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]{Georisk Project, |
---|
65 | Geospatial and Earh Monitoring Division, |
---|
66 | Geoscience Australia, Canberra, Australia} |
---|
67 | |
---|
68 | \address[ANU]{Department of Mathematics, |
---|
69 | Australian National University, Canberra, Australia} |
---|
70 | |
---|
71 | \address[UQ]{University of Queensland, Brisbane, Australia} |
---|
72 | |
---|
73 | |
---|
74 | % Use the \verb|abstract| environment. |
---|
75 | \begin{abstract} |
---|
76 | Modelling the effects on the built environment of natural hazards such |
---|
77 | as riverine flooding, storm surges and tsunami is critical for |
---|
78 | understanding their economic and social impact on our urban |
---|
79 | communities. Geoscience Australia and the Australian National |
---|
80 | University have developed a hydrodynamic inundation modelling tool |
---|
81 | called ANUGA to help simulate the impact of these hazards. |
---|
82 | The core of ANUGA is a Python implementation of a finite-volume method |
---|
83 | for solving the conservative form of the Shallow Water Wave equation. |
---|
84 | |
---|
85 | In this paper, a number of tests are performed to validate ANUGA. These tests |
---|
86 | range from benchmark problems to wave and flume tank examples. |
---|
87 | ANUGA is available as Open Source to enable |
---|
88 | free access to the software and allow the scientific community to |
---|
89 | use, 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 | |
---|
106 | Hydrodynamic Modelling \sep Model validation \sep |
---|
107 | Finite-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 | |
---|
121 | Hydrodynamic modelling allows impacts from flooding, storm-surge and |
---|
122 | tsunami to be better understood, their impacts to be anticipated and, |
---|
123 | with appropriate planning, their effects to be mitigated. A significant |
---|
124 | proportion of the Australian population reside in the coastal |
---|
125 | corridors, thus the potential of significant disruption and loss |
---|
126 | is real. The extent of |
---|
127 | inundation is critically linked to the event, tidal conditions, |
---|
128 | bathymetry and topography and it not feasible to make impact |
---|
129 | predictions using heuristics alone. |
---|
130 | Geoscience |
---|
131 | Australia in collaboration with the Mathematical Sciences Institute, |
---|
132 | Australian National University, is developing a software application |
---|
133 | called ANUGA to model the hydrodynamics of floods, storm surges and |
---|
134 | tsunami. These hazards are modelled using the conservative shallow |
---|
135 | water equations which are described in section~\ref{sec:model}. In |
---|
136 | ANUGA these equations are solved using a finite volume method as |
---|
137 | described in section~\ref{sec:model}. A more complete discussion of the |
---|
138 | method can be found in \citet{Nielsen2005} where the model and solution |
---|
139 | technique is validated on a standard tsunami benchmark data set |
---|
140 | or in \citet{Roberts2007} where the numerical method and parallelisation |
---|
141 | of ANUGA is discussed. |
---|
142 | This modelling capability is part of |
---|
143 | Geoscience Australia's ongoing research effort to model and |
---|
144 | understand the potential impact from natural hazards in order to |
---|
145 | reduce their impact on Australian communities \citep{Nielsen2006}. |
---|
146 | ANUGA is currently being trialled for flood |
---|
147 | modelling \citep{Rigby2008}. |
---|
148 | |
---|
149 | The validity of other hydrodynamic models have been reported |
---|
150 | elsewhere, with \citet{Hubbard02} providing an |
---|
151 | excellent review of 1D and 2D models and associated validation |
---|
152 | tests. They described the evolution of these models from fixed, nested |
---|
153 | to adaptive grids and the ability of the solvers to cope with the |
