be provided in describing the simple example \item \code{time}: a numeric array containing times for model evaluation \end{itemize} The only difference between the STS format and the SWW format is the former does not contain a list specifying the points at the vertices of each of the triangles (\code{volumes}). Consequently information (arrays) stored within an STS file such as \code{elevation} can be accessed in exactly the same way as it would be extracted from an SWW file. A TMS file is used to store time series data that is independent of position. \subsection{Mesh File Formats} A mesh file is a file that has a specific format suited to triangular meshes and their outlines. A mesh file can have one of two formats: it can be either a TSH file, which is an ASCII file, or an MSH file, which is a NetCDF file. A mesh file can be generated from the function \function{create_mesh_from_regions()} (see Section \ref{sec:meshgeneration}) and be used to initialise a domain. A mesh file can define the outline of the mesh -- the vertices and line segments that enclose the region in which the mesh is created -- and the triangular mesh itself, which is specified by listing the triangles and their vertices, and the segments, which are those sides of the triangles that are associated with boundary conditions. In addition, a mesh file may contain 'holes' and/or 'regions'. A hole represents an area where no mesh is to be created, while a region is a labelled area used for defining properties of a mesh, such as friction values. A hole or region is specified by a point and bounded by a number of segments that enclose that point. A mesh file can also contain a georeference, which describes an offset to be applied to $x$ and $y$ values -- e.g.\ to the vertices. \subsection{Formats for Storing Arbitrary Points and Attributes} A CSV/TXT file is used to store data representing arbitrary numerical attributes associated with a set of points. The format for an CSV/TXT file is:\\ \\ first line: \code{[column names]}\\ other lines: \code{[x value], [y value], [attributes]}\\ for example: \begin{verbatim} x, y, elevation, friction 0.6, 0.7, 4.9, 0.3 1.9, 2.8, 5.0, 0.3 2.7, 2.4, 5.2, 0.3 \end{verbatim} The delimiter is a comma. The first two columns are assumed to be $x$ and $y$ coordinates. A PTS file is a NetCDF representation of the data held in an points CSV file. If the data is associated with a set of $N$ points, then the data is stored using an $N \times 2$ numeric array of float variables for the points and an $N \times 1$ numeric array for each attribute. \subsection{ArcView Formats} Files of the three formats ASC, PRJ and ERS are all associated with data from ArcView. An ASC file is an ASCII representation of DEM output from ArcView. It contains a header with the following format: \begin{tabular}{l l} \code{ncols} & \code{753}\\ \code{nrows} & \code{766}\\ \code{xllcorner} & \code{314036.58727982}\\ \code{yllcorner} & \code{6224951.2960092}\\ \code{cellsize} & \code{100}\\ \code{NODATA_value} & \code{-9999} \end{tabular} The remainder of the file contains the elevation data for each grid point in the grid defined by the above information. A PRJ file is an ArcView file used in conjunction with an ASC file to represent metadata for a DEM. \subsection{DEM Format} A DEM file in \anuga is a NetCDF representation of regular DEM data. \subsection{Other Formats} \subsection{Basic File Conversions} \label{sec:basicfileconversions} \begin{funcdesc}{sww2dem}{(basename_in, basename_out=None, quantity=None, reduction=None, cellsize=10, number_of_decimal_places=None, NODATA_value=-9999, easting_min=None, easting_max=None, northing_min=None, northing_max=None, verbose=False, origin=None, datum='WGS84', format='ers', block_size=None} Module: \module{shallow_water.data_manager} Takes data from an SWW file \code{basename_in} and converts it to DEM format (ASC or ERS) of a desired grid size \code{cellsize} in metres. The user can select how many decimal places the output data is represented with by using \code{number_of_decimal_places}, with the default being 3. The $easting$ and $northing$ values are used if the user wishes to determine the output within a specified rectangular area. The \code{reduction} input refers to a function to reduce the quantities over all time step of the SWW file, e.g.\ maximum, or an index referring to a time-step to extract a time-slice of data. \end{funcdesc} \begin{funcdesc}{dem2pts}{basename_in, basename_out=None, easting_min=None, easting_max=None, northing_min=None, northing_max=None, use_cache=False, verbose=False} Module: \module{shallow\_water.data\_manager} Takes DEM data (a NetCDF file representation of data from a regular Digital Elevation Model) and converts it to PTS format. \end{funcdesc} \begin{funcdesc}{urs2sts}{basename_in, basename_out=None, weights=None, verbose=False, origin=None,mean_stage=0.0, zscale=1.0, ordering_filename=None} Module: \module{shallow\_water.data\_manager} Takes URS data (timeseries data in mux2 format) and converts it to STS format. The optional filename \code{ordering\_filename} specifies the permutation of indices of points to select along with their longitudes and latitudes. This permutation will also be stored in the STS file. If absent, all points are taken and the permutation will be trivial, i.e.\ $0, 1, \ldots, N-1$, where $N$ is the total number of points stored. \end{funcdesc} \begin{funcdesc}{csv2building\_polygons}{file\_name, floor\_height=3} Module: \module{shallow\_water.data\_manager} Convert CSV files of the form: \begin{verbatim} easting,northing,id,floors 422664.22,870785.46,2,0 422672.48,870780.14,2,0 422668.17,870772.62,2,0 422660.35,870777.17,2,0 422664.22,870785.46,2,0 422661.30,871215.06,3,1 422667.50,871215.70,3,1 422668.30,871204.86,3,1 422662.21,871204.33,3,1 422661.30,871215.06,3,1 \end{verbatim} to a dictionary of polygons with \code{id} as key. The associated number of \code{floors} are converted to m above MSL and returned as a separate dictionary also keyed by \code{id}. Optional parameter \code{floor_height} is the height of each building story. These can e.g.\ be converted to a \code{Polygon_function} for use with \code{add_quantity} as shown on page \pageref{add quantity}. \end{funcdesc} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{\anuga mathematical background} \label{cd:mathematical background} \section{Introduction} This chapter outlines the mathematics underpinning \anuga. \section{Model} \label{sec:model} The shallow water wave equations are a system of differential conservation equations which describe the flow of a thin layer of fluid over terrain. The form of the equations are: \[ \frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial x}+\frac{\partial \GG}{\partial y}=\SSS \] where $\UU=\left[ {{\begin{array}{*{20}c} h & {uh} & {vh} \\ \end{array} }} \right]^T$ is the vector of conserved quantities; water depth $h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities entering the system are bed elevation $z$ and stage (absolute water level) $w$, where the relation $w = z + h$ holds true at all times. The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given by \[ \EE=\left[ {{\begin{array}{*{20}c} {uh} \hfill \\ {u^2h+gh^2/2} \hfill \\ {uvh} \hfill \\ \end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c} {vh} \hfill \\ {vuh} \hfill \\ {v^2h+gh^2/2} \hfill \\ \end{array} }} \right] \] and the source term (which includes gravity and friction) is given by \[ \SSS=\left[ {{\begin{array}{*{20}c} 0 \hfill \\ -{gh(z_{x} + S_{fx} )} \hfill \\ -{gh(z_{y} + S_{fy} )} \hfill \\ \end{array} }} \right] \] where $S_f$ is the bed friction. The friction term is modelled using Manning's resistance law \[ S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy} =\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}} \] in which $\eta$ is the Manning resistance coefficient. The model does not currently include consideration of kinematic viscosity or dispersion. As demonstrated in our papers, \cite{ZR1999,nielsen2005} these equations and their implementation in \anuga provide a reliable model of general flows associated with inundation such as dam breaks and tsunamis. \section{Finite Volume Method} \label{sec:fvm} We use a finite-volume method for solving the shallow water wave equations \cite{ZR1999}. The study area is represented by a mesh of triangular cells as in Figure~\ref{fig:mesh} in which the conserved quantities of water depth $h$, and horizontal momentum $(uh, vh)$, in each volume are to be determined. The size of the triangles may be varied within the mesh to allow greater resolution in regions of particular interest. \begin{figure}[htp] \begin{center} \includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-five} \caption{Triangular mesh used in our finite volume method. Conserved quantities $h$, $uh$ and $vh$ are associated with the centroid of each triangular cell.