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1%Anuga validation publication
2%
3%Geoscience Australia and others 2007-2008
4       
5% Use the Elsevier LaTeX document class
6%\documentclass{elsart3p} % Two column
7%\documentclass{elsart1p} % One column
8%\documentclass[draft]{elsart} % Basic
9\documentclass{elsart} % Basic
10
11% Useful packages
12\usepackage{graphicx} % avoid epsfig or earlier such packages
13\usepackage{url}      % for URLs and DOIs
14\usepackage{amsmath}  % many want amsmath extensions
15\usepackage{amsfonts}
16\usepackage{underscore}
17\usepackage{natbib}   % Suggested by the Elsevier style
18                      % Use \citep and \citet instead of \cite
19                     
20
21% Local LaTeX commands
22%\newcommand{\Python}{\textsc{Python}}
23%\newcommand{\VPython}{\textsc{VPython}}
24\newcommand{\pypar}{\textsc{mpi}}
25\newcommand{\Metis}{\textsc{Metis}}
26\newcommand{\mpi}{\textsc{mpi}}
27
28\newcommand{\UU}{\mathbf{U}}
29\newcommand{\VV}{\mathbf{V}}
30\newcommand{\EE}{\mathbf{E}}
31\newcommand{\GG}{\mathbf{G}}
32\newcommand{\FF}{\mathbf{F}}
33\newcommand{\HH}{\mathbf{H}}
34\newcommand{\SSS}{\mathbf{S}}
35\newcommand{\nn}{\mathbf{n}}
36
37\newcommand{\code}[1]{\texttt{#1}}
38
39
40
41
42\begin{document}
43
44
45\begin{frontmatter}
46\title{On The Validation of A Hydrodynamic Model}
47
48
49\author[GA]{D.~S.~Gray}
50\ead{Duncan.Gray@ga.gov.au}
51\author[GA]{O.~M.~Nielsen}
52\ead{Ole.Nielsen@ga.gov.au}
53\author[GA]{M.~J.~Sexton}
54\ead{Jane.Sexton@ga.gov.au}
55\author[GA]{L.~Fountain}
56\author[GA]{K.~VanPutten}
57\author[ANU]{S.~G.~Roberts}
58\ead{Stephen.Roberts@anu.edu.au}
59\author[UQ]{T.~Baldock}
60\ead{Tom.Baldock@uq.edu.au}
61\author[UQ]{M.~Barnes}
62\ead{Matthew.Barnes@uq.edu.au}
63
64\address[GA]{Natural Hazard Impacts Project,
65 Geospatial and Earh Monitoring Division,
66 Geoscience Australia, Canberra, Australia} 
67 
68\address[ANU]{Department of Mathematics,
69Australian National University, Canberra, Australia} 
70
71\address[UQ]{University of Queensland, Brisbane, Australia}
72
73
74% Use the \verb|abstract| environment.
75\begin{abstract}
76Modelling the effects on the built environment of natural hazards such
77as riverine flooding, storm surges and tsunami is critical for
78understanding their economic and social impact on our urban
79communities.  Geoscience Australia and the Australian National
80University have developed a hydrodynamic inundation modelling tool
81called ANUGA to help simulate the impact of these hazards.
82The core of ANUGA is a Python implementation of a finite-volume method
83for solving the conservative form of the Shallow Water Wave equation.
84
85In this paper, a number of tests are performed to validate ANUGA. These tests
86range from benchmark problems to wave and flume tank examples.
87ANUGA is available as Open Source to enable
88free access to the software and allow the scientific community to
89use, validate and contribute to the software in the future.
90
91%This method allows the study area to be represented by an unstructured
92%mesh with variable resolution to suit the particular problem.  The
93%conserved quantities are water level (stage) and horizontal momentum.
94%An important capability of ANUGA is that it can robustly model the
95%process of wetting and drying as water enters and leaves an area. This
96%means that it is suitable for simulating water flow onto a beach or
97%dry land and around structures such as buildings.