---|
154 | moving shoreline. They highlighted the difficulty in verifying the |
---|
155 | nonlinear shallow water equations themselves as the only standard |
---|
156 | analytical solution is that of \citet{Carrier58} that is strictly for |
---|
157 | non-breaking waves. Further, |
---|
158 | whilst there is a 2D analytic solution from \citet{Thacker81}, it appears |
---|
159 | that the circular island wave tank example of Briggs et al will become |
---|
160 | the standard data set to verify the equations. |
---|
161 | |
---|
162 | This paper will describe the validation outputs in a similar way to |
---|
163 | \citet{Hubbard02} to |
---|
164 | present an exhaustive validation of the numerical model. |
---|
165 | Further to these tests, we will |
---|
166 | incorporate a test to verify friction values. The tests reported in |
---|
167 | this 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 | |
---|
184 | Throughout the paper, qualitative comparisons will be drawn against |
---|
185 | other models. Moreover, all source code necessary to reproduce the |
---|
186 | results reported in this paper is available as part of the ANUGA |
---|
187 | distribution in the form of a test suite. It is thus possible for |
---|
188 | anyone to readily verify that the implementation meets the |
---|
189 | requirements 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}. |
---|
199 | The six case studies to validation and verify ANUGA |
---|
200 | will be presented in section~\ref{sec:validation}, with the |
---|
201 | conclusions outlined in section~\ref{sec:conclusions}. |
---|
202 | |
---|
203 | NOTE: This is just a brain dump at the moment and needs to be incorporated properly |
---|
204 | in the text somewhere. |
---|
205 | |
---|
206 | Need some discussion on Bousssinesq type models - Boussinesq equations get the |
---|
207 | nonlinearity and dispersive effects to a high degree of accuracy |
---|
208 | |
---|
209 | moving wet-dry boundary algorithms - applicability to coastal engineering |
---|
210 | |
---|
211 | Fuhrman and Madesn 2008 \cite{Fuhrman2008}do validation - they have a Boussinesq type |
---|
212 | model, finite |
---|
213 | difference (therefore needing a supercomputer), 4th order, four stage RK time stepping |
---|
214 | scheme. |
---|
215 | |
---|
216 | their tests are (1) nonlinear run-up on periodic and transient waves on a sloping |
---|
217 | beach with excellent comparison to analytic solutions (2) 2d parabolic basin |
---|
218 | (3) solitary wave evolution through 2d triangular channel (4) solitary wave evolution on |
---|
219 | conical island (we need to compare to their computation time and note they use a |
---|
220 | vertical exaggeration for their images) |
---|
221 | |
---|
222 | excellent accuracy mentioned - but what is it - what does it mean? |
---|
223 | |
---|
224 | of interest is that they mention mass conservation and calculate it throughout the simulations |
---|
225 | |
---|
226 | Kim et al \cite{DaiHong2007} use Riemann solver - talk about improved accuracy by using 2nd order upwind |
---|
227 | scheme. Use finite volume on a structured mesh. Do parabolic basic and circular island. Needed? |
---|
228 | |
---|
229 | Delis et all 2008 \cite{Delis2008}- finite volume, Godunov-type explicit scheme coupled with Roe's |
---|
230 | approximate Riemann solver. It accurately describes breaking waves as bores or hydraulic jumps |
---|
231 | and conserves volume across flow discontinuties - is this just a result of finite volume? |
---|
232 | |
---|
233 | They also show mass conservation for most of the simulations |
---|
234 | |
---|
235 | similar range of validation tests that compare well - our job to compare to these as well |
---|
236 | |
---|
237 | \section{Mathematical model, numerical scheme and implementation} |
---|
238 | \label{sec:model} |
---|
239 | |
---|
240 | The ANUGA model is based on the shallow water wave equations which are |
