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13 | |
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14 | % The preamble is to contain your own \LaTeX\ commands and to say |
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15 | % what packages to use. Three useful packages are the following: |
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16 | \usepackage{graphicx} % avoid epsfig or earlier such packages |
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17 | \usepackage{url} % for URLs and DOIs |
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18 | \newcommand{\doi}[1]{\url{http://dx.doi.org/#1}} |
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19 | \usepackage{amsmath} % many want amsmath extensions |
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20 | \usepackage{amsfonts} |
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21 | \usepackage{underscore} |
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22 | % Avoid loading unused packages (as done by some \LaTeX\ editors). |
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23 | |
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24 | % Create title and authors using \verb|\maketitle|. Separate authors by |
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25 | % \verb|\and| and put addresses in \verb|\thanks| command with |
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26 | % \verb|\url| command \verb|\protect|ed. |
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27 | \title{On The Validation of A Hydrodynamic Model} |
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28 | |
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29 | \author{ |
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30 | D.~S.~Gray\thanks{Natural Hazard Impacts Project, Geospatial and |
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31 | Earth Monitoring Division, Geoscience Australia, Symonston, |
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32 | \textsc{Australia}. \protect\url{mailto:Duncan.Gray@ga.gov.au}}\footnotemark[1] |
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33 | \and |
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34 | T.~Baldock\thanks{University of Queensland, Brisbane, \textsc{Australia}. |
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35 | \protect\url{mailto:tom.baldock@uq.edu.au}}\footnotemark[2] |
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36 | \and |
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37 | O.~M.~Nielsen\footnotemark[1] |
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38 | \and |
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39 | M.~J.~Sexton\footnotemark[1] |
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40 | \and |
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41 | N.~Bartzis\footnotemark[1] |
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42 | \and |
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43 | S.~G.~Roberts\thanks{Department of Mathematics, Australian National University, |
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44 | Canberra, \textsc{Australia}. \protect\url{mailto:stephen.roberts@anu.edu.au}}} |
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45 | |
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46 | \date{30 May 2008} |
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47 | |
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48 | \newcommand{\ANUGA}{\textsc{ANUGA}} |
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49 | \newcommand{\Python}{\textsc{Python}} |
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50 | \newcommand{\VPython}{\textsc{VPython}} |
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51 | \newcommand{\pypar}{\textsc{mpi}} |
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52 | \newcommand{\Metis}{\textsc{Metis}} |
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53 | \newcommand{\mpi}{\textsc{mpi}} |
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54 | |
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55 | \newcommand{\UU}{\mathbf{U}} |
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56 | \newcommand{\VV}{\mathbf{V}} |
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57 | \newcommand{\EE}{\mathbf{E}} |
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58 | \newcommand{\GG}{\mathbf{G}} |
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59 | \newcommand{\FF}{\mathbf{F}} |
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60 | \newcommand{\HH}{\mathbf{H}} |
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61 | \newcommand{\SSS}{\mathbf{S}} |
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62 | \newcommand{\nn}{\mathbf{n}} |
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63 | |
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64 | \newcommand{\code}[1]{\texttt{#1}} |
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65 | |
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66 | |
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67 | |
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68 | \begin{document} |
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69 | |
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70 | % Use default \verb|\maketitle|. |
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71 | \maketitle |
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72 | |
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73 | % Use the \verb|abstract| environment. |
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74 | \begin{abstract} |
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75 | Modelling the effects on the built environment of natural hazards such |
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76 | as riverine flooding, storm surges and tsunami is critical for |
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77 | understanding their economic and social impact on our urban |
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78 | communities. Geoscience Australia and the Australian National |
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79 | University have developed a hydrodynamic inundation modelling tool |
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80 | called \ANUGA{} to help simulate the impact of these hazards. |
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81 | The core of \ANUGA{} is a \Python{} implementation of a finite-volume method |
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82 | for solving the conservative form of the Shallow Water Wave equation. |
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83 | In this paper we describe the model, the architecture and a range of |
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84 | validations that have been carried out to establish confidence in the model. |
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85 | |
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86 | |
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87 | \ANUGA{} is availbale as Open Source to enable |
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88 | free access to the software and allow the scientific community to |
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89 | use, validate and contribute to the software in the future. |
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90 | |
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91 | %This method allows the study area to be represented by an unstructured |
