Changeset 4128
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 Dec 31, 2006, 1:50:19 PM (17 years ago)
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anuga_work/publications/linuxconf_2006/paper_ole_nielsen.tex
r4124 r4128 68 68 communities. Geoscience Australia and the Australian National 69 69 University have developed a hydrodynamic inundation modelling tool 70 called \AnuGA{} to help simulate the impact of these hazards. 70 called \AnuGA{} to help simulate the impact of these hazards. 71 71 The core of \AnuGA{} is a \Python{} implementation of a finitevolume method 72 72 for solving the conservative form of the Shallow Water Wave equation. … … 238 238 The flux $\HH_{ij}$ is evaluated using a numerical flux function 239 239 $\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow 240 water flux in the sense that for all vectors $\UU$ and$\nn$240 water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$ 241 241 $$ 242 242 H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 . … … 245 245 Then 246 246 $$ 247 \HH_{ij} = \HH(\ overline{\UU}_i(m_{ij})),248 \ overline{\UU}_i(m_{ij})),\mathbf{n}_{ij})247 \HH_{ij} = \HH(\UU_i(m_{ij}), 248 \UU_j(m_{ij}); \mathbf{n}_{ij}) 249 249 $$ 250 250 where $m_{ij}$ is the midpoint of the \textit{ij}th edge and 251 $\mathbf{n}_{ij}$ is the outward pointing normal on the252 \textit{ij}th edge. The function $\ overline{\UU}_i(x)$ for $x \in253 T_i$ is obtained from the average values, $\UU_i$, ofthe $i$th and251 $\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the 252 \textit{ij}th edge. The function $\UU_i(x)$ for $x \in 253 T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and 254 254 neighbouring cells. 255 255 … … 285 285 \label{sec:software} 286 286 287 \AnuGA{} is mostly written in the objectoriented programming 288 language \Python{} with computationally intensive parts implemented 289 as highly optimised shared objects written in C. 287 \AnuGA{} is mostly written in the objectoriented programming 288 language \Python{} with computationally intensive parts implemented 289 as highly optimised shared objects written in C. 290 290 291 291 \Python{} is known for its clarity, elegance, efficiency and … … 297 297 changing requirements throughout its lifetime. 298 298 299 The fundamental object in \AnuGA{} is the \code{Domain} which 300 inherits functionality from a hierarchy of increasingly specialised 301 classes starting with a basic structural Mesh to classes implementing 302 the finitevolume scheme described in section \ref{sec:fvm}. Other classes 303 are \code{Quantity} which represents values of one variable across the mesh 304 along with their associated operations, \code{Geospatial_data} which 305 represents georeferenced elevation data and a collection of \code{Boundary} 306 classes which allows for a 'pluggable' way of driving the model. 307 The conserved quantities updated automatically by the numerical scheme 308 are stage (water level) $w$, $x$momentum $uh$ and $y$momentum 309 $vh$. The quanitites elevation $z$ and friction $\eta$ are 310 quantities that are not updated automaticall but can be changed explicitly311 during runtime if the user wishes to do so. 312 313 To set up a scenario the user specifies the study area along with any internal 314 regions where increased mesh resolution is required. External edges may 315 be labelled using symbolic tags which are subsequently used to bind 316 boundary condition objects to tagged segments of the mesh boundary. 317 The mesh is then generated using \AnuGA{}'s builtin mesh generator and 318 converted into the \code{Domain} object which provides all methods used to 299 The fundamental object in \AnuGA{} is the \code{Domain} which 300 inherits functionality from a hierarchy of increasingly specialised 301 classes starting with a basic structural Mesh to classes implementing 302 the finitevolume scheme described in section \ref{sec:fvm}. Other classes 303 are \code{Quantity} which represents values of one variable across the mesh 304 along with their associated operations, \code{Geospatial_data} which 305 represents georeferenced elevation data and a collection of \code{Boundary} 306 classes which allows for a 'pluggable' way of driving the model. 307 The conserved quantities updated automatically by the numerical scheme 308 are stage (water level) $w$, $x$momentum $uh$ and $y$momentum 309 $vh$. The quanitites elevation $z$ and friction $\eta$ are 310 quantities that are not updated automatically but can be changed explicitly 311 during runtime if the user wishes to do so. 312 313 To set up a scenario the user specifies the study area along with any internal 314 regions where increased mesh resolution is required. External edges may 315 be labelled using symbolic tags which are subsequently used to bind 316 boundary condition objects to tagged segments of the mesh boundary. 317 The mesh is then generated using \AnuGA{}'s builtin mesh generator and 318 converted into the \code{Domain} object which provides all methods used to 319 319 setup and run the flow simulation. Figure \ref{fig:anuga mesh} shows an example of a mesh generated by \AnuGA{}. 320 320 \begin{figure} … … 322 322 \includegraphics[width=4in,keepaspectratio=true]{tsunamifig1} 323 323 \caption{Triangular mesh used in our finite volume method. Conserved 324 quantities $h$, $uh$ and $vh$ are associated with each triangular cell.} 324 quantities $h$, $uh$ and $vh$ are associated with each triangular cell.} 325 325 \label{fig:anuga mesh} 326 326 \end{center} … … 338 338 one of the following forms: 339 339 340 \begin{itemize} 341 \item A constant value as in domain.set_quantity('stage', 1)which340 \begin{itemize} 341 \item A constant value as in \code{domain.set_quantity('stage', 1)} which 342 342 will set the initial water level to 1 m everywhere. 343 \item Another quantity or a linear combination of quantities. If q1344 and q2are two arbitrary quantities defined within the same domain,345 the expression set_quantity('stage', q1*(3*q2 + 5))will set the stage343 \item Another quantity or a linear combination of quantities. If \code{q1} 344 and \code{q2} are two arbitrary quantities defined within the same domain, 345 the expression \code{domain.set_quantity('stage', q1*(3*q2 + 5))} will set the stage 346 346 quantity accordingly. One common application of this would be to 347 347 assign the stage as a constant depth above the bed elevation. 348 \item An arbitrary function (or a callable object), f(x, y), where x349 and y are assumed to be vectors. The quantity will be assigned values by350 evaluating fat each location within the mesh.348 \item An arbitrary function (or a callable object), \code{f(x, y)}, where \code{x} 349 and \code{y} are assumed to be vectors. The quantity will be assigned values by 350 evaluating \code{f} at each location within the mesh. 351 351 \item An arbitrary set of points and associated values (wrapped into a 352 352 Geospatial_data object). The points need not coincide with triangle … … 361 361 \item A Numerical Python array (or a list of numbers) ordered 362 362 according to the internal data structure. 363 \end{itemize} 364 The parameter locationdetermines whether the values should be365 assigned to triangle edge midpoints or vertices and regionallows the363 \end{itemize} 364 The parameter \code{location} determines whether the values should be 365 assigned to triangle edge, midpoints or vertices and \code{region} allows the 366 366 operation to be restricted to a region specified by a symbolic tag or 367 a set of indices. 367 a set of indices. 368 368 369 369 Boundary conditions are bound to symbolic tags through the method 370 370 \code{domain.set_boundary} which takes as input a lookup table (implemented 371 as a Python dictionary) of the form \code{\{tag:~boundary_object\}}. 371 as a Python dictionary) of the form \code{\{tag:~boundary_object\}}. 372 372 The boundary objects are all assumed to be callable functions of vectors x 373 373 and y. Several predefined standard boundary objects are available and … … 377 377 boundaries. 378 378 379 Forcing terms can be written according to a fixed protocol and added 380 to the model using the idiom \code{domain.forcing_terms.append(F)} where F is379 Forcing terms can be written according to a fixed protocol and added 380 to the model using the idiom \code{domain.forcing_terms.append(F)} where \code{F} is 381 381 assumed to be a userdefined callable object. 382 382 … … 387 387 large speeds and small triangles, time steps can become very small. 388 388 In order to access the state of the simulation at regular time 389 intervals, \AnuGA{} uses the method evolve: 390 \begin{verbatim} 391 For t in domain.evolve(yieldstep, duration): 389 intervals, \AnuGA{} uses the method evolve: 390 \begin{verbatim} 391 For t in domain.evolve(yieldstep, duration): 392 392 <model interrogation and modification> 393 \end{verbatim} 393 \end{verbatim} 394 394 The parameter \code{duration} specifies the time period over which 395 395 evolve operates, and control is passed to the body of the forloop at … … 402 402 Python generator hence the reference to 'yield' in the parameter name. 403 403 404 Figure \ref{fig:beach runup} shows a simulation of water flowing onto a 405 hypothetical beach with obstacles. 404 Figure \ref{fig:beach runup} shows a simulation of water flowing onto a 405 hypothetical beach with obstacles. 406 406 A number of complex patterns are captured in this example including a shock where water reflected off the wall far (at the right hand side) meets the main flow. Other physical features are the standing waves and interference patterns. 407 407 See the \AnuGA{} User Manual at \url{http://sourceforge.net/projects/anuga} for more details and examples. … … 475 475 476 476 \section{Conclusions} 477 \label{sec:6} 477 \label{sec:6} 478 478 \AnuGA{} is a flexible and robust modelling system 479 479 that simulates hydrodynamics by solving the shallow water wave … … 484 484 \AnuGA{} can take as input bathymetric and topographic datasets and 485 485 simulate the behaviour of riverine flooding, storm surge, 486 tsunami or even dam breaks. 486 tsunami or even dam breaks. 487 487 Initial validation using wave tank data supports \AnuGA{}'s 488 488 ability to model complex scenarios. Further validation will be … … 493 493 understand the potential impact from natural hazards in order to 494 494 reduce their impact on Australian communities (see \cite{Nielsen2006}). 495 The \AnuGA{} source code is available 495 The \AnuGA{} source code is available 496 496 at \url{http://sourceforge.net/projects/anuga}. 497 497
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