---|
241 | widely regarded as suitable for modelling 2D flows subject to the |
---|
242 | assumptions that horizontal scales (e.g. wave lengths) greatly exceed |
---|
243 | the depth, vertical velocities are negligible and the fluid is treated |
---|
244 | as inviscid and incompressible. See e.g. the classical texts |
---|
245 | \citet{Stoker57} and \citet{Peregrine67} for the background or |
---|
246 | \citet{Roberts1999} for more details on the mathematical model |
---|
247 | used by ANUGA. |
---|
248 | |
---|
249 | The conservation form of the shallow water wave |
---|
250 | equations used in ANUGA are: |
---|
251 | \[ |
---|
252 | \frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial |
---|
253 | x}+\frac{\partial \GG}{\partial y}=\SSS |
---|
254 | \] |
---|
255 | where $\UU=\left[ {{\begin{array}{*{20}c} |
---|
256 | h & {uh} & {vh} \\ |
---|
257 | \end{array} }} \right]^T$ is the vector of conserved quantities; water depth |
---|
258 | $h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities |
---|
259 | entering the system are bed elevation $z$ and stage (absolute water |
---|
260 | level above a reference datum such as Mean Sea Level) $w$, |
---|
261 | where the relation $w = z + h$ holds true at all times. |
---|
262 | The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given |
---|
263 | by |
---|
264 | \[ |
---|
265 | \EE=\left[ {{\begin{array}{*{20}c} |
---|
266 | {uh} \hfill \\ |
---|
267 | {u^2h+gh^2/2} \hfill \\ |
---|
268 | {uvh} \hfill \\ |
---|
269 | \end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c} |
---|
270 | {vh} \hfill \\ |
---|
271 | {vuh} \hfill \\ |
---|
272 | {v^2h+gh^2/2} \hfill \\ |
---|
273 | \end{array} }} \right] |
---|
274 | \] |
---|
275 | and the source term (which includes gravity and friction) is given |
---|
276 | by |
---|
277 | \[ |
---|
278 | \SSS=\left[ {{\begin{array}{*{20}c} |
---|
279 | 0 \hfill \\ |
---|
280 | -{gh(z_{x} + S_{fx} )} \hfill \\ |
---|
281 | -{gh(z_{y} + S_{fy} )} \hfill \\ |
---|
282 | \end{array} }} \right] |
---|
283 | \] |
---|
284 | where $S_f$ is the bed friction. The friction term is modelled using |
---|
285 | Manning's resistance law |
---|
286 | \[ |
---|
287 | S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy} |
---|
288 | =\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}} |
---|
289 | \] |
---|
290 | in which $\eta$ is the Manning resistance coefficient. |
---|
291 | |
---|
292 | %%As demonstrated in our papers, \cite{modsim2005,Roberts1999} these |
---|
293 | %%equations provide an excellent model of flows associated with |
---|
294 | %%inundation such as dam breaks and tsunamis. Question - how do we |
---|
295 | %%know it is excellent? |
---|
296 | |
---|
297 | ANUGA uses a finite-volume method as |
---|
298 | described in \citet{Roberts2007} where the study area is represented by an |
---|
299 | unstructured triangular mesh in which the vector of conserved quantities |
---|
300 | $\UU$ is maintained and updated over time. The flexibility afforded by |
---|
301 | allowing unstructed meshes rather than fixed resolution grids |
---|
302 | is the ability for the user to refine the mesh in areas of interest |
---|
303 | while leaving other areas coarse and thereby conserving computational |
---|
304 | resources. |
---|
305 | |
---|
306 | |
---|
307 | The approach used in ANUGA are distinguished from many |
---|
308 | other implementations (e.g. \citet{Hubbard02} or \citet{Zhang07}) by the |
---|
309 | following features: |
---|
310 | \begin{itemize} |
---|
311 | \item The fluxes across each edge are computed using the semi-discrete |
---|
312 | central-upwind scheme for approximating the Riemann problem |
---|
313 | proposed by \citet{KurNP2001}. This scheme deals with different |
---|
314 | flow regimes such as shocks, rarefactions and sub to super |
---|
315 | critical flow transitions using one general approach. We have |
---|