} \label{fig:mesh} \end{center} \end{figure} The equations constituting the finite-volume method are obtained by integrating the differential conservation equations over each triangular cell of the mesh. Introducing some notation we use $i$ to refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the set of indices referring to the cells neighbouring the $i$th cell. Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is the length of the edge between the $i$th and $j$th cells. By applying the divergence theorem we obtain for each volume an equation which describes the rate of change of the average of the conserved quantities within each cell, in terms of the fluxes across the edges of the cells and the effect of the source terms. In particular, rate equations associated with each cell have the form $$ \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i $$ where \begin{itemize} \item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell, \item $\SSS_i$ is the source term associated with the $i$th cell, and \item $\HH_{ij}$ is the outward normal flux of material across the \textit{ij}th edge. \end{itemize} %\item $l_{ij}$ is the length of the edge between the $i$th and $j$th %cells %\item $m_{ij}$ is the midpoint of %the \textit{ij}th edge, %\item %$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing %normal along the \textit{ij}th edge, and The The flux $\HH_{ij}$ is evaluated using a numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$ $$ H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 . $$ Then $$ \HH_{ij} = \HH(\UU_i(m_{ij}), \UU_j(m_{ij}); \mathbf{n}_{ij}) $$ where $m_{ij}$ is the midpoint of the \textit{ij}th edge and $\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the \textit{ij}th edge. The function $\UU_i(x)$ for $x \in T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and neighbouring cells. We use a second order reconstruction to produce a piece-wise linear function construction of the conserved quantities for all $x \in T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}). This function is allowed to be discontinuous across the edges of the cells, but the slope of this function is limited to avoid artificially introduced oscillations. Godunov's method (see \cite{Toro1992}) involves calculating the numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly solving the corresponding one dimensional Riemann problem normal to the edge. We use the central-upwind scheme of \cite{KurNP2001} to calculate an approximation of the flux across each edge. \begin{figure}[htp] \begin{center} \includegraphics[width=8.0cm,keepaspectratio=true]{graphics/step-reconstruct} \caption{From the values of the conserved quantities at the centroid of the cell and its neighbouring cells, a discontinuous piecewise linear reconstruction of the conserved quantities is obtained.} \label{fig:mesh:reconstruct} \end{center} \end{figure} In the computations presented in this paper we use an explicit Euler time stepping method with variable timestepping adapted to the observed CFL condition: \begin{equation} \Delta t = \min_{k,i=[0,1,2]} \min \left( \frac{r_k}{v_{k,i}}, \frac{r_{n_{k,i}}}{v_{k,i}} \right ) \label{eq:CFL condition} \end{equation} where $r_k$ is the radius of the $k$'th triangle and $v_{k,i}$ is the maximal velocity across edge joining triangle $k$ and it's $i$'th neighbour, triangle $n_{k,i}$, as calculated by the numerical flux function using the central upwind scheme of \cite{KurNP2001}. The symbol $r_{n_{k,i}}$ denotes the radius of the $i$'th neighbour of triangle $k$. The radii are calculated as radii of the inscribed circles of each triangle. \section{Flux limiting} The shallow water equations are solved numerically using a finite volume method on an unstructured triangular grid. The upwind central scheme due to Kurganov and Petrova is used as an approximate Riemann solver for the computation of inviscid flux functions. This makes it possible to handle discontinuous solutions. To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary we employ a new flux limiter that ensures that unphysical fluxes are never encounted. Let $u$ and $v$ be the velocity components in the $x$ and $y$ direction, $w$ the absolute water level (stage) and $z$ the bed elevation. The latter are assumed to be relative to the same height datum. The conserved quantities tracked by \anuga are momentum in the $x$-direction ($\mu = uh$), momentum in the $y$-direction ($\nu = vh$) and depth ($h = w-z$). The flux calculation requires access to the velocity vector $(u, v)$ where each component is obtained as $u = \mu/h$ and $v = \nu/h$ respectively. In the presence of very small water depths, these calculations become numerically unreliable and will typically cause unphysical speeds. We have employed a flux limiter which replaces the calculations above with the limited approximations. \begin{equation} \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h}, \end{equation} where $h_0$ is a regularisation parameter that controls the minimal magnitude of the denominator. Taking the limits we have for $\hat{u}$ \[ \lim_{h \rightarrow 0} \hat{u} = \lim_{h \rightarrow 0} \frac{\mu}{h + h_0/h} = 0 \] and \[ \lim_{h \rightarrow \infty} \hat{u} = \lim_{h \rightarrow \infty} \frac{\mu}{h + h_0/h} = \frac{\mu}{h} = u \] with similar results for $\hat{v}$. The maximal value of $\hat{u}$ is attained when $h+h_0/h$ is minimal or (by differentiating the denominator) \[ 1 - h_0/h^2 = 0 \] or \[ h_0 = h^2 \] \anuga has a global parameter $H_0$ that controls the minimal depth which is considered in the various equations. This parameter is typically set to $10^{-3}$. Setting \[ h_0 = H_0^2 \] provides a reasonable balance between accurracy and stability. In fact, setting $h=H_0$ will scale the predicted speed by a factor of $0.5$: \[ \left[ \frac{\mu}{h + h_0/h} \right]_{h = H_0} = \left[ \frac{\mu}{H_0 + H_0^2/H_0} \right] = \frac{\mu}{2 H_0} = \frac{\mu}{2 h} = \frac{u}{2} \] In general, for multiples of the minimal depth $N H_0$ one obtains \begin{equation} \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} = \frac{\mu}{N H_0 + H_0/N} = \frac{\mu}{h (1 + 1/N^2)} \label{eq:flux limit multiple} \end{equation} which converges quadratically to the true value with the multiple N. Although this equation can be used for any depth, we have restricted its use to depths less than $10 * H_0$ (or 1 cm) to computational resources. According to Equation \ref{eq:flux limit multiple} this cutoff affects the calculated velocity by less than 1 \%. %The developed numerical model has been applied to several test cases %as well as to real flows. numeric tests prove the robustness and accuracy of the model. \section{Slope limiting} A 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. However 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. Let $w, z, h$ be the stage, bed elevation and depth at the centroid and let $w_i, z_i, h_i$ be the stage, bed elevation