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anuga_user_manual.tex
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% 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{verbatim}
\newcommand{\verbatiminputB}[1]{%
\verbatiminput{#1}\endgroup}
\def\verbatiminputunderscore{\begingroup
\catcode`\_=12
\verbatiminputB}
\usepackage{graphicx}
\usepackage{hyperref}
\usepackage[australian]{babel}
\usepackage{datetime}
\usepackage[hang,small,bf]{caption}
\usepackage{amsbsy,enumerate}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing,shadows,calc}
\input{definitions}
%\input{epydoc_api}
%%%%%
% Set penalties for widows, etc, very high
%%%%%
\widowpenalty=10000
\clubpenalty=10000
\raggedbottom
\title{\anuga User Manual}
\author{Stephen Roberts, Ole Nielsen, Duncan Gray, Jane Sexton, Gareth Davies}
% Please at least include a long-lived email address;
% the rest is at your discretion.
\authoraddress{Geoscience Australia \\
Email: \email{anuga-user@lists.sourceforge.net}
}
%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.
\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: 2012-05-16 21:22:03 +1000 (Wed, 16 May 2012) $
%$LastChangedRevision: 8427 $
%$LastChangedBy: davies $
\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 operators 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 releases of \anuga and this manual are available on github at
\url{http://github.com/GeoscienceAustralia/anuga_core/releases}.
A snapshot of the current work in progress is at
\url{http://github.com/GeoscienceAustralia/anuga_core}.
This manual describes \anuga version \version. To check for later versions of this manual
go to \url{http://github.com/GeoscienceAustralia/anuga_core/doc/anuga_user_manual.pdf}.
\section{Scope}
This manual covers only what is needed to operate the software after
installation and configuration. It does not include 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://github.com/GeoscienceAustralia/anuga_core/INSTALL.rst}.
\section{Audience}
Readers are assumed to be familiar with the Python Programming language and
its object oriented approach.
A good Python tutorial is
\url{https://docs.python.org/2/tutorial}.
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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{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 and the bed (using the
latest algorithms (see section~\ref{ch:algorithm})
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 operators that may
drive the system such as rainfall, abstraction of water, erosion, culverts
See section \ref{sec:operators} for details of operators 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 numpy
structures.
The visualisation 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.
\section{Which flow algorithm}
\label{ch:algorithm}
Up to version \verb|2.0| our default flow algorithm assumed a continuous
bed. This allowed allowed for a robust algorithm, but did lead to complications
associated with well balancing and the introduction of useful structures such as riverwalls.
Form version \verb|1.3| we have made available flow algorithms which can use
discontinuous bed and have introduced riverwalls for those algorithms. In addition,
for those algorithms, it has been much easier to deal with operations that change the bed (such as erosion).
To choose a particular flow algorithm use the following command in your \anuga{} script:
\begin{verbatim}
domain.set_flow_algorithm('alg')
\end{verbatim}
where \verb|alg| is one of the following:
\begin{center}
\begin{tabular}{| l |p{6cm} |p{6cm}| }
\hline \hline
\verb|alg| & Description & Comments \\ \hline
\verb|DE0| & Uses first order timestepping and a fairly diffusive second order spatial approximation. & Very robust, more accuate than \verb|1_5|. This is our default algorithm since version \verb|2.0|. Useful for standard flow problems and tsunamis. \\ \hline
\verb|DE1| & Uses second order timestepping and a much less diffusive second order spatial approximation. &More accurate than, but about 1/2 the speed of \verb|DE0|. Useful for problems with forced waves or tidal flows over many tidal cycles. \\ \hline
\verb|DE2| & Uses third order timestepping and the same spatial approximation as \verb|DE1| & Slightly more accurate than \verb|DE1|. About 1/3 the speed of \verb|DE0|. \\ \hline
\hline
\verb|1_5| & Uses first order timestepping and similar spatial approximation to \verb|DE0|. & Very robust, slighty fast than \verb|DE0|. The default algorithm before version \verb|2.0|. \\ \hline
\verb|2_0| & Uses second order timestepping and similar spatial approximation to \verb|DE1|. &More accurate than, but about 1/2 the speed of \verb|1_5| \\ \hline
\verb|2_5| & uses third order timestepping and similar spatial approximation to \verb|DE1| . & Slightly more accurate than \verb|2_0|. About 1/3 the speed of \verb|2_0|.\\ \hline
\hline
\end{tabular}
\end{center}
From version \verb|2.0| the default algorithm is \verb|DE0|. Usually there is no need to change from the default algorithm.