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92 | %mesh with variable resolution to suit the particular problem. The |
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93 | %conserved quantities are water level (stage) and horizontal momentum. |
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94 | %An important capability of ANUGA is that it can robustly model the |
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95 | %process of wetting and drying as water enters and leaves an area. This |
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96 | %means that it is suitable for simulating water flow onto a beach or |
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97 | %dry land and around structures such as buildings. |
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98 | |
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99 | |
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100 | \end{abstract} |
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101 | |
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102 | % By default we include a table of contents in each paper. |
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103 | %\tableofcontents |
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104 | |
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105 | % Use \verb|\section|, \verb|\subsection|, \verb|\subsubsection| and |
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106 | % possibly \verb|\paragraph| to structure your document. Make sure |
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107 | % you \verb|\label| them for cross-referencing with \verb|\ref|\,. |
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108 | |
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109 | %\clearpage |
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110 | \section{Introduction} |
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111 | \label{sec:intro} |
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112 | |
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113 | The Indian Ocean tsunami on 26 December 2004 demonstrated the |
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114 | potentially catastrophic consequences of natural hazards. While the |
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115 | scale of the impact from such events is not common, smaller-scale |
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116 | tsunami regularly threaten coastal communities |
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117 | around the world. Earthquakes which occur in the Java Trench near |
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118 | Indonesia (e.g.~\cite{TsuMIS1995} or \cite{Baldwin-2006}) and along |
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119 | the Puysegur Ridge to the south of New Zealand (e.g.~\cite{LebKC1998}) |
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120 | have potential to generate tsunami that may threaten Australia's |
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121 | northwestern and southeastern coastlines. In addition, the |
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122 | preferential development of Australian coastal corridors means that |
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123 | inundation from hydrological disasters such as tsunami or storm-surge |
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124 | of even a few hundred metres beyond the shoreline has increased |
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125 | potential to cause significant disruption and loss. The extent of |
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126 | inundation is critically linked to the event, tidal conditions, |
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127 | bathymetry and topography and it not feasible to make impact |
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128 | predictions using heuristics alone. |
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129 | |
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130 | Hydrodynamic modelling allows impacts from flooding, storm-surge and |
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131 | tsunami to be better understood, their impacts to be anticipated and, |
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132 | with appropriate planning, their effects to be mitigated. Geoscience |
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133 | Australia in collaboration with the Mathematical Sciences Institute, |
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134 | Australian National University, is developing a software application |
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135 | called \ANUGA{} to model the hydrodynamics of floods, storm surges and |
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136 | tsunami. These hazards are modelled using the conservative shallow |
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137 | water equations which are described in section~\ref{sec:model}. In |
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138 | \ANUGA{} these equations are solved using a finite volume method as |
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139 | described in section~\ref{sec:fvm}. A more complete discussion of the |
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140 | method can be found in \cite{modsim2005} where the model and solution |
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141 | technique is validated on a standard tsunami benchmark data set. |
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142 | Section~\ref{sec:software} describes the software implementation and |
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143 | the API while section~\ref{sec:validation} presents some |
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144 | validation results. |
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145 | |
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146 | |
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147 | \section{Model} |
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148 | \label{sec:model} |
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149 | |
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150 | The shallow water wave equations are a system of differential |
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151 | conservation equations which describe the flow of a thin layer of |
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152 | fluid over terrain. The form of the equations are: |
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153 | \[ |
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154 | \frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial |
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155 | x}+\frac{\partial \GG}{\partial y}=\SSS |
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156 | \] |
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157 | where $\UU=\left[ {{\begin{array}{*{20}c} |
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158 | h & {uh} & {vh} \\ |
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159 | \end{array} }} \right]^T$ is the vector of conserved quantities; water depth |
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160 | $h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities |
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161 | entering the system are bed elevation $z$ and stage (absolute water |
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162 | level) $w$, where the relation $w = z + h$ holds true at all times. |
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163 | The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given |
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164 | by |
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165 | \[ |
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166 | \EE=\left[ {{\begin{array}{*{20}c} |
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167 | {uh} \hfill \\ |
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168 | {u^2h+gh^2/2} \hfill \\ |
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169 | {uvh} \hfill \\ |
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170 | \end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c} |
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171 | {vh} \hfill \\ |
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172 | {vuh} \hfill \\ |
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173 | {v^2h+gh^2/2} \hfill \\ |
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174 | \end{array} }} \right] |
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175 | \] |
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176 | and the source term (which includes gravity and friction) is given |
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177 | by |
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178 | \[ |
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179 | \SSS=\left[ {{\begin{array}{*{20}c} |
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180 | 0 \hfill \\ |
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181 | -{gh(z_{x} + S_{fx} )} \hfill \\ |
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182 | -{gh(z_{y} + S_{fy} )} \hfill \\ |
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183 | \end{array} }} \right] |
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184 | \] |
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185 | where $S_f$ is the bed friction. The friction term is modelled using |
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186 | Manning's resistance law |
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187 | \[ |
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188 | S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy} |
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189 | =\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}} |
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190 | \] |
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191 | in which $\eta$ is the Manning resistance coefficient. |
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192 | |
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193 | As demonstrated in our papers, \cite{modsim2005,Rob99l} these |
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194 | equations provide an excellent model of flows associated with |
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195 | inundation such as dam breaks and tsunamis. |
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196 | |
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197 | \section{Finite Volume Method} |
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198 | \label{sec:fvm} |
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199 | |
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200 | We use a finite-volume method for solving the shallow water wave |
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201 | equations \cite{Rob99l}. The study area is represented by a mesh of |
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202 | triangular cells as in Figure~\ref{fig:mesh} in which the conserved |
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203 | quantities of water depth $h$, and horizontal momentum $(uh, vh)$, |
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204 | in each volume are to be determined. The size of the triangles may |
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205 | be varied within the mesh to allow greater resolution in regions of |
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206 | particular interest. |
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207 | |
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208 | \begin{figure} |
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209 | \begin{center} |
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210 | \includegraphics[width=5.0cm,keepaspectratio=true]{step-five} |
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211 | \caption{Triangular mesh used in our finite volume method. Conserved |
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212 | quantities $h$, $uh$ and $vh$ are associated with the centroid of |
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213 | each triangular cell.} \label{fig:mesh} |
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214 | \end{center} |
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215 | \end{figure} |
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216 | |
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217 | The equations constituting the finite-volume method are obtained by |
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218 | integrating the differential conservation equations over each |
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219 | triangular cell of the mesh. Introducing some notation we use $i$ to |
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220 | refer to the $i$th triangular cell $T_i$, and ${\cal N}(i)$ to the |
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221 | set of indices referring to the cells neighbouring the $i$th cell. |
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222 | Then $A_i$ is the area of the $i$th triangular cell and $l_{ij}$ is |
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223 | the length of the edge between the $i$th and $j$th cells. |
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224 | |
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225 | By applying the divergence theorem we obtain for each volume an |
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226 | equation which describes the rate of change of the average of the |
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227 | conserved quantities within each cell, in terms of the fluxes across |
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228 | the edges of the cells and the effect of the source terms. In |
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229 | particular, rate equations associated with each cell have the form |
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230 | $$ |
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231 | \frac{d\UU_i }{dt}+ \frac1{A_i}\sum\limits_{j\in{\cal N}(i)} \HH_{ij} l_{ij} = \SSS_i |
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232 | $$ |
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233 | where |
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234 | \begin{itemize} |
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235 | \item $\UU_i$ the vector of conserved quantities averaged over the $i$th cell, |
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236 | \item $\SSS_i$ is the source term associated with the $i$th cell, |
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237 | and |
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238 | \item $\HH_{ij}$ is the outward normal flux of |
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239 | material across the \textit{ij}th edge. |
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240 | \end{itemize} |
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241 | |
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242 | |
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243 | %\item $l_{ij}$ is the length of the edge between the $i$th and $j$th |
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244 | %cells |
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245 | %\item $m_{ij}$ is the midpoint of |
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246 | %the \textit{ij}th edge, |
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247 | %\item |
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248 | %$\mathbf{n}_{ij} = (n_{ij,1} , n_{ij,2})$is the outward pointing |
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249 | %normal along the \textit{ij}th edge, and The |
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250 | |
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251 | The flux $\HH_{ij}$ is evaluated using a numerical flux function |
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252 | $\HH(\cdot, \cdot ; \ \cdot)$ which is consistent with the shallow |
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253 | water flux in the sense that for all conservation vectors $\UU$ and normal vectors $\nn$ |
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254 | $$ |
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255 | H(\UU,\UU;\ \nn) = \EE(\UU) n_1 + \GG(\UU) n_2 . |
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256 | $$ |
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257 | |
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258 | Then |
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259 | $$ |
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260 | \HH_{ij} = \HH(\UU_i(m_{ij}), |
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261 | \UU_j(m_{ij}); \mathbf{n}_{ij}) |
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262 | $$ |
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263 | where $m_{ij}$ is the midpoint of the \textit{ij}th edge and |
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264 | $\mathbf{n}_{ij}$ is the outward pointing normal, with respect to the $i$th cell, on the |
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265 | \textit{ij}th edge. The function $\UU_i(x)$ for $x \in |
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266 | T_i$ is obtained from the vector $\UU_k$ of conserved average values for the $i$th and |
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267 | neighbouring cells. |
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268 | |
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269 | We use a second order reconstruction to produce a piece-wise linear |
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270 | function construction of the conserved quantities for all $x \in |
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271 | T_i$ for each cell (see Figure~\ref{fig:mesh:reconstruct}. This |
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272 | function is allowed to be discontinuous across the edges of the |
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273 | cells, but the slope of this function is limited to avoid |
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274 | artificially introduced oscillations. |
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275 | |
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276 | Godunov's method (see \cite{Toro-92}) involves calculating the |
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277 | numerical flux function $\HH(\cdot, \cdot ; \ \cdot)$ by exactly |
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278 | solving the corresponding one dimensional Riemann problem normal to |
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279 | the edge. We use the central-upwind scheme of \cite{KurNP2001} to |
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280 | calculate an approximation of the flux across each edge. |
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281 | |
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282 | \begin{figure} |
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283 | \begin{center} |
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284 | \includegraphics[width=5.0cm,keepaspectratio=true]{step-reconstruct} |
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285 | \caption{From the values of the conserved quantities at the centroid |
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286 | of the cell and its neighbouring cells, a discontinuous piecewise |
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287 | linear reconstruction of the conserved quantities is obtained.} |
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288 | \label{fig:mesh:reconstruct} |
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289 | \end{center} |
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290 | \end{figure} |
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291 | |
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292 | In the computations presented in this paper we use an explicit Euler |
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293 | time stepping method with variable timestepping adapted to the |
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294 | observed CFL condition. |
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295 | |
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296 | |
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297 | \section{Software Implementation} |
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298 | \label{sec:software} |
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299 | |
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300 | \ANUGA{} is mostly written in the object-oriented programming |
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301 | language \Python{} with computationally intensive parts implemented |
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302 | as highly optimised shared objects written in C. |
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303 | |
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304 | \Python{} is known for its clarity, elegance, efficiency and |
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305 | reliability. Complex software can be built in \Python{} without undue |
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306 | distractions arising from idiosyncrasies of the underlying software |
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307 | language syntax. In addition, \Python{}'s automatic memory management, |
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308 | dynamic typing, object model and vast number of libraries means that |
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309 | software can be produced quickly and can be readily adapted to |
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310 | changing requirements throughout its lifetime. |
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311 | |
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312 | The fundamental object in \ANUGA{} is the \code{Domain} which |
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313 | inherits functionality from a hierarchy of increasingly specialised |
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314 | classes starting with a basic structural Mesh to classes implementing |
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315 | the finite-volume scheme described in section \ref{sec:fvm}. Other classes |
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316 | are \code{Quantity} which represents values of one variable across the mesh |
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317 | along with their associated operations, \code{Geospatial_data} which |
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318 | represents georeferenced elevation data and a collection of \code{Boundary} |
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319 | classes which allows for a 'pluggable' way of driving the model. |
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320 | The conserved quantities updated automatically by the numerical scheme |
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321 | are stage (water level) $w$, $x$-momentum $uh$ and $y$-momentum |
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322 | $vh$. The quanitites elevation $z$ and friction $\eta$ are |
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323 | quantities that are not updated automatically but can be changed explicitly |
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324 | during run-time if the user wishes to do so. |
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325 | |
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326 | To set up a scenario the user specifies the study area along with any internal |
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327 | regions where increased mesh resolution is required. External edges may |
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328 | be labelled using symbolic tags which are subsequently used to bind |
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329 | boundary condition objects to tagged segments of the mesh boundary. |
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330 | The mesh is then generated using \ANUGA{}'s built-in mesh generator and |
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331 | converted into the \code{Domain} object which provides all methods used to |
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332 | setup and run the flow simulation. Figure \ref{fig:anuga mesh} shows an example of a mesh generated by \ANUGA{}. |
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333 | \begin{figure} |
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334 | \begin{center} |
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335 | \includegraphics[width=4in,keepaspectratio=true]{triangular-mesh} |
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336 | \caption{Triangular mesh used in our finite volume method. Conserved |
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337 | quantities $h$, $uh$ and $vh$ are associated with each triangular cell.} |
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338 | \label{fig:anuga mesh} |
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339 | \end{center} |
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340 | \end{figure} |
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341 | |
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342 | |
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343 | |
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344 | Next step is to setup initial conditions for each \code{Quantity} object. For |
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345 | the elevation $z$ this is typically obtained from bathymetric and |
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346 | topographic data sets. Setting initial values for quantities is done |
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347 | through the method \code{domain.set_quantity(name, X, location, |
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348 | region)} where name is the name of the quantity (e.g.\ 'stage', |
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349 | 'xmomentum', 'ymomentum', 'elevation' or 'friction'). The variable X |
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350 | represents the source data for populating the quantity and may take |
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351 | one of the following forms: |
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352 | |
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353 | \begin{itemize} |
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354 | \item A constant value as in \code{domain.set_quantity('stage', 1)} which |
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355 | will set the initial water level to 1 m everywhere. |
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356 | \item Another quantity or a linear combination of quantities. If \code{q1} |
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357 | and \code{q2} are two arbitrary quantities defined within the same domain, |
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358 | the expression \code{domain.set_quantity('stage', q1*(3*q2 + 5))} will set the stage |
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359 | quantity accordingly. One common application of this would be to |
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360 | assign the stage as a constant depth above the bed elevation. |
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361 | \item An arbitrary function (or a callable object), \code{f(x, y)}, where \code{x} |
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362 | and \code{y} are assumed to be vectors. The quantity will be assigned values by |
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363 | evaluating \code{f} at each location within the mesh. |
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364 | \item An arbitrary set of points and associated values (wrapped into a |
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365 | Geospatial_data object). The points need not coincide with triangle |
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366 | vertices or centroids and a penalised least squares technique is |
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367 | employed to populate the quantity in a smooth and stable way. |
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368 | Since the least squares technique can be time consuming for large |
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369 | problems, \code{set_quantity} employs a caching technique which automatically |
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370 | decides whether to perform the computations or retrieve them from a |
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371 | cache. This will typically speed up the build by several orders of |
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372 | magnitude after each computation has been performed once. |
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373 | \item A filename containing points and attributes. |
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374 | \item A Numerical Python array (or a list of numbers) ordered |
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375 | according to the internal data structure. |
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376 | \end{itemize} |
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377 | The parameter \code{location} determines whether the values should be |
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378 | assigned to triangle edge, midpoints or vertices and \code{region} allows the |
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379 | operation to be restricted to a region specified by a symbolic tag or |
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380 | a set of indices. |
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381 | |
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382 | Boundary conditions are bound to symbolic tags through the method |
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383 | \code{domain.set_boundary} which takes as input a lookup table (implemented |
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384 | as a Python dictionary) of the form \code{\{tag:~boundary_object\}}. |
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385 | The boundary objects are all assumed to be callable functions of vectors x |
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386 | and y. Several predefined standard boundary objects are available and |
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387 | it is relatively straightforward to define problem-specific custom |
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388 | boundaries if needed. The predefined boundary conditions include |
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389 | Dirichlet, Reflective, Transmissive, Temporal, and Spatio-Temporal |
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390 | boundaries. |
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391 | |
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392 | Forcing terms can be written according to a fixed protocol and added |
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393 | to the model using the idiom \code{domain.forcing_terms.append(F)} where \code{F} is |
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394 | assumed to be a user-defined callable object. |
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395 | |
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396 | When the simulation is running, the length of each time step is |
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397 | determined from the maximal speeds encountered and the sizes of |
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398 | triangles in order not to violate the CFL condition which specifies |
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399 | that no information should skip any triangles in one time step. With |
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400 | large speeds and small triangles, time steps can become very small. |
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401 | In order to access the state of the simulation at regular time |
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402 | intervals, \ANUGA{} uses the method evolve: |
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403 | \begin{verbatim} |
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404 | For t in domain.evolve(yieldstep, duration): |
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405 | <model interrogation and modification> |
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406 | \end{verbatim} |
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407 | The parameter \code{duration} specifies the time period over which |
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408 | evolve operates, and control is passed to the body of the for-loop at |
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409 | each fixed time step called \code{yieldstep}. The internal workings |
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410 | of the numerical scheme and its variable time stepping are thus |
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411 | decoupled from the fixed time stepping of the evolve loop. This means |
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412 | that the user of the API may access the model at fixed timesteps to |
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413 | e.g.\ store model outputs, interrogate quantities or change the model |
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414 | itself at runtime. The evolve method has been implemented using a |
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415 | Python generator hence the reference to 'yield' in the parameter name. |
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416 | |
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417 | Figure \ref{fig:beach runup} shows a simulation of water flowing onto a |
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418 | hypothetical beach with obstacles. |
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419 | 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. |
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420 | See the \ANUGA{} User Manual at \url{http://sourceforge.net/projects/anuga} for more details and examples. |
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421 | \begin{figure} |
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422 | \begin{center} |
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423 | \includegraphics[width=4in,keepaspectratio=true]{runup} |
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424 | \caption{A hypothetical runup scenario.} |
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425 | \label{fig:beach runup} |
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426 | \end{center} |
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427 | \end{figure} |
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428 | |
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429 | |
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430 | |
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431 | \section{Validation} |
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432 | \label{sec:validation} The process of validating the \ANUGA{} |
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433 | application is in its early stages, however initial indications are |
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434 | encouraging. |
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435 | |
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436 | As part of the Third International Workshop on Long-wave Runup |
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437 | Models in 2004 (\url{http://www.cee.cornell.edu/longwave}), four |
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438 | benchmark problems were specified to allow the comparison of |
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439 | numerical, analytical and physical models with laboratory and field |
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440 | data. One of these problems describes a wave tank simulation of the |
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441 | 1993 Okushiri Island tsunami off Hokkaido, Japan \cite{MatH2001}. A |
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442 | significant feature of this tsunami was a maximum run-up of 32~m |
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443 | observed at the head of the Monai Valley. This run-up was not |
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444 | uniform along the coast and is thought to have resulted from a |
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445 | particular topographic effect. Among other features, simulations of |
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446 | the Hokkaido tsunami should capture this run-up phenomenon. |
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447 | |
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448 | \begin{figure}[htbp] |
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449 | \centerline{\includegraphics[width=4in]{okushiri-gauge-5.eps}} |
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450 | \caption{Comparison of wave tank and \ANUGA{} water stages at gauge |
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451 | 5.}\label{fig:val} |
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452 | \end{figure} |
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453 | |
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454 | |
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455 | \begin{figure}[htbp] |
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456 | \centerline{\includegraphics[width=4in]{okushiri-model.eps}} |
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457 | \caption{Complex reflection patterns and run-up into Monai Valley |
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458 | simulated by \ANUGA{} and visualised using our netcdf OSG |
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459 | viewer.}\label{fig:run} |
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460 | \end{figure} |
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461 | |
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462 | |
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463 | The wave tank simulation of the Hokkaido tsunami was used as the |
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464 | first scenario for validating \ANUGA{}. The dataset provided |
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465 | bathymetry and topography along with initial water depth and the |
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466 | wave specifications. The dataset also contained water depth time |
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467 | series from three wave gauges situated offshore from the simulated |
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468 | inundation area. |
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469 | |
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470 | Figure~\ref{fig:val} compares the observed wave tank and modelled |
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471 | \ANUGA{} water depth (stage height) at one of the gauges. The plots |
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472 | show good agreement between the two time series, with \ANUGA{} |
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473 | closely modelling the initial draw down, the wave shoulder and the |
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474 | subsequent reflections. The discrepancy between modelled and |
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475 | simulated data in the first 10 seconds is due to the initial |
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476 | condition in the physical tank not being uniformly zero. Similarly |
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477 | good comparisons are evident with data from the other two gauges. |
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478 | Additionally, \ANUGA{} replicates exceptionally well the 32~m Monai |
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479 | Valley run-up, and demonstrates its occurrence to be due to the |
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480 | interaction of the tsunami wave with two juxtaposed valleys above |
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481 | the coastline. The run-up is depicted in Figure~\ref{fig:run}. |
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482 | |
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483 | This successful replication of the tsunami wave tank simulation on a |
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484 | complex 3D beach is a positive first step in validating the \ANUGA{} |
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485 | modelling capability. Subsequent validation will be conducted as |
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486 | additional datasets become available. |
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487 | |
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488 | |
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489 | \section{Conclusions} |
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490 | \label{sec:6} |
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491 | \ANUGA{} is a flexible and robust modelling system |
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492 | that simulates hydrodynamics by solving the shallow water wave |
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493 | equation in a triangular mesh. It can model the process of wetting |
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494 | and drying as water enters and leaves an area and is capable of |
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495 | capturing hydraulic shocks due to the ability of the finite-volume |
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496 | method to accommodate discontinuities in the solution. |
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497 | \ANUGA{} can take as input bathymetric and topographic datasets and |
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498 | simulate the behaviour of riverine flooding, storm surge, |
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499 | tsunami or even dam breaks. |
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500 | Initial validation using wave tank data supports \ANUGA{}'s |
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501 | ability to model complex scenarios. Further validation will be |
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502 | pursued as additional datasets become available. |
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503 | \ANUGA{} is already being used to model the behaviour of |
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504 | hydrodynamic natural hazards. This modelling capability is part of |
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505 | Geoscience Australia's ongoing research effort to model and |
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506 | understand the potential impact from natural hazards in order to |
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507 | reduce their impact on Australian communities (see \cite{Nielsen2006}). |
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508 | The \ANUGA{} source code is available |
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509 | at \url{http://sourceforge.net/projects/anuga}. |
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510 | |
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511 | \bibliographystyle{plain} |
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512 | \bibliography{anuga-bibliography} |
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513 | |
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514 | |
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515 | |
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516 | |
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517 | \end{document} |
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