and depth at vertex $i$. Define the minimal depth across all vertices as $\hmin$ as \[ \hmin = \min_i h_i \] Let $\tilde{w_i}$ be the stage obtained from a gradient limiter limiting on stage only. The corresponding depth is then defined as \[ \tilde{h_i} = \tilde{w_i} - z_i \] We would use this limiter in deep water which we will define (somewhat boldly) as \[ \hmin \ge \epsilon \] Similarly, let $\bar{w_i}$ be the stage obtained from a gradient limiter limiting on depth respecting the bed slope. The corresponding depth is defined as \[ \bar{h_i} = \bar{w_i} - z_i \] We introduce the concept of a balanced stage $w_i$ which is obtained as the linear combination \[ w_i = \alpha \tilde{w_i} + (1-\alpha) \bar{w_i} \] or \[ w_i = z_i + \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} \] where $\alpha \in [0, 1]$. Since $\tilde{w_i}$ is obtained in 'deep' water where the bedslope is ignored we have immediately that \[ \alpha = 1 \mbox{ for } \hmin \ge \epsilon %or dz=0 \] %where the maximal bed elevation range $dz$ is defined as %\[ % dz = \max_i |z_i - z| %\] If $\hmin < \epsilon$ we want to use the 'shallow' limiter just enough that no negative depths occur. Formally, we will require that \[ \alpha \tilde{h_i} + (1-\alpha) \bar{h_i} > \epsilon, \forall i \] or \begin{equation} \alpha(\tilde{h_i} - \bar{h_i}) > \epsilon - \bar{h_i}, \forall i \label{eq:limiter bound} \end{equation} There are two cases: \begin{enumerate} \item $\bar{h_i} \le \tilde{h_i}$: The deep water (limited using stage) vertex is at least as far away from the bed than the shallow water (limited using depth). In this case we won't need any contribution from $\bar{h_i}$ and can accept any $\alpha$. E.g.\ $\alpha=1$ reduces Equation \ref{eq:limiter bound} to \[ \tilde{h_i} > \epsilon \] whereas $\alpha=0$ yields \[ \bar{h_i} > \epsilon \] all well and good. \item $\bar{h_i} > \tilde{h_i}$: In this case the the deep water vertex is closer to the bed than the shallow water vertex or even below the bed. In this case we need to find an $\alpha$ that will ensure a positive depth. Rearranging Equation \ref{eq:limiter bound} and solving for $\alpha$ one obtains the bound \[ \alpha < \frac{\epsilon - \bar{h_i}}{\tilde{h_i} - \bar{h_i}}, \forall i \] \end{enumerate} Ensuring Equation \ref{eq:limiter bound} holds true for all vertices one arrives at the definition \[ \alpha = \min_{i} \frac{\bar{h_i} - \epsilon}{\bar{h_i} - \tilde{h_i}} \] which will guarantee that no vertex 'cuts' through the bed. Finally, should $\bar{h_i} < \epsilon$ and therefore $\alpha < 0$, we suggest setting $\alpha=0$ and similarly capping $\alpha$ at 1 just in case. %Furthermore, %dropping the $\epsilon$ ensures that alpha is always positive and also %provides a numerical safety {??) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Basic \anuga Assumptions} \section{Time} Physical model time cannot be earlier than 1 Jan 1970 00:00:00. If one wished to recreate scenarios prior to that date it must be done using some relative time (e.g.\ 0). The \anuga domain has an attribute \code{starttime} which is used in cases where the simulation should be started later than the beginning of some input data such as those obtained from boundaries or forcing functions (hydrographs, file_boundary etc). The \code{domain.startime} may be adjusted in \code{file_boundary} in the case the input data does not itself start until a later time. \section{Spatial data} \subsection{Projection} All spatial data relates to the WGS84 datum (or GDA94) and assumes a projection into UTM with false easting of 500000 and false northing of 1000000 on the southern hemisphere (0 on the northern hemisphere). All locations must consequently be specified in Cartesian coordinates (eastings, northings) or (x,y) where the unit is metres. Alternative projections can be used, but \anuga does have the concept of a UTM zone that must be the same for all coordinates in the model. \subsection{Internal coordinates} It is important to realise that for numerical precision \anuga uses coordinates that are relative to the lower left node of the rectangle containing the mesh ($x_{\mbox{min}}$, $y_{\mbox{min}}$). This origin is referred to internally as \code{xllcorner}, \code{yllcorner} following the ESRI ASCII grid notation. The SWW file format also includes \code{xllcorner}, \code{yllcorner} and any coordinate in the file should be adjusted by adding this origin. See Section \ref{sec:sww format}. Throughout the \anuga interface, functions have optional boolean arguments \code{absolute} which controls whether spatial data received is using the internal representation (\code{absolute=False}) or the user coordinate set (\code{absolute=True}). See e.g.\ \code{get_vertex_coordinates()} on \pageref{pg:get vertex coordinates}. DEMs, meshes and boundary conditions can have different origins. However, the internal representation in \anuga will use the origin of the mesh. \subsection{Polygons} When generating a mesh it is assumed that polygons do not cross. Having polygons that cross can cause bad meshes to be produced or the mesh generation itself may fail. %OLD %The dataflow is: (See data_manager.py and from scenarios) % % %Simulation scenarios %--------------------% %% % %Sub directories contain scrips and derived files for each simulation. %The directory ../source_data contains large source files such as %DEMs provided externally as well as MOST tsunami simulations to be used %as boundary conditions. % %Manual steps are: % Creation of DEMs from argcview (.asc + .prj) % Creation of mesh from pmesh (.tsh) % Creation of tsunami simulations from MOST (.nc) %% % %Typical scripted steps are% % % prepare_dem.py: Convert asc and prj files supplied by arcview to % native dem and pts formats% % % prepare_pts.py: Convert netcdf output from MOST to an SWW file suitable % as boundary condition% % % prepare_mesh.py: Merge DEM (pts) and mesh (tsh) using least squares % smoothing. The outputs are tsh files with elevation data.% % % run_simulation.py: Use the above together with various parameters to % run inundation simulation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \appendix \chapter{Supporting Tools} \label{ch:supportingtools} This section describes a number of supporting tools, supplied with \anuga, that offer a variety of types of functionality and can enhance the basic capabilities of \anuga. \section{caching} \label{sec:caching} The \code{cache} function is used to provide supervised caching of function results. A Python function call of the form: \begin{verbatim} result = func(arg1, ..., argn) \end{verbatim} can be replaced by: \begin{verbatim} from caching import cache result = cache(func,(arg1, ..., argn)) \end{verbatim} which returns the same output but reuses cached results if the function has been computed previously in the same context. \code{result} and the arguments can be simple types, tuples, list, dictionaries or objects, but not unhashable types such as functions or open file objects. The function \code{func} may be a member function of an object or a module. This type of caching is particularly useful for computationally intensive functions with few frequently used combinations of input arguments. Note that if the inputs or output are very large caching may not save time because disc access may dominate the execution time. If the function definition changes after a result has been cached, this will be detected by examining the functions bytecode and the function will be recomputed. However, caching will not detect changes in modules used by \code{func}. In this case the cache must be cleared manually. Options are set by means of the function \code{set_option(key, value)}, where \code{key} is a key associated with a Python dictionary \code{options}. This dictionary stores settings such as the name of the directory used, the maximum number of cached files allowed, and so on. The \code{cache} function allows