\section{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), though we have run over 2 zones by projecting onto one zone and
living with the distortion.
\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.
%\item \anuga contains no tsunami-genic functionality relating to earthquakes.
\end{itemize}
\pagebreak
\section{Citing \anuga}
When citing \anuga cite this manual:
Bibtex entry:
\begin{verbatim}
@manual{anugamanual,
title={ANUGA User Manual},
author={Roberts, S and Nielsen, O. and Gray, D. and Sexton, J. and Davies, G.},
organization={Geoscience Australia},
url={https://github.com/GeoscienceAustralia/anuga_core/blob/master/doc/anuga_user_manual.pdf},
year={2015}
}
\end{verbatim}
or this article
Bibtex entry:
\begin{verbatim}
@article{nielsen2005hydrodynamic,
title={Hydrodynamic modelling of coastal inundation},
author={Nielsen, O and Roberts, S and Gray, D and McPherson, A and Hitchman, A},
journal={MODSIM 2005 International Congress on Modelling and Simulation},
pages={518--523},
year={2005}
}
\end{verbatim}
%=====================================
\section{Installation}
We suggest visiting the github repository \url{https://github.com/GeoscienceAustralia/anuga_core}, in particular \url{https://github.com/GeoscienceAustralia/anuga_core/wiki} to find up to date instructions on installing \anuga{} on Ubuntu and Windows.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
What follows is a discussion of the structure and operation of a
script called \file{runup.py} (which is available in the \file{examples}
directory of \file{anuga_core}.
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}
\section{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}
\section{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}
\verbatiminputunderscore{../../anuga_core/examples/runup.py}
\section{Establishing the Domain}\index{domain, establishing}
The very first thing to do is import the various modules, of which the
\anuga{} module is the most important.
%
\begin{verbatim}
import anuga
\end{verbatim}
%
Then we need to set up the triangular mesh to be used for the
scenario. This is carried out through the statement:
\begin{verbatim}
domain = anuga.rectangular_cross_domain(10, 5, len1=10.0, len2=5.0)
\end{verbatim}
%
The above assignment sets up a $10 \times
5$ rectangular mesh, triangulated in a regular way with boundary tags \code{'left'}, \code{'right'},
\code{'top'} or \code{'bottom'}.
It is also possible to set up a domain from ``first principles'' using \code{points}, \code{vertices} and \code{boundary} via the assignment:
\begin{verbatim}
domain = anuga.Domain(points, vertices, boundary)
\end{verbatim}
where
\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 with each a symbolic tag.
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}.
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.
\section{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}.
\subsection{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.
\subsection{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.
\subsection{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.
\section{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}
\section{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.
\section{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:anuga_viewer}). 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:
\verbatiminputunderscore{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{anuga_viewer}. 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{anuga_viewer} is described in more detail in Section \ref{sec:anuga_viewer}.
\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
%====================================================
\chapter{A slightly more complex example}
\label{sec:channelexample}
The next example is about water-flow 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.
\section{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}
\section{The Code}
Here is the code for the first version of the channel flow \file{channel1.py}:
\verbatiminputunderscore{../../anuga_core/examples/channel1.py}
In discussing the details of this example, we follow the outline
given above, discussing each major step of the code in turn.
\section{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
hypotenuse 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{anuga_viewer} 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}
%=========================================
\section{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}:
\verbatiminputunderscore{../../anuga_core/examples/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.
\section{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}
\section{Flow through more complex topographies}
Here is the code for the third version of the channel flow \file{channel3.py}:
\verbatiminputunderscore{../../anuga_core/examples/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}
%==========================================================
\chapter{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.
}
\section{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).