98
99\end{abstract}
100
101
102\begin{keyword}
103% keywords here, in the form: keyword \sep keyword
104% PACS codes here, in the form: \PACS code \sep code
105
106Hydrodynamic Modelling \sep Model validation \sep
107Finite-volumes \sep Shallow water wave equation
108
109\end{keyword}
110
111\date{\today()}
112\end{frontmatter}
113
114
115
116
117% Begin document in earnest
118\section{Introduction}
119\label{sec:intro}
120
121Hydrodynamic modelling allows impacts from flooding, storm-surge and
122tsunami to be better understood, their impacts to be anticipated and,
123with appropriate planning, their effects to be mitigated.  A significant
124proportion of the Australian population reside in the coastal
125corridors, thus the potential of significant disruption and loss
126is real.  The extent of
127inundation is critically linked to the event, tidal conditions,
128bathymetry and topography and it not feasible to make impact
129predictions using heuristics alone.
130Geoscience
131Australia in collaboration with the Mathematical Sciences Institute,
132Australian National University, is developing a software application
133called ANUGA to model the hydrodynamics of floods, storm surges and
134tsunami. These hazards are modelled using the conservative shallow
135water equations which are described in section~\ref{sec:model}. In
136ANUGA these equations are solved using a finite volume method as
137described in section~\ref{sec:model}.  A more complete discussion of the
138method can be found in \citet{Nielsen2005} where the model and solution
139technique is validated on a standard tsunami benchmark data set
140or in \citet{Roberts2007} where the numerical method and parallelisation
141of ANUGA is discussed.
142This modelling capability is part of
143Geoscience Australia's ongoing research effort to model and
144understand the potential impact from natural hazards in order to
145reduce their impact on Australian communities \citep{Nielsen2006}.
146ANUGA is currently being trialled for flood
147modelling \citep{Rigby2008}.
148
149The validity of other hydrodynamic models have been reported
150elsewhere, with \citet{Hubbard02} providing an
151excellent review of 1D and 2D models and associated validation
152tests. They described the evolution of these models from fixed, nested
153to adaptive grids and the ability of the solvers to cope with the
154moving shoreline. They highlighted the difficulty in verify the
155nonlinear shallow water equations themselves as the only standard
156analytical solution is that of \citet{Carrier58} that is strictly for
157non-breaking waves. Further,
158whilst there is a 2D analytic solution from \citet{Thacker81}, it appears
159that the circular island wave tank example of Briggs et al will become
160the standard data set to verify the equations.
161
162This paper will describe the validation outputs in a similar way to
163\citet{Hubbard02} to
164present an exhaustive validation of the numerical model.
165Further to these tests, we will
166incorporate a test to verify friction values. The tests reported in
167this paper are:
168\begin{itemize}
169  \item Verification against the 1D analytical solution of Carrier and
170  Greenspan (p~\pageref{sec:carrier})
171  \item Testing against 1D (flume) data sets to verify wave height and
172  velocity (p~\pageref{sec:stage and velocity})
173  \item Determining friction values from 1D flume data sets
174  (p~\pageref{sec:friction})
175  \item Validation against a genuinely 2D analytical
176  solution of the model equations (p~\ref{sec:XXX})
177  \item Testing against the 2D Okushiri benchmark problem
178  (p~\pageref{sec:okushiri})   
179  \item Testing against the 2D data sets modelling wave run-up around a circular island by Briggs et al.
180  (p~\pageref{sec:circular island})
181\end{itemize}   
182
183
184Throughout the paper, qualitative comparisons will be drawn against
185other models.  Moreover, all source code necessary to reproduce the
186results reported in this paper is available as part of the ANUGA
187distribution in the form of a test suite. It is thus possible for
188anyone to readily verify that the implementation meets the
189requirements set out by these benchmarks.
190 
191
192%Hubbard and Dodd's model, OTT-2D, has some similarities to ANUGA, and
193%whilst the mesh can be refined, it is based on rectangular mesh.
194
195%The ANUGA model and numerical scheme is briefly described in
196%section~\ref{sec:model}.  A more detailed description of the numerical
197%scheme and software implementation can be found in \citet{Nielsen2005} and
198%\citet{Roberts2007}.
199The six case studies to validation and verify ANUGA
200will be presented in section~\ref{sec:validation}, with the
201conclusions outlined in section~\ref{sec:conclusions}.
202
203
204\section{Mathematical model, numerical scheme and implementation}
205\label{sec:model}
206
207The ANUGA model is based on the shallow water wave equations which are
208widely regarded as suitable for modelling 2D flows subject to the
209assumptions that horizontal scales (e.g. wave lengths) greatly exceed
210the depth, vertical velocities are negligible and the fluid is treated
211as inviscid and incompressible. See e.g. the classical texts
212\citet{Stoker57} and \citet{Peregrine67} for the background or
213\citet{Roberts1999} for more details on the mathematical model
214used by ANUGA.