the user also to specify a list of dependent files. If any of these have been changed, the function is recomputed and the results stored again. %Other features include support for compression and a capability to \ldots USAGE: \nopagebreak \begin{verbatim} result = cache(func, args, kwargs, dependencies, cachedir, verbose, compression, evaluate, test, return_filename) \end{verbatim} \pagebreak \section{anuga\_viewer} \label{sec:animate} The output generated by \anuga may be viewed by means of the visualisation tool \code{anuga\_viewer}, which takes an SWW file generated by \anuga and creates a visual representation of the data. Examples may be seen in Figures \ref{fig:runupstart} and \ref{fig:runup2}. To view an SWW file with \code{anuga\_viewer} in the Windows environment you have to run it in a command line as in \begin{verbatim} anuga_viewer \end{verbatim} or if a georeferenced tif file (or jpg cut to the same shape as the domain) is needed \begin{verbatim} anuga_viewer \end{verbatim} %, you can simply drag the %icon representing the file over an icon on the desktop for the %\code{anuga\_viewer} executable file (or a shortcut to it), or set up a %file association to make files with the extension \code{.sww} open %with \code{animate}. Alternatively, you can operate \code{animate} %from the command line. %% \pagebreak %% \section{\anuga viewer -- animate} %% \label{sec:animate} %% The output generated by \anuga may be viewed by %% means of the visualisation tool \code{animate}, which takes an %% SWW file generated by \anuga and creates a visual representation %% of the data. Examples may be seen in Figures \ref{fig:runupstart} %% and \ref{fig:runup2}. To view an SWW file with %% \code{animate} in the Windows environment, you can simply drag the %% icon representing the file over an icon on the desktop for the %% \code{animate} executable file (or a shortcut to it), or set up a %% file association to make files with the extension \code{.sww} open %% with \code{animate}. Alternatively, you can operate \code{animate} %% from the command line. %% Upon starting the viewer, you will see an interactive moving-picture %% display. You can use the keyboard and mouse to slow down, speed up or %% stop the display, change the viewing position or carry out a number %% of other simple operations. Help is also displayed when you press %% the \code{h} key. %% The main keys operating the interactive screen are: %% \begin{center} %% \begin{tabular}{|ll|} \hline %% \code{h} & toggle on-screen help display \\ %% \code{w} & toggle wireframe \\ %% space bar & start/stop\\ %% up/down arrows & increase/decrease speed\\ %% left/right arrows & direction in time \emph{(when running)}\\ %% & step through simulation \emph{(when stopped)}\\ %% left mouse button & rotate\\ %% middle mouse button & pan\\ %% right mouse button & zoom\\ \hline %% \end{tabular} %% \end{center} %% % \vfill %% The following describes how to operate \code{animate} from the command line: %% Usage: \code{animate [options] swwfile \ldots}\\ \nopagebreak %% where: \\ \nopagebreak %% \begin{tabular}{ll} %% \code{--display } & \code{MONITOR | POWERWALL | REALITY\_CENTER |}\\ %% & \code{HEAD\_MOUNTED\_DISPLAY}\\ %% \code{--rgba} & Request a RGBA colour buffer visual\\ %% \code{--stencil} & Request a stencil buffer visual\\ %% \code{--stereo} & Use default stereo mode which is \code{ANAGLYPHIC} if not \\ %% & overridden by environmental variable\\ %% \code{--stereo } & \code{ANAGLYPHIC | QUAD\_BUFFER | HORIZONTAL\_SPLIT |}\\ %% & \code{VERTICAL\_SPLIT | LEFT\_EYE | RIGHT\_EYE |}\\ %% & \code{ON | OFF} \\ %% \code{-alphamax } & Maximum transparency clamp value\\ %% \code{-alphamin } & Transparency value at \code{hmin}\\ %% \code{-cullangle } & Cull triangles steeper than this value\\ %% \code{-help} & Display this information\\ %% \code{-hmax } & Height above which transparency is set to %% \code{alphamax}\\ %% \code{-hmin } & Height below which transparency is set to %% zero\\ %% \code{-lightpos ,,} & $x,y,z$ of bedslope directional light ($z$ is %% up, default is overhead)\\ %% \code{-loop} & Repeated (looped) playback of \code{.swm} files\\ %% \code{-movie } & Save numbered images to named directory and %% quit\\ %% \code{-nosky} & Omit background sky\\ %% \code{-scale } & Vertical scale factor\\ %% \code{-texture } & Image to use for bedslope topography\\ %% \code{-tps } & Timesteps per second\\ %% \code{-version} & Revision number and creation (not compile) %% date\\ %% \end{tabular} \pagebreak \section{utilities/polygons} \declaremodule{standard}{utilities.polygon} \refmodindex{utilities.polygon} \begin{classdesc}{ = Polygon_function}{regions, default=0.0, geo_reference=None} Module: \code{utilities.polygon} Creates a callable object that returns one of a specified list of values when evaluated at a point \code{(x, y)}, depending on which polygon, from a specified list of polygons, the point belongs to. \code{regions} is a list of pairs \code{(P, v)}, where each \code{P} is a polygon and each \code{v} is either a constant value or a function of coordinates \code{x} and \code{y}, specifying the return value for a point inside \code{P}. \code{default} may be used to specify a value (or a function) for a point not lying inside any of the specified polygons. When a point lies in more than one polygon, the return value is taken to be the value for whichever of these polygon appears later in the list. %FIXME (Howard): CAN x, y BE VECTORS? \code{geo_reference} refers to the status of points that are passed into the function. Typically they will be relative to some origin. Typical usage may take the form: \begin{verbatim} set_quantity('elevation', Polygon_function([(P1, v1), (P2, v2)], default=v3, geo_reference=domain.geo_reference)) \end{verbatim} \end{classdesc} \begin{funcdesc}{ = read_polygon}{filename, split=','} Module: \code{utilities.polygon} Reads the specified file and returns a polygon. Each line of the file must contain exactly two numbers, separated by a delimiter, which are interpreted as coordinates of one vertex of the polygon. \code{filename} is the path to the file to read. \code{split} sets the delimiter character between the numbers on one line of the file. If not specified, the delimiter is the ',' character. \end{funcdesc} \label{ref:function_populate_polygon} \begin{funcdesc}{populate_polygon}{polygon, number_of_points, seed=None, exclude=None} Module: \code{utilities.polygon} Populates the interior of the specified polygon with the specified number of points, selected by means of a uniform distribution function. \code{polygon} is the polygon to populate. \code{number_of_points} is the (optional) number of points. \code{seed}is the optional seed for random number generator. \code{exclude} is a list of polygons (inside main polygon) from where points should be excluded. \end{funcdesc} \label{ref:function_point_in_polygon} \begin{funcdesc}{ = point_in_polygon}{polygon, delta=1e-8} Module: \code{utilities.polygon} Returns a point inside the specified polygon and close to the edge. The distance between the returned point and the nearest point of the polygon is less than $\sqrt{2}$ times the second argument \code{delta}, which is taken as $10^{-8}$ by default. \end{funcdesc} \label{ref:function_inside_polygon} \begin{funcdesc}{ = inside_polygon}{points, polygon, closed=True, verbose=False} Module: \code{utilities.polygon} Get a set of points that lie inside a given polygon. \code{points} is the list of points to test. \code{polygon} is the polygon to test the points against. \code{closed} specifies if points on the polygon edge are considered to be inside or outside the polygon -- \code{True} means they are inside. Returns a numeric array comprising the indices of the points in the list that lie inside the polygon. If none of the points are inside, returns \code{zeros((0,), 'l') (ie, an empty numeric array)}. Compare with \code{outside_polygon()}, page \pageref{ref:function_outside_polygon}. \end{funcdesc} \label{ref:function_outside_polygon} \begin{funcdesc}{ = outside_polygon}{points, polygon, closed=True, verbose=False} Module: \code{utilities.polygon} Get a set of points that lie outside a given polygon. \code{points} is the list of points to test. \code{polygon} is the polygon to test the points against. \code{closed} specifies if points on the polygon edge are considered to be outside or inside the polygon -- \code{True} means they are outside. Returns a numeric array comprising the indices of the points in the list that lie outside the polygon. If none of the points are outside, returns \code{zeros((0,), 'l')} (ie, an empty numeric array). Compare with \code{inside_polygon()}, page \pageref{ref:function_inside_polygon}. \end{funcdesc} \label{ref:function_is_inside_polygon} \begin{funcdesc}{ = is_inside_polygon}{point, polygon, closed=True, verbose=False} Module: \code{utilities.polygon} Determines if a single point is inside a polygon. \code{point} is the point to test. \code{polygon} is the polygon to test \code{point} against. \code{closed} is a flag that forces the function to consider a point on the polygon edge to be inside or outside -- if \code{True} a point on the edge is considered inside the polygon. Returns \code{True} if \code{point} is inside \code{polygon}. Compare with \code{inside_polygon()}, page \pageref{ref:function_inside_polygon}. \end{funcdesc} \label{ref:function_is_outside_polygon} \begin{funcdesc}{ = is_outside_polygon}{point, polygon, closed=True, verbose=False, % points_geo_ref=None, polygon_geo_ref=None } Module: \code{utilities.polygon} Determines if a single point is outside a polygon. \code{point} is the point to test. \code{polygon} is the polygon to test \code{point} against. \code{closed} is a flag that forces the function to consider a point on the polygon edge to be outside or inside -- if \code{True} a point on the edge is considered inside the polygon. %\code{points_geo_ref} is ?? % %\code{polygon_geo_ref} is ?? Compare with \code{outside_polygon()}, page \pageref{ref:function_outside_polygon}. \end{funcdesc} \label{ref:function_point_on_line} \begin{funcdesc}{ = point_on_line}{point, line, rtol=1.0e-5, atol=1.0e-8} Module: \code{utilities.polygon} Determine if a point is on a line to some tolerance. The line is considered to extend past its end-points. \code{point} is the point to test ([$x$, $y$]). \code{line} is the line to test \code{point} against ([[$x1$,$y1$], [$x2$,$y2$]]). \code{rtol} is the relative tolerance to use when testing for coincidence. \code{atol} is the absolute tolerance to use when testing for coincidence. Returns \code{True} if the point is on the line, else \code{False}. \end{funcdesc} \label{ref:function_separate_points_by_polygon} \begin{funcdesc}{(indices, count) = separate_points_by_polygon}{points, polygon, closed=True, check_input=True, verbose=False} \indexedcode{separate_points_by_polygon} Module: \code{utilities.polygon} Separate a set of points into points that are inside and outside a polygon. \code{points} is a list of points to separate. \code{polygon} is the polygon used to separate the points. \code{closed} determines whether points on the polygon edge should be regarded as inside or outside the polygon. \code{True} means they are inside. \code{check_input} specifies whether the input parameters are checked -- \code{True} means check the input parameters. The function returns a tuple \code{(indices, count)} where \code{indices} is a list of point $indices$ from the input \code{points} list, with the indices of points inside the polygon at the left and indices of points outside the polygon listed at the right. The \code{count} value is the count (from the left) of the indices of the points $inside$ the polygon. \end{funcdesc} \begin{funcdesc}{ = polygon_area}{polygon} Module: \code{utilities.polygon} Returns area of an arbitrary polygon (reference http://mathworld.wolfram.com/PolygonArea.html). \end{funcdesc} \begin{funcdesc}{[$x_{min}$, $x_{max}$, $y_{min}$, $y_{max}$] = plot_polygons} {polygons_points, style=None, figname=None, label=None, verbose=False} Module: \code{utilities.polygon} Plot a list of polygons to a file. \code{polygons_points} is a list of polygons to plot. \code{style} is a list of style strings to be applied to the corresponding polygon in \code{polygons_points}. A polygon can be closed for plotting purposes by assigning the style string 'line' to it in the appropriate place in the \code{style} list. The default style is 'line'. \code{figname} is the path to the file to save the plot in. If not specified, use \file{test_image.png}. The function returns a list containing the minimum and maximum of the points in all the input polygons, i.e.\ \code{[$x_{min}$, $x_{max}$, $y_{min}$, $y_{max}$]}. \end{funcdesc} \pagebreak \section{coordinate_transforms} \pagebreak \section{geospatial_data} \label{sec:geospatial} This describes a class that represents arbitrary point data in UTM coordinates along with named attribute values. %FIXME (Ole): This gives a LaTeX error %\declaremodule{standard}{geospatial_data} %\refmodindex{geospatial_data} \begin{classdesc}{Geospatial_data} {data_points=None, attributes=None, geo_reference=None, default_attribute_name=None, file_name=None, latitudes=None, longitudes=None, points_are_lats_longs=False, max_read_lines=None, load_file_now=True, verbose=False} Module: \code{geospatial_data.geospatial_data} This class is used to store a set of data points and associated attributes, allowing these to be manipulated by methods defined for the class. The data points are specified either by reading them from a NetCDF or CSV file, identified through the parameter \code{file_name}, or by providing their \code{x}- and \code{y}-coordinates in metres, either as a sequence of 2-tuples of floats or as an $M \times 2$ numeric array of floats, where $M$ is the number of points. Coordinates are interpreted relative to the origin specified by the object \code{geo_reference}, which contains data indicating the UTM zone, easting and northing. If \code{geo_reference} is not specified, a default is used. Attributes are specified through the parameter \code{attributes}, set either to a list or array of length $M$ or to a dictionary whose keys are the attribute names and whose values are lists or arrays of length $M$. One of the attributes may be specified as the default attribute, by assigning its name to \code{default_attribute_name}. If no value is specified, the default attribute is taken to be the first one. Note that the \code{Geospatial_data} object currently reads entire datasets into memory i.e.\ no memomry blocking takes place. For this we refer to the \code{set_quantity()} method which will read PTS and CSV files into \anuga using memory blocking allowing large files to be used. \end{classdesc} \begin{methoddesc}{\emph{}.import_points_file} {file_name, delimiter=None, verbose=False} Module: \code{geospatial_data.geospatial_data} Import a TXT, CSV or PTS points data file into a code{Geospatial_data} object. \code{file_name} is the path to a TXT, CSV or PTS points data file. \code{delimiter} is currently unused. \end{methoddesc} \begin{methoddesc}{\emph{}.export_points_file}{file_name, absolute=True, as_lat_long=False, isSouthHemisphere=True} Module: \code{geospatial_data.geospatial_data} Export a CSV or PTS points data file from a \code{Geospatial_data} object. \code{file_name} is the path to the CSV or PTS points file to write. \code{absolute} determines if the exported data is absolute or relative to the \code{Geospatial_data} object geo_reference. If \code{True} the exported data is absolute. \code{as_lat_long} exports the points data as latitudes and longitudes if \code{True}. \code{isSouthHemisphere} has effect only if \code{as_lat_long} is \code{True} and causes latitude/longitude values to be for the southern (\code{True}) or northern