316 | found this scheme to be pleasingly simple, robust and efficient. |
---|
317 | \item ANUGA does not employ a shoreline detection algorithm as the |
---|
318 | central-upwind scheme is capable of resolving fluxes arising between |
---|
319 | wet and dry cells. ANUGA does optionally bypass unnecessary |
---|
320 | computations for dry-dry cell boundaries purely to improve performance. |
---|
321 | \item ANUGA employs a second order spatial reconstruction of triangles |
---|
322 | to produce a piece-wise linear function construction of the conserved |
---|
323 | quantities. This function is allowed to be discontinuous across the |
---|
324 | edges of the cells, but the slope of this function is limited to avoid |
---|
325 | artificially introduced oscillations. This approach provides good |
---|
326 | approximation of steep gradients in the solution. However, |
---|
327 | where the depths are very small compared to the bed-slope a linear |
---|
328 | combination between second order and first order reconstructions is |
---|
329 | employed to guarantee numerical stability that may arise form very |
---|
330 | small depths. |
---|
331 | \end{itemize} |
---|
332 | |
---|
333 | In the computations presented in this paper we use an explicit Euler |
---|
334 | time stepping method with variable timestepping subject to the |
---|
335 | CFL condition: |
---|
336 | \[ |
---|
337 | \delta t = \min_k \frac{r_k}{v_k} |
---|
338 | \] |
---|
339 | where $r_k$ refers to the radius of the inscribed circle of triangle |
---|
340 | $k$, $v_k$ refers to the maximal velocity calculated from fluxes |
---|
341 | passing in or out of triangle $k$ and $\delta t$ is the resulting |
---|
342 | 'safe' timestep to be used for the next iteration. |
---|
343 | |
---|
344 | |
---|
345 | ANUGA utilises a general velocity limiter described in the |
---|
346 | manual which guarantees a gradual compression of computed velocities |
---|
347 | in the presence of very shallow depths: |
---|
348 | \begin{equation} |
---|
349 | \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h}, |
---|
350 | \end{equation} |
---|
351 | where $h_0$ is a regularisation parameter that controls the minimal |
---|
352 | magnitude of the denominator. The default value is $h_0 = 10^{-6}$. |
---|
353 | |
---|
354 | |
---|
355 | ANUGA is mostly written in the object-oriented programming |
---|
356 | language Python with computationally intensive parts implemented |
---|
357 | as highly optimised shared objects written in C. |
---|
358 | |
---|
359 | Python is known for its clarity, elegance, efficiency and |
---|
360 | reliability. Complex software can be built in Python without undue |
---|
361 | distractions arising from idiosyncrasies of the underlying software |
---|
362 | language syntax. In addition, Python's automatic memory management, |
---|
363 | dynamic typing, object model and vast number of libraries means that |
---|
364 | ANUGA scripts can be produced quickly and can be adapted fairly easily to |
---|
365 | changing requirements. |
---|
366 | |
---|
367 | |
---|
368 | |
---|
369 | \section{Validation} |
---|
370 | \label{sec:validation} Validation is an ongoing process and the purpose of this paper |
---|
371 | is to describe a range of tests that validate ANUGA as a hydrodynamic model. |
---|
372 | This section will describe the six tests outlined in section~\ref{sec:intro}. |
---|
373 | Run times where specified measure the model time only and exclude model setup, |
---|
374 | data conversions etc. All examples were timed on a a 2GHz 64-bit |
---|
375 | Dual-Core AMD Opteron(tm) series 2212 Linux server. %This is a tornado compute node (cat /proc/cpuinfo). |
---|
376 | |
---|
377 | |
---|
378 | \subsection{1D analytical validation} |
---|
379 | |
---|
380 | Tom Baldock has done something here for that NSW report |
---|
381 | |
---|
382 | \subsection{Stage and Velocity Validation in a Flume} |