215
216The conservation form of the shallow water wave
217equations used in ANUGA are:
218\[
219\frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial
220x}+\frac{\partial \GG}{\partial y}=\SSS
221\]
222where $\UU=\left[ {{\begin{array}{*{20}c}
223 h & {uh} & {vh} \\
224\end{array} }} \right]^T$ is the vector of conserved quantities; water depth
225$h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities
226entering the system are bed elevation $z$ and stage (absolute water
227level above a reference datum such as Mean Sea Level) $w$,
228where the relation $w = z + h$ holds true at all times.
229The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given
230by
231\[
232\EE=\left[ {{\begin{array}{*{20}c}
233 {uh} \hfill \\
234 {u^2h+gh^2/2} \hfill \\
235 {uvh} \hfill \\
236\end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c}
237 {vh} \hfill \\
238 {vuh} \hfill \\
239 {v^2h+gh^2/2} \hfill \\
240\end{array} }} \right]
241\]
242and the source term (which includes gravity and friction) is given
243by
244\[
245\SSS=\left[ {{\begin{array}{*{20}c}
246 0 \hfill \\
247 -{gh(z_{x} + S_{fx} )} \hfill \\
248 -{gh(z_{y} + S_{fy} )} \hfill \\
249\end{array} }} \right]
250\]
251where $S_f$ is the bed friction. The friction term is modelled using
252Manning's resistance law
253\[
254S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy}
255=\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}
256\]
257in which $\eta$ is the Manning resistance coefficient.
258
259%%As demonstrated in our papers, \cite{modsim2005,Roberts1999} these
260%%equations provide an excellent model of flows associated with
261%%inundation such as dam breaks and tsunamis. Question - how do we
262%%know it is excellent?
263
264ANUGA uses a finite-volume method as
265described in \citet{Roberts2007} where the study area is represented by an
266unstructured triangular mesh in which the vector of conserved quantities
267$\UU$ is maintained and updated over time. The flexibility afforded by
268allowing unstructed meshes rather than fixed resolution grids
269is the ability for the user to refine the mesh in areas of interest
270while leaving other areas coarse and thereby conserving computational
271resources.
272
273
274The approach used in ANUGA are distinguished from many
275other implementations (e.g. \citet{Hubbard02} or \citet{Zhang07}) by the
276following features:
277\begin{itemize}
278    \item The fluxes across each edge are computed using the semi-discrete
279    central-upwind scheme for approximating the Riemann problem
280    proposed by \citet{KurNP2001}. This scheme deals with different
281    flow regimes such as shocks, rarefactions and sub to super
282    critical flow transitions using one general approach. We have
283    found this scheme to be pleasingly simple, robust and efficient.
284    \item ANUGA does not employ a shoreline detection algorithm as the
285    central-upwind scheme is capable of resolving fluxes arising between
286    wet and dry cells. ANUGA does optionally bypass unnecessary
287    computations for dry-dry cell boundaries purely to improve performance.
288    \item ANUGA employs a second order spatial reconstruction of triangles
289    to produce a piece-wise linear function construction of the conserved
290    quantities. This function is allowed to be discontinuous across the
291    edges of the cells, but the slope of this function is limited to avoid
292    artificially introduced oscillations. This approach provides good
293    approximation of steep gradients in the solution. However,
294    where the depths are very small compared to the bed-slope a linear
295    combination between second order and first order reconstructions is
296    employed to guarantee numerical stability that may arise form very
297    small depths.
298\end{itemize}     
299   
300In the computations presented in this paper we use an explicit Euler
301time stepping method with variable timestepping subject to the
302CFL condition:
303\[
304  \delta t = \min_k \frac{r_k}{v_k} 
305\]
306where $r_k$ refers to the radius of the inscribed circle of triangle
307$k$, $v_k$ refers to the maximal velocity calculated from fluxes
308passing in or out of triangle $k$ and $\delta t$ is the resulting
309'safe' timestep to be used for the next iteration.