hemispheres (\code{False}). \end{methoddesc} \begin{methoddesc}{points = \emph{}.get_data_points} {absolute=True, geo_reference=None, as_lat_long=False, isSouthHemisphere=True} Module: \code{geospatial_data.geospatial_data} Get the coordinates for all the data points as an $N \times 2$ array. \code{absolute} determines if the exported data is absolute or relative to the \code{Geospatial_data} object geo_reference. If \code{True} the exported data is absolute. \code{geo_reference} is the geo_reference the points are relative to, if supplied. \code{as_lat_long} exports the points data as latitudes and longitudes if \code{True}. \code{isSouthHemisphere} has effect only if \code{as_lat_long} is \code{True} and causes latitude/longitude values to be for the southern (\code{True}) or northern hemispheres (\code{False}). \end{methoddesc} \begin{methoddesc}{\emph{}.set_attributes}{attributes} Module: \code{geospatial_data.geospatial_data} Set the attributes for a \code{Geospatial_data} object. \code{attributes} is the new value for the object's attributes. May be a dictionary or \code{None}. \end{methoddesc} \begin{methoddesc}{atributes = \emph{}.get_attributes}{attribute_name=None} Module: \code{geospatial_data.geospatial_data} Get a named attribute from a \code{Geospatial_data} object. \code{attribute_name} is the name of the desired attribute. If \code{None}, return the default attribute. \end{methoddesc} \begin{methoddesc}{\emph{}.get_all_attributes}{} Module: \code{geospatial_data.geospatial_data} Get all attributes of a \code{Geospatial_data} object. Returns \code{None} or the attributes dictionary (which may be empty). \end{methoddesc} \begin{methoddesc}{\emph{}.set_default_attribute_name}{default_attribute_name} Module: \code{geospatial_data.geospatial_data} Set the default attribute name of a \code{Geospatial_data} object. \code{default_attribute_name} is the new default attribute name. \end{methoddesc} \begin{methoddesc}{\emph{}.set_geo_reference}{geo_reference} Module: \code{geospatial_data.geospatial_data} Set the internal geo_reference of a \code{Geospatial_data} object. \code{geo_reference} is the new internal geo_reference for the object. If \code{None} will use the default geo_reference. If the \code{Geospatial_data} object already has an internal geo_reference then the points data will be changed to use the new geo_reference. \end{methoddesc} \begin{methoddesc}{\emph{}.__add__}{other} Module: \code{geospatial_data.geospatial_data} The \code{__add__()} method is defined so it is possible to add two \code{Geospatial_data} objects. \end{methoddesc} \label{ref:function_clip} \begin{methoddesc}{geospatial = \emph{}.clip}{polygon, closed=True, verbose=False} Module: \code{geospatial_data.geospatial_data} Clip a \code{Geospatial_data} object with a polygon. \code{polygon} is the polygon to clip the \code{Geospatial_data} object with. This may be a list of points, an $N \times 2$ array or a \code{Geospatial_data} object. \code{closed} determines whether points on the \code{polygon} edge are inside (\code{True}) or outside (\code{False}) the polygon. Returns a new \code{Geospatial_data} object representing points inside the Compare with \code{clip_outside()}, page \pageref{ref:function_clip_outside}. specified polygon. \end{methoddesc} \label{ref:function_clip_outside} \begin{methoddesc}{geospatial = \emph{}.clip_outside} {polygon, closed=True, verbose=False} Module: \code{geospatial_data.geospatial_data} Clip a \code{Geospatial_data} object with a polygon. \code{polygon} is the polygon to clip the \code{Geospatial_data} object with. This may be a list of points, an $N \times 2$ array or a \code{Geospatial_data} object. \code{closed} determines whether points on the \code{polygon} edge are inside (\code{True}) or outside (\code{False}) the polygon. Returns a new \code{Geospatial_data} object representing points outside the specified polygon. Compare with \code{clip()}, page \pageref{ref:function_clip}. \end{methoddesc} \begin{methoddesc}{(g1, g2) = \emph{}.split} {factor=0.5, seed_num=None, verbose=False} Module: \code{geospatial_data.geospatial_data} Split a \code{Geospatial_data} object into two objects of predetermined ratios. \code{factor} is the ratio of the size of the first returned object to the original object. If '0.5' is supplied, the two resulting objects will be of equal size. \code{seed_num}, if supplied, will be the random number generator seed used for the split. Points of the two new geospatial_data object are selected RANDOMLY. Returns two geospatial_data objects that are disjoint sets of the original. \end{methoddesc} \subsection{Miscellaneous Functions} The functions here are not \code{Geospatial_data} object methods, but are used with them. \begin{methoddesc}{X = find_optimal_smoothing_parameter} {data_file, alpha_list=None, mesh_file=None, boundary_poly=None, mesh_resolution=100000, north_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} Module: \code{geospatial_data.geospatial_data} Calculate the minimum covariance from a set of points in a file. It does this by removing a small random sample of points from \code{data_file} and creating models with different alpha values from \code{alpha_list} and cross validates the predicted value to the previously removed point data. Returns the alpha value which has the smallest covariance. \code{data_file} is the input data file and must not contain points outside the boundaries defined and is either a PTS, TXT or CSV file. \code{alpha_list} is the list of alpha values to use. \code{mesh_file} is the path to a mesh file to create (if supplied). If \code{None} a mesh file will be created (named \file{temp.msh}). NOTE: if there is a \code{mesh_resolution} defined or any boundaries are defined, any input \code{mesh_file} value is ignored. \code{mesh_resolution} is the maximum area size for a triangle. \code{north_boundary}\\ \code{south_boundary}\\ \code{east_boundary}\\ \code{west_boundary} are the boundary values to use. \code{plot_name} is the path name of the plot file to write. \code{seed_num} is the random number generator seed to use. The function returns a tuple \code{(min_covar, alpha)} where \code{min_covar} is the minumum normalised covariance and \code{alpha} is the alpha value that created it. A plot file is also written. This is an example of function usage: \nopagebreak \begin{verbatim} convariance_value, alpha = $\backslash$ find_optimal_smoothing_parameter(data_file=fileName, alpha_list=[0.0001, 0.01, 1], mesh_file=None, mesh_resolution=3, north_boundary=5, south_boundary=-5, east_boundary=5, west_boundary=-5, plot_name='all_alphas', seed_num=100000, verbose=False) \end{verbatim} NOTE: The function will not work if the \code{data_file} extent is greater than the \code{boundary_poly} polygon or any of the boundaries, e.g.