---|
383 | \label{sec:stage and velocity} |
---|
384 | This section will describe tilting flume tank experiments that were |
---|
385 | conducted at the Gordon McKay Hydraulics Laboratory at the University of |
---|
386 | Queensland that confirm ANUGA's ability to estimate wave height |
---|
387 | and velocity. The same flume tank simulations were also used |
---|
388 | to explore Manning's friction and this will be described in the next section. |
---|
389 | |
---|
390 | The flume was set up for dam-break experiments, having a |
---|
391 | water reservior at one end. The flume was glass-sided, 3m long, 0.4m |
---|
392 | in wide, and 0.4m deep, with a PVC bottom. The reservoir in the flume |
---|
393 | was 0.75m long. For this experiment the reservoir water was 0.2m |
---|
394 | deep. At time zero the reservoir gate is manually opened and the water flows |
---|
395 | into the other side of the flume. The water ran up a flume slope of |
---|
396 | 0.03 m/m. To accurately model the bed surface a Manning's friction |
---|
397 | value of 0.01, representing PVC was used. |
---|
398 | |
---|
399 | % Neale, L.C. and R.E. Price. Flow characteristics of PVC sewer pipe. |
---|
400 | % Journal of the Sanitary Engineering Division, Div. Proc 90SA3, ASCE. |
---|
401 | % pp. 109-129. 1964. |
---|
402 | |
---|
403 | Acoustic displacement sensors that produced a voltage that changed |
---|
404 | with the water depth was positioned 0.4m from the reservoir gate. The |
---|
405 | water velocity was measured with an Acoustic Doppler Velocimeter 0.45m |
---|
406 | from the reservoir gate. This sensor only produced reliable results 4 |
---|
407 | seconds after the reservoir gate opened, due to limitations of the sensor. |
---|
408 | |
---|
409 | |
---|
410 | % Validation UQ flume |
---|
411 | % at X:\anuga_validation\uq_sloped_flume_2008 |
---|
412 | % run run_dam.py to create sww file and .csv files |
---|
413 | % run plot.py to create graphs heere automatically |
---|
414 | % The Coasts and Ports '2007 paper is in TRIM d2007-17186 |
---|
415 | \begin{figure}[htbp] |
---|
416 | \centerline{\includegraphics[width=4in]{uq-flume-depth}} |
---|
417 | \caption{Comparison of wave tank and ANUGA water height at .4 m |
---|
418 | from the gate}\label{fig:uq-flume-depth} |
---|
419 | \end{figure} |
---|
420 | |
---|
421 | \begin{figure}[htbp] |
---|
422 | \centerline{\includegraphics[width=4in]{uq-flume-velocity}} |
---|
423 | \caption{Comparison of wave tank and ANUGA water velocity at .45 m |
---|
424 | from the gate}\label{fig:uq-flume-velocity} |
---|
425 | \end{figure} |
---|
426 | |
---|
427 | Figure~\ref{fig:uq-flume-depth} shows that ANUGA predicts the actual |
---|
428 | water depth very well, although there is an initial drop in water depth |
---|
429 | within the first second that is not simulated by ANUGA. |
---|
430 | Water depth and velocity are coupled as described by the nonlinear |
---|
431 | shallow water equations, thus if one of these quantities accurately |
---|
432 | estimates the measured values, we would expect the same for the other |
---|
433 | quantity. This is demonstrated in Figure~\ref{fig:uq-flume-velocity} |
---|
434 | where the water velocity is also predicted accurately. Sediment |
---|
435 | transport studies rely on water velocity estimates in the region where |
---|
436 | the sensors cannot provide this data. With water velocity being |
---|
437 | accurately predicted, studies such as sediment transport can now use |
---|
438 | reliable estimates. |
---|
439 | |
---|
440 | |
---|
441 | \subsection{Okushiri Wavetank Validation} |
---|
442 | \label{sec:okushiri} |
---|
443 | As part of the Third International Workshop on Long-wave Runup |
---|
444 | Models in 2004 (\url{http://www.cee.cornell.edu/longwave}), four |
---|
445 | benchmark problems were specified to allow the comparison of |
---|
446 | numerical, analytical and physical models with laboratory and field |