310
311
312ANUGA utilises a general velocity limiter described in the
313manual which guarantees a gradual compression of computed velocities
314in the presence of very shallow depths:
315\begin{equation}
316  \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h},
317\end{equation}
318where $h_0$ is a regularisation parameter that controls the minimal
319magnitude of the denominator. The default value is $h_0 = 10^{-6}$.
320
321
322ANUGA is mostly written in the object-oriented programming
323language Python with computationally intensive parts implemented
324as highly optimised shared objects written in C.
325
326Python is known for its clarity, elegance, efficiency and
327reliability. Complex software can be built in Python without undue
328distractions arising from idiosyncrasies of the underlying software
329language syntax. In addition, Python's automatic memory management,
330dynamic typing, object model and vast number of libraries means that
331ANUGA scripts can be produced quickly and can be adapted fairly easily to
332changing requirements.
333
334
335
336\section{Validation}
337\label{sec:validation} Validation is an ongoing process and the purpose of this paper
338is to describe a range of tests that validate ANUGA as a hydrodynamic model.
339This section will describe the six tests outlined in section~\ref{sec:intro}.
340Run times where specified measure the model time only and exclude model setup,
341data conversions etc. All examples were timed on a a 2GHz 64-bit
342Dual-Core AMD Opteron(tm) series 2212 Linux server. %This is a tornado compute node (cat /proc/cpuinfo).   
343
344
345\subsection{1D analytical validation}
346
347Tom Baldock has done something here for that NSW report
348
349\subsection{Stage and Velocity Validation in a Flume}
350\label{sec:stage and velocity}
351This section will describe tilting flume tank experiments that were
352conducted at the Gordon McKay Hydraulics Laboratory at the University of
353Queensland that confirm ANUGA's ability to estimate wave height
354and velocity. The same flume tank simulations were also used
355to explore Manning's friction and this will be described in the next section.
356
357The flume was set up for dam-break experiments, having a
358water reservior at one end.  The flume was glass-sided, 3m long, 0.4m
359in wide, and 0.4m deep, with a PVC bottom. The reservoir in the flume
360was 0.75m long.  For this experiment the reservoir water was 0.2m
361deep. At time zero the reservoir gate is manually opened and the water flows
362into the other side of the flume.  The water ran up a flume slope of
3630.03 m/m.  To accurately model the bed surface a Manning's friction
364value of 0.01, representing PVC was used.
365
366% Neale, L.C. and R.E. Price.  Flow characteristics of PVC sewer pipe.
367% Journal of the Sanitary Engineering Division, Div. Proc 90SA3, ASCE.
368% pp. 109-129.  1964.
369
370Acoustic displacement sensors that produced a voltage that changed
371with the water depth was positioned 0.4m from the reservoir gate. The
372water velocity was measured with an Acoustic Doppler Velocimeter 0.45m
373from the reservoir gate.  This sensor only produced reliable results 4
374seconds after the reservoir gate opened, due to limitations of the sensor.
375
376
377% Validation UQ flume
378% at X:\anuga_validation\uq_sloped_flume_2008
379% run run_dam.py to create sww file and .csv files
380% run plot.py to create graphs heere automatically
381% The Coasts and Ports '2007 paper is in TRIM d2007-17186
382\begin{figure}[htbp]
383\centerline{\includegraphics[width=4in]{uq-flume-depth}}
384\caption{Comparison of wave tank and ANUGA water height at .4 m
385  from the gate}\label{fig:uq-flume-depth}
386\end{figure}
387
388\begin{figure}[htbp]
389\centerline{\includegraphics[width=4in]{uq-flume-velocity}}
390\caption{Comparison of wave tank and ANUGA water velocity at .45 m
391  from the gate}\label{fig:uq-flume-velocity}
392\end{figure}
393
394Figure~\ref{fig:uq-flume-depth} shows that ANUGA predicts the actual
395water depth very well, although there is an initial drop in water depth
396within the first second that is not simulated by ANUGA.
397Water depth and velocity are coupled as described by the nonlinear
398shallow water equations, thus if one of these quantities accurately
399estimates the measured values, we would expect the same for the other
400quantity. This is demonstrated in Figure~\ref{fig:uq-flume-velocity}
401where the water velocity is also predicted accurately. Sediment
402transport studies rely on water velocity estimates in the region where
403the sensors cannot provide this data.  With water velocity being
404accurately predicted, studies such as sediment transport can now use
405reliable estimates.
406
407
408\subsection{1D flume tank to verify friction}
409\label{sec:friction}
410The same tilting flume tank was used to validate stage and velocity
411was used to validate the ANUGA friction model. A ground slope of 1:20,
412reservior lenght of 0.85m and damn depth of 0.4 m was used to verify
413the friction. The PVC bottom of the tank is equivalent to a friction
414value of 0.01.  {\bf Add ref } Depth sensors were placed 0.2, 0.3,
4150.4, 0.5 and 0.6 m from the bed gate.
416
417 
418As described in the model equations in ~\ref{sec:model}, the bed
419friction is modelled using the Manning's model. {\bf Add the formula}
420Validation of this model was carried out by comparing results
421from ANUGA against experimental results from flume wave tanks.
422 
423This experiment was simulated twice by ANUGA: without using the
424friction model {\bf Duncan says: It really used the friction model, with a
425value of 0.0, representing no friction model.  Is it ok to say
426'without using the model?'} and using the friction model with a
427Manning's friction value of 0.01.  The results from both of these
428simulations were compared against the experimental flume tank results
429using the Root Mean Square Relative Error (RMSRE). The RMSRE was
430summed over all of the depth sensors, for the first 30 seconds of the
431experiment.  This resulted in one number which represents the error
432between tow data sets, with a lower number representing less
433differences.  The RMSRE for no friction model was 0.380, the RMSRE for
434the friction model with a Manning's friction value of 0.01 was
4350.358. So for this experiment using a friction value given from a
436standard fricition table improved the accuracy of the ANUGA
437simulation.  {\bf Add ref to table}
438
439% Validation UQ friction
440% at X:\anuga_validation\uq_friction_2007
441% run run_dam.py to create sww file and .csv files
442% run plot.py to create graphs, and move them here
443\begin{figure}[htbp]
444\centerline{\includegraphics[width=4in]{uq-friction-depth}}
445\caption{Comparison of wave tank and ANUGA water height at .4 m
446  from the gate, simulated using a Mannings friction of 0.0 and
447  0.1.}\label{fig:uq-friction-depth}
448\end{figure}
449
450\subsection{Okushiri Wavetank Validation}
451\label{sec:okushiri}
452As part of the Third International Workshop on Long-wave Runup
453Models in 2004 (\url{http://www.cee.cornell.edu/longwave}), four
454benchmark problems were specified to allow the comparison of
455numerical, analytical and physical models with laboratory and field
456data. One of these problems describes a wave tank simulation of the
4571993 Okushiri Island tsunami off Hokkaido, Japan \cite{MatH2001}. A
458significant feature of this tsunami was a maximum run-up of 32~m
459observed at the head of the Monai Valley. This run-up was not
460uniform along the coast and is thought to have resulted from a
461particular topographic effect. Among other features, simulations of
462the Hokkaido tsunami should capture this run-up phenomenon.
463
464This dataset has been used by to validate tsunami models by
465a number of tsunami scientists. Examples include Titov ... lit review
466here on who has used this example for verification (Leharne?)
467
468\begin{figure}[htbp]
469%\centerline{\includegraphics[width=4in]{okushiri-gauge-5.eps}}
470\centerline{\includegraphics[width=4in]{ch5.png}}
471\centerline{\includegraphics[width=4in]{ch7.png}}
472\centerline{\includegraphics[width=4in]{ch9.png}}
473\caption{Comparison of wave tank and ANUGA water stages at gauge
4745,7 and 9.}\label{fig:val}
475\end{figure}
476
477
478\begin{figure}[htbp]
479\centerline{\includegraphics[width=4in]{okushiri-model.jpg}}
480\caption{Complex reflection patterns and run-up into Monai Valley
481simulated by ANUGA and visualised using our netcdf OSG
482viewer.}\label{fig:run}
483\end{figure}
484
485The wave tank simulation of the Hokkaido tsunami was used as the
486first scenario for validating ANUGA. The dataset provided
487bathymetry and topography along with initial water depth and the
488wave specifications. The dataset also contained water depth time
489series from three wave gauges situated offshore from the simulated
490inundation area. The ANUGA model comprised $41404$ triangles
491and took about $1330$ s to run on the test platform described in
492Section~\ref{sec:validation}.
493
494The script to run this example is available in the ANUGA distribution in the subdirectory
495\code{anuga_validation/automated_validation_tests/okushiri_tank_validation}.
496
497
498Figure~\ref{fig:val} compares the observed wave tank and modelled
499ANUGA water depth (stage height) at one of the gauges. The plots
500show good agreement between the two time series, with ANUGA
501closely modelling the initial draw down, the wave shoulder and the
502subsequent reflections. The discrepancy between modelled and
503simulated data in the first 10 seconds is due to the initial
504condition in the physical tank not being uniformly zero. Similarly
505good comparisons are evident with data from the other two gauges.
506Additionally, ANUGA replicates exceptionally well the 32~m Monai
507Valley run-up, and demonstrates its occurrence to be due to the
508interaction of the tsunami wave with two juxtaposed valleys above
509the coastline. The run-up is depicted in Figure~\ref{fig:run}.
510
511This successful replication of the tsunami wave tank simulation on a
512complex 3D beach is a positive first step in validating the ANUGA
513modelling capability.
514
515\subsection{Runup of solitary wave on circular island wavetank validation}
516\label{sec:circular island}
517This section will describe the ANUGA results for the experiments
518conducted by Briggs et al (1995). Here, a 30x25m basin with a conical
519island is situated near the centre and a directional wavemaker is used
520to produce planar solitary waves of specified crest lenghts and
521heights. A series of gauges were distributed within the experimental
522setup. As described by Hubbard and Dodd \cite{Hubbard02}, a number of
523researchers have used this benchmark problem to test their numerical
524models. {\bf Jane: check whether these results are now avilable as
525they were not in 2002}. Hubbard and Dodd \cite{Hubbard02} note that a
526particular 3D model appears to obtain slightly better results than the
5272D ones reported but that 3D models are unlikely to be competitive in
528terms of computing power for applications in coastal engineering at
529least. Choi et al \cite{Choi07} use a 3D RANS model (based on the
530Navier-Stokes equations) for the same problem and find a very good
531comparison with laboratory and 2D numerical results. An obvious
532advantage of the 3D model is its ability to investigate the velocity
533field and Choi et al also report on the limitation of depth-averaged
5342D models for run-up simulations of this type.
535
536Once results are availble, need to compare to Hubbard and Dodd and draw any conclusions
537from nested rectangular grid vs unstructured gird.
538Figure \ref{fig:circular screenshots} shows a sequence of screenshots depicting the evolution of the solitary wave as it hits the circular island.
539
540\begin{figure}[htbp]
541\centerline{
542  \includegraphics[width=5cm]{circular1.png}
543  \includegraphics[width=5cm]{circular2.png}}
544\centerline{
545  \includegraphics[width=5cm]{circular3.png}
546  \includegraphics[width=5cm]{circular4.png}}
547\centerline{
548  \includegraphics[width=5cm]{circular5.png}
549  \includegraphics[width=5cm]{circular6.png}}
550\centerline{
551  \includegraphics[width=5cm]{circular7.png}
552  \includegraphics[width=5cm]{circular8.png}}
553\centerline{
554  \includegraphics[width=5cm]{circular9.png}
555  \includegraphics[width=5cm]{circular10.png}}
556\caption{Screenshots of the evolution of solitary wave around circular island.}
557\label{fig:circular screenshots}
558\end{figure}
559
560
561\clearpage
562
563\section{Conclusions}
564\label{sec:conclusions}
565ANUGA is a flexible and robust modelling system
566that simulates hydrodynamics by solving the shallow water wave
567equation in a triangular mesh. It can model the process of wetting
568and drying as water enters and leaves an area and is capable of
569capturing hydraulic shocks due to the ability of the finite-volume
570method to accommodate discontinuities in the solution.
571ANUGA can take as input bathymetric and topographic datasets and
572simulate the behaviour of riverine flooding, storm surge,
573tsunami or even dam breaks.
574Initial validation using wave tank data supports ANUGA's
575ability to model complex scenarios. Further validation will be
576pursued as additional datasets become available.
577The ANUGA source code and validation case studies reported here are available
578at \url{http://sourceforge.net/projects/anuga}.
579
580something about use on flood modelling community and their validation initiatives
581
582
583%\bibliographystyle{plainnat}
584\bibliographystyle{elsart-harv}
585\bibliography{anuga-bibliography}
586
587\end{document}
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