\ \code{north_boundary}, etc. \end{methoddesc} \pagebreak \section{Graphical Mesh Generator GUI} The program \code{graphical_mesh_generator.py} in the \code{pmesh} module allows the user to set up the mesh of the problem interactively. It can be used to build the outline of a mesh or to visualise a mesh automatically generated. Graphical Mesh Generator will let the user select various modes. The current allowable modes are $vertex$, $segment$, $hole$ or $region$. The mode describes what sort of object is added or selected in response to mouse clicks. When changing modes any prior selected objects become deselected. In general the left mouse button will add an object and the right mouse button will select an object. A selected object can de deleted by pressing the the middle mouse button (scroll bar). \pagebreak \section{class Alpha_Shape} \emph{Alpha shapes} are used to generate close-fitting boundaries around sets of points. The alpha shape algorithm produces a shape that approximates to the 'shape formed by the points' -- or the shape that would be seen by viewing the points from a coarse enough resolution. For the simplest types of point sets, the alpha shape reduces to the more precise notion of the convex hull. However, for many sets of points the convex hull does not provide a close fit and the alpha shape usually fits more closely to the original point set, offering a better approximation to the shape being sought. In \anuga, an alpha shape is used to generate a polygonal boundary around a set of points before mesh generation. The algorithm uses a parameter $\alpha$ that can be adjusted to make the resultant shape resemble the shape suggested by intuition more closely. An alpha shape can serve as an initial boundary approximation that the user can adjust as needed. The following paragraphs describe the class used to model an alpha shape and some of the important methods and attributes associated with instances of this class. \label{class:alpha_shape} \begin{classdesc}{Alpha_Shape}{points, alpha=None} Module: \code{alpha_shape} Instantiate an instance of the \code{Alpha_Shape} class. \code{points} is an $N \times 2$ list of points (\code{[[x1, y1],[x2, y2]}\ldots\code{]}). \code{alpha} is the 'fitting' parameter. \end{classdesc} \begin{funcdesc}{alpha_shape_via_files}{point_file, boundary_file, alpha= None} Module: \code{alpha_shape} This function reads points from the specified point file \code{point_file}, computes the associated alpha shape (either using the specified value for \code{alpha} or, if no value is specified, automatically setting it to an optimal value) and outputs the boundary to a file named \code{boundary_file}. This output file lists the coordinates \code{(x, y)} of each point in the boundary, using one line per point. \end{funcdesc} \label{ref:method_set_boundary_type} \begin{methoddesc}{\emph{}.set_boundary_type} {raw_boundary=True, remove_holes=False, smooth_indents=False, expand_pinch=False, boundary_points_fraction=0.2} Module: \code{alpha_shape} This function sets internal state that controls how the \code{Alpha_shape} boundary is presented or exported. \code{raw_boundary} sets the type to $raw$ if \code{True}, i.e.\ the regular edges of the alpha shape. \code{remove_holes}, if \code{True} removes small holes ('small' is defined by \code{boundary_points_fraction}). \code{smooth_indents}, if \code{True} removes sharp triangular indents in the boundary. \code{expand_pinch}, if \code{True} tests for pinch-off and corrects -- preventing a boundary vertex from having more than two edges. \end{methoddesc} \label{ref:method_get_boundary} \begin{methoddesc}{boundary = \emph{}.get_boundary}{} Module: \code{alpha_shape} Returns a list of tuples representing the boundary of the alpha shape. Each tuple represents a segment in the boundary by providing the indices of its two endpoints. See \code{set_boundary_type()}, page \pageref{ref:method_set_boundary_type}. \end{methoddesc} \label{ref:method_write_boundary} \begin{methoddesc}{\emph{}.write_boundary}{file_name} Module: \code{alpha_shape} Writes the list of 2-tuples returned by \code{get_boundary()} to the file \code{file_name}, using one line per tuple. See \code{set_boundary_type()}, page \pageref{ref:method_set_boundary_type}. \\ See \code{get_boundary()}, page \pageref{ref:method_get_boundary}. \end{methoddesc} \pagebreak \section{Numerical Tools} The following table describes some useful numerical functions that may be found in the module \module{utilities.numerical\_tools}: \begin{tabular}{|p{7.4cm} p{8.6cm}|} \hline \code{angle(v1, v2=None)} & Angle between two-dimensional vectors \code{v1} and \code{v2}, or between \code{v1} and the $x$-axis if \code{v2} is \code{None}. Value is in range $0$ to $2\pi$. \\ & \\ \code{normal\_vector(v)} & Normal vector to \code{v}.\\ & \\ \code{mean(x)} & Mean value of a vector \code{x}.\\ & \\ \code{cov(x, y=None)} & Covariance of vectors \code{x} and \code{y}. If \code{y} is \code{None}, returns \code{cov(x, x)}.\\ & \\ \code{err(x, y=0, n=2, relative=True)} & Relative error of $\parallel$\code{x}$-$\code{y}$\parallel$ to $\parallel$\code{y}$\parallel$ (2-norm if \code{n} = 2 or Max norm if \code{n} = \code{None}). If denominator evaluates to zero or if \code{y} is omitted or if \code{relative=False}, absolute error is returned.\\ & \\ \code{norm(x)} & 2-norm of \code{x}.\\ & \\ \code{corr(x, y=None)} & Correlation of \code{x} and \code{y}. If \code{y} is \code{None} returns autocorrelation of \code{x}.\\ & \\ \code{ensure\_numeric(A, typecode=None)} & Returns a numeric array for any sequence \code{A}. If \code{A} is already a numeric array it will be returned unaltered. Otherwise, an attempt is made to convert it to a numeric array. (Needed because \code{array(A)} can cause memory overflow.)\\ & \\ \code{histogram(a, bins, relative=False)} & Standard histogram. If \code{relative} is \code{True}, values will be normalised against the total and thus represent frequencies rather than counts.\\ & \\ \code{create\_bins(data, number\_of\_bins=None)} & Safely create bins for use with histogram. If \code{data} contains only one point or is constant, one bin will be created. If \code{number\_of\_bins} is omitted, 10 bins will be created.\\ \hline \end{tabular} \section{Finding the Optimal Alpha Value} The function ???? more to come very soon %?% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %?% %?% \chapter{Modules available in \anuga} %?% %?% %?% %abstract_2d_finite_volumes %?% %?% \section{\module{abstract_2d_finite_volumes.domain}} %?% Generic module for 2D triangular domains for finite-volume computations of conservation laws %?% \declaremodule[domain]{}{domain} %?% \label{mod:domain} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.ermapper_grids}} %?% \declaremodule[ermappergrids]{}{ermapper_grids} %?% \label{mod:ermapper_grids} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.general_mesh} } %?% \declaremodule[generalmesh]{}{general_mesh} %?% \label{mod:general_mesh} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.generic_boundary_conditions} } %?% \declaremodule[genericboundaryconditions]{}{generic_boundary_conditions} %?% \label{mod:generic_boundary_conditions} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.mesh_factory} } %?% \declaremodule[meshfactory]{}{mesh_factory} %?% \label{mod:mesh_factory} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.mesh_factory} } %?% \declaremodule[meshfactory]{}{mesh_factory} %?% \label{mod:mesh_factory} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.neighbour_mesh} } %?% \declaremodule[neighbourmesh]{}{neighbour_mesh} %?% \label{mod:neighbour_mesh} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.pmesh2domain} } %?% \declaremodule[pmesh2domain]{}{pmesh2domain} %?% \label{mod:pmesh2domain} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.quantity}} %?% \declaremodule{}{quantity} %?% \label{mod:quantity} %?% %?% \begin{verbatim} %?% Class Quantity - Implements values at each triangular element %?% %?% To create: %?% %?% Quantity(domain, vertex_values) %?% %?% domain: Associated domain structure. Required. %?% %?% vertex_values: Nx3 array of values at each vertex for each element. %?% Default None %?% %?% If vertex_values are None Create array of zeros compatible with domain. %?% Otherwise check that it is compatible with dimenions of domain. %?% Otherwise raise an exception %?% \end{verbatim} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.region} } %?% \declaremodule[region]{}{region} %?% \label{mod:region} %?% %?% %?% \section{\module{abstract_2d_finite_volumes.util} } %?% \declaremodule[util]{}{util} %?% \label{mod:util} %?% %?% %?% advection %?% alpha_shape %?% caching %?% coordinate_transforms %?% culvert_flows %?% damage_modelling %?% euler %?% fit_interpolate %?% geospatial_data %?% lib %?% load_mesh %?% mesh_engine %?% pmesh %?% SConstruct %?% shallow_water %?% utilities %?% %?% %?% \section{\module{shallow\_water}} %?% %?% 2D triangular domains for finite-volume %?% computations of the shallow water wave equation. %?% This module contains a specialisation of class Domain from module domain.py consisting of methods specific to the Shallow Water %?% Wave Equation %?% %?% \declaremodule[shallowwater]{}{shallow\_water} %?% \label{mod:shallowwater} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{\anuga Full-scale Validations} \section{Overview} There are some long-running validations that are not included in the small-scale validations that run when you execute the \module{validate_all.py} script in the \module{anuga_validation/automated_validation_test} directory. These validations are not run automatically since they can take a large amount of time and require an internet connection and user input. \section{Patong Beach} The Patong Beach validation is run from the \module{automated_validation_tests/patong_beach_validation} directory. Just execute the \module{validate_patong.py} script in that directory. This will run a Patong Beach simulation and compare the generated SWW file with a known good copy of that file. The script attempts to refresh the validation data files from master copies held on the Sourceforge project site. If you don't have an internet connection you may still run the validation, as long as you have the required files. You may download the validation data files by hand and then run the validation. Just go to the \anuga Sourceforge project download page at \module{http://sourceforge.net/project/showfiles.php?group_id=172848} and select the \module{validation_data} package, \module{patong-1.0} release. You need the \module{data.tgz} file and one or more of the \module{patong.sww.\{BASIC|TRIAL|FINAL\}.tgz} files. The BASIC validation is the quickest and the FINAL validation is the slowest. The \module{validate.py} script will use whatever files you have, BASIC first and FINAL last. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Frequently Asked Questions} The Frequently Asked Questions have been move to the online FAQ at: \\ \url{https://datamining.anu.edu.au/anuga/wiki/FrequentlyAskedQuestions} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Glossary} \begin{tabular}{|lp{10cm}|c|} \hline \emph{Term} & \emph{Definition} & \emph{Page}\\ \hline \indexedbold{\anuga} & Name of software (joint development between ANU and GA) & \pageref{def:anuga}\\ \indexedbold{bathymetry} & offshore elevation & \\ \indexedbold{conserved quantity} & conserved (stage, x and y momentum) & \\ % \indexedbold{domain} & The domain of a function is the set of all input values to the function.& \\ \indexedbold{Digital Elevation Model (DEM)} & DEMs are digital files consisting of points of elevations, sampled systematically at equally spaced intervals.& \\ \indexedbold{Dirichlet boundary} & A boundary condition imposed on a differential equation that specifies the values the solution is to take on the boundary of the domain. & \pageref{def:dirichlet boundary}\\ \indexedbold{edge} & A triangular cell within the computational mesh can be depicted as a set of vertices joined by lines (the edges). & \\ \indexedbold{elevation} & refers to bathymetry and topography & \\ \indexedbold{evolution} & integration of the shallow water wave equations over time & \\ \indexedbold{finite volume method} & The method evaluates the terms in the shallow water wave equation as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. & \\ \indexedbold{forcing term} & &\\ \indexedbold{flux} & the amount of flow through the volume per unit time & \\ \indexedbold{grid} & Evenly spaced mesh & \\ \indexedbold{latitude} & The angular distance on a mericlear north and south of the equator, expressed in degrees and minutes. & \\ \indexedbold{longitude} & The angular distance east or west, between the meridian of a particular place on Earth and that of the Prime Meridian (located in Greenwich, England) expressed in degrees or time.& \\ \indexedbold{Manning friction coefficient} & &\\ \indexedbold{mesh} & Triangulation of domain &\\ \indexedbold{mesh file} & A TSH or MSH file & \pageref{def:mesh file}\\ \indexedbold{NetCDF} & &\\ \indexedbold{node} & A point at which edges meet & \\ \indexedbold{northing} & A rectangular (x,y) coordinate measurement of distance north from a north-south reference line, usually a meridian used as the axis of origin within a map zone or projection. Northing is a UTM (Universal Transverse Mercator) coordinate. & \\ \indexedbold{points file} & A PTS or CSV file & \\ \hline \end{tabular} \begin{tabular}{|lp{10cm}|c|} \hline \indexedbold{polygon} & A sequence of points in the plane. \anuga represents a polygon either as a list consisting of Python tuples or lists of length 2 or as an $N \times 2$ numeric array, where $N$ is the number of points. The unit square, for example, would be represented either as \code{[ [0,0], [1,0], [1,1], [0,1] ]} or as \code{array( [0,0], [1,0], [1,1], [0,1] )}. NOTE: For details refer to the module \module{utilities/polygon.py}. & \\ \indexedbold{resolution} & The maximal area of a triangular cell in a mesh & \\ \indexedbold{reflective boundary} & Models a solid wall. Returns same conserved quantities as those present in the neighbouring volume but reflected. Specific to the shallow water equation as it works with the momentum quantities assumed to be the second and third conserved quantities. & \pageref{def:reflective boundary}\\ \indexedbold{stage} & &\\ % \indexedbold{try this} \indexedbold{animate} & visualisation tool used with \anuga & \pageref{sec:animate}\\ \indexedbold{time boundary} & Returns values for the conserved quantities as a function of time. The user must specify the domain to get access to the model time. & \pageref{def:time boundary}\\ \indexedbold{topography} & onshore elevation &\\ \indexedbold{transmissive boundary} & & \pageref{def:transmissive boundary}\\ \indexedbold{vertex} & A point at which edges meet. & \\ \indexedbold{xmomentum} & conserved quantity (note, two-dimensional SWW equations say only \code{x} and \code{y} and NOT \code{z}) &\\ \indexedbold{ymomentum} & conserved quantity & \\ \hline \end{tabular} %The \code{\e appendix} markup need not be repeated for additional %appendices. % % The ugly "%begin{latexonly}" pseudo-environments are really just to % keep LaTeX2HTML quiet during the \renewcommand{} macros; they're % not really valuable. % % If you don't want the Module Index, you can remove all of this up % until the second \input line. % %?% %begin{latexonly} %?% %\renewcommand{\indexname}{Module Index} %?% %end{latexonly} %?% \input{mod\jobname.ind} % Module Index %begin{latexonly} %\renewcommand{\indexname}{Index} %end{latexonly} \input{\jobname.ind} % Index \begin{thebibliography}{99} %\begin{thebibliography} \bibitem[nielsen2005]{nielsen2005} {\it Hydrodynamic modelling of coastal inundation}. Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman. In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9.\\ http://www.mssanz.org.au/modsim05/papers/nielsen.pdf \bibitem[grid250]{grid250} Australian Bathymetry and Topography Grid, June 2005. Webster, M.A. and Petkovic, P. Geoscience Australia Record 2005/12. ISBN: 1-920871-46-2.\\ http://www.ga.gov.au/meta/ANZCW0703008022.html \bibitem[ZR1999]{ZR1999} \newblock {Catastrophic Collapse of Water Supply Reservoirs in Urban Areas}. \newblock C.~Zoppou and S.~Roberts. \newblock {\em ASCE J. Hydraulic Engineering}, 125(7):686--695, 1999. \bibitem[Toro1999]{Toro1992} \newblock Riemann problems and the waf method for solving the two-dimensional shallow water equations. \newblock E.~F. Toro. \newblock {\em Philosophical Transactions of the Royal Society, Series A}, 338:43--68, 1992. \bibitem{KurNP2001} \newblock Semidiscrete central-upwind schemes for hyperbolic conservation laws and hamilton-jacobi equations. \newblock A.~Kurganov, S.~Noelle, and G.~Petrova. \newblock {\em SIAM Journal of Scientific Computing}, 23(3):707--740, 2001. \end{thebibliography} % \end{thebibliography}{99} \end{document}