---|
447 | data. One of these problems describes a wave tank simulation of the |
---|
448 | 1993 Okushiri Island tsunami off Hokkaido, Japan \cite{MatH2001}. A |
---|
449 | significant feature of this tsunami was a maximum run-up of 32~m |
---|
450 | observed at the head of the Monai Valley. This run-up was not |
---|
451 | uniform along the coast and is thought to have resulted from a |
---|
452 | particular topographic effect. Among other features, simulations of |
---|
453 | the Hokkaido tsunami should capture this run-up phenomenon. |
---|
454 | |
---|
455 | This dataset has been used by to validate tsunami models by |
---|
456 | a number of tsunami scientists. Examples include Titov ... lit review |
---|
457 | here on who has used this example for verification (Leharne?) |
---|
458 | |
---|
459 | \begin{figure}[htbp] |
---|
460 | %\centerline{\includegraphics[width=4in]{okushiri-gauge-5.eps}} |
---|
461 | \centerline{\includegraphics[width=4in]{ch5.png}} |
---|
462 | \centerline{\includegraphics[width=4in]{ch7.png}} |
---|
463 | \centerline{\includegraphics[width=4in]{ch9.png}} |
---|
464 | \caption{Comparison of wave tank and ANUGA water stages at gauge |
---|
465 | 5,7 and 9.}\label{fig:val} |
---|
466 | \end{figure} |
---|
467 | |
---|
468 | |
---|
469 | \begin{figure}[htbp] |
---|
470 | \centerline{\includegraphics[width=4in]{okushiri-model.jpg}} |
---|
471 | \caption{Complex reflection patterns and run-up into Monai Valley |
---|
472 | simulated by ANUGA and visualised using our netcdf OSG |
---|
473 | viewer.}\label{fig:run} |
---|
474 | \end{figure} |
---|
475 | |
---|
476 | The wave tank simulation of the Hokkaido tsunami was used as the |
---|
477 | first scenario for validating ANUGA. The dataset provided |
---|
478 | bathymetry and topography along with initial water depth and the |
---|
479 | wave specifications. The dataset also contained water depth time |
---|
480 | series from three wave gauges situated offshore from the simulated |
---|
481 | inundation area. The ANUGA model comprised $41404$ triangles |
---|
482 | and took about $1330$ s to run on the test platform described in |
---|
483 | Section~\ref{sec:validation}. |
---|
484 | |
---|
485 | The script to run this example is available in the ANUGA distribution in the subdirectory |
---|
486 | \code{anuga_validation/automated_validation_tests/okushiri_tank_validation}. |
---|
487 | |
---|
488 | |
---|
489 | Figure~\ref{fig:val} compares the observed wave tank and modelled |
---|
490 | ANUGA water depth (stage height) at one of the gauges. The plots |
---|
491 | show good agreement between the two time series, with ANUGA |
---|
492 | closely modelling the initial draw down, the wave shoulder and the |
---|
493 | subsequent reflections. The discrepancy between modelled and |
---|
494 | simulated data in the first 10 seconds is due to the initial |
---|
495 | condition in the physical tank not being uniformly zero. Similarly |
---|
496 | good comparisons are evident with data from the other two gauges. |
---|
497 | Additionally, ANUGA replicates exceptionally well the 32~m Monai |
---|
498 | Valley run-up, and demonstrates its occurrence to be due to the |
---|
499 | interaction of the tsunami wave with two juxtaposed valleys above |
---|
500 | the coastline. The run-up is depicted in Figure~\ref{fig:run}. |
---|
501 | |
---|
502 | This successful replication of the tsunami wave tank simulation on a |
---|
503 | complex 3D beach is a positive first step in validating the ANUGA |
---|
504 | modelling capability. |
---|
505 | |
---|
506 | \subsection{Runup of solitary wave on circular island wavetank validation} |
---|
507 | \label{sec:circular island} |
---|
508 | This section will describe the ANUGA results for the experiments |
---|
509 | conducted by Briggs et al (1995). Here, a 30x25m basin with a conical |
---|
510 | island is situated near the centre and a directional wavemaker is used |
---|
511 | to produce planar solitary waves of specified crest lenghts and |
---|
512 | heights. A series of gauges were distributed within the experimental |
---|
513 | setup. As described by Hubbard and Dodd \cite{Hubbard02}, a number of |
---|
514 | researchers have used this benchmark problem to test their numerical |
---|
515 | models. {\bf Jane: check whether these results are now avilable as |
---|
516 | they were not in 2002}. Hubbard and Dodd \cite{Hubbard02} note that a |
---|
517 | particular 3D model appears to obtain slightly better results than the |
---|
518 | 2D ones reported but that 3D models are unlikely to be competitive in |
---|
519 | terms of computing power for applications in coastal engineering at |
---|
520 | least. Choi et al \cite{Choi07} use a 3D RANS model (based on the |
---|
521 | Navier-Stokes equations) for the same problem and find a very good |
---|
522 | comparison with laboratory and 2D numerical results. An obvious |
---|
523 | advantage of the 3D model is its ability to investigate the velocity |
---|
524 | field and Choi et al also report on the limitation of depth-averaged |
---|
525 | 2D models for run-up simulations of this type. |
---|
526 | |
---|
527 | Once results are availble, need to compare to Hubbard and Dodd and draw any conclusions |
---|
528 | from nested rectangular grid vs unstructured gird. |
---|
529 | Figure \ref{fig:circular screenshots} shows a sequence of screenshots depicting the evolution of the solitary wave as it hits the circular island. |
---|
530 | |
---|
531 | \begin{figure}[htbp] |
---|
532 | \centerline{ |
---|
533 | \includegraphics[width=5cm]{circular1.png} |
---|
534 | \includegraphics[width=5cm]{circular2.png}} |
---|
535 | \centerline{ |
---|
536 | \includegraphics[width=5cm]{circular3.png} |
---|
537 | \includegraphics[width=5cm]{circular4.png}} |
---|
538 | \centerline{ |
---|
539 | \includegraphics[width=5cm]{circular5.png} |
---|
540 | \includegraphics[width=5cm]{circular6.png}} |
---|
541 | \centerline{ |
---|
542 | \includegraphics[width=5cm]{circular7.png} |
---|
543 | \includegraphics[width=5cm]{circular8.png}} |
---|
544 | \centerline{ |
---|
545 | \includegraphics[width=5cm]{circular9.png} |
---|
546 | \includegraphics[width=5cm]{circular10.png}} |
---|
547 | \caption{Screenshots of the evolution of solitary wave around circular island.} |
---|
548 | \label{fig:circular screenshots} |
---|
549 | \end{figure} |
---|
550 | |
---|
551 | |
---|
552 | \clearpage |
---|
553 | |
---|
554 | \section{Conclusions} |
---|
555 | \label{sec:conclusions} |
---|
556 | ANUGA is a flexible and robust modelling system |
---|
557 | that simulates hydrodynamics by solving the shallow water wave |
---|
558 | equation in a triangular mesh. It can model the process of wetting |
---|
559 | and drying as water enters and leaves an area and is capable of |
---|
560 | capturing hydraulic shocks due to the ability of the finite-volume |
---|
561 | method to accommodate discontinuities in the solution. |
---|
562 | ANUGA can take as input bathymetric and topographic datasets and |
---|
563 | simulate the behaviour of riverine flooding, storm surge, |
---|
564 | tsunami or even dam breaks. |
---|
565 | Initial validation using wave tank data supports ANUGA's |
---|
566 | ability to model complex scenarios. Further validation will be |
---|
567 | pursued as additional datasets become available. |
---|
568 | The ANUGA source code and validation case studies reported here are available |
---|
569 | at \url{http://sourceforge.net/projects/anuga}. |
---|
570 | |
---|
571 | something about use on flood modelling community and their validation initiatives |
---|
572 | |
---|
573 | |
---|
574 | %\bibliographystyle{plainnat} |
---|
575 | \bibliographystyle{elsart-harv} |
---|
576 | \bibliography{anuga-bibliography} |
---|
577 | |
---|
578 | \end{document} |
---|