1 | %Anuga validation publication |
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2 | % |
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3 | %Geoscience Australia and others 2007-2008 |
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4 | |
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5 | % Use the Elsevier LaTeX document class |
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6 | %\documentclass{elsart3p} % Two column |
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17 | \usepackage{natbib} % Suggested by the Elsevier style |
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22 | %\newcommand{\Python}{\textsc{Python}} |
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23 | %\newcommand{\VPython}{\textsc{VPython}} |
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24 | \newcommand{\pypar}{\textsc{mpi}} |
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25 | \newcommand{\Metis}{\textsc{Metis}} |
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26 | \newcommand{\mpi}{\textsc{mpi}} |
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27 | |
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28 | \newcommand{\UU}{\mathbf{U}} |
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29 | \newcommand{\VV}{\mathbf{V}} |
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30 | \newcommand{\EE}{\mathbf{E}} |
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31 | \newcommand{\GG}{\mathbf{G}} |
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32 | \newcommand{\FF}{\mathbf{F}} |
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33 | \newcommand{\HH}{\mathbf{H}} |
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34 | \newcommand{\SSS}{\mathbf{S}} |
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35 | \newcommand{\nn}{\mathbf{n}} |
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36 | |
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37 | \newcommand{\code}[1]{\texttt{#1}} |
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38 | |
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40 | |
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41 | |
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42 | \begin{document} |
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43 | |
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44 | |
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45 | \begin{frontmatter} |
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46 | \title{On The Validation of A Hydrodynamic Model} |
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47 | |
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48 | |
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49 | \author[GA]{D.~S.~Gray} |
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50 | \ead{Duncan.Gray@ga.gov.au} |
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51 | \author[GA]{O.~M.~Nielsen} |
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52 | \ead{Ole.Nielsen@ga.gov.au} |
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53 | \author[GA]{M.~J.~Sexton} |
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54 | \ead{Jane.Sexton@ga.gov.au} |
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55 | \author[GA]{L.~Fountain} |
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56 | \author[GA]{K.~VanPutten} |
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57 | \author[ANU]{S.~G.~Roberts} |
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58 | \ead{Stephen.Roberts@anu.edu.au} |
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59 | \author[UQ]{T.~Baldock} |
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60 | \ead{Tom.Baldock@uq.edu.au} |
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61 | \author[UQ]{M.~Barnes} |
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62 | \ead{Matthew.Barnes@uq.edu.au} |
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63 | |
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64 | \address[GA]{Georisk Project, |
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65 | Geospatial and Earh Monitoring Division, |
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66 | Geoscience Australia, Canberra, Australia} |
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67 | |
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68 | \address[ANU]{Department of Mathematics, |
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69 | Australian National University, Canberra, Australia} |
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70 | |
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71 | \address[UQ]{University of Queensland, Brisbane, Australia} |
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72 | |
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73 | |
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74 | % Use the \verb|abstract| environment. |
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75 | \begin{abstract} |
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76 | Modelling the effects on the built environment of natural hazards such |
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77 | as riverine flooding, storm surges and tsunami is critical for |
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78 | understanding their economic and social impact on our urban |
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79 | communities. Geoscience Australia and the Australian National |
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80 | University have developed a hydrodynamic inundation modelling tool |
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81 | called ANUGA to help simulate the impact of these hazards. |
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82 | The core of ANUGA is a Python implementation of a finite-volume method |
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83 | for solving the conservative form of the Shallow Water Wave equation. |
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84 | |
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85 | In this paper, a number of tests are performed to validate ANUGA. These tests |
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86 | range from benchmark problems to wave and flume tank examples. |
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87 | ANUGA is available 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 | \end{abstract} |
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100 | |
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101 | |
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102 | \begin{keyword} |
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103 | % keywords here, in the form: keyword \sep keyword |
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104 | % PACS codes here, in the form: \PACS code \sep code |
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105 | |
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106 | Hydrodynamic Modelling \sep Model validation \sep |
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107 | Finite-volumes \sep Shallow water wave equation |
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108 | |
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109 | \end{keyword} |
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110 | |
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111 | \date{\today()} |
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112 | \end{frontmatter} |
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113 | |
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114 | |
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115 | |
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116 | |
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117 | % Begin document in earnest |
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118 | \section{Introduction} |
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119 | \label{sec:intro} |
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120 | |
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121 | Hydrodynamic modelling allows impacts from flooding, storm-surge and |
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122 | tsunami to be better understood, their impacts to be anticipated and, |
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123 | with appropriate planning, their effects to be mitigated. A significant |
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124 | proportion of the Australian population reside in the coastal |
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125 | corridors, thus the potential of significant disruption and loss |
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126 | is real. The extent of |
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127 | inundation is critically linked to the event, tidal conditions, |
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128 | bathymetry and topography and it not feasible to make impact |
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129 | predictions using heuristics alone. |
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130 | Geoscience |
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131 | Australia in collaboration with the Mathematical Sciences Institute, |
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132 | Australian National University, is developing a software application |
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133 | called ANUGA to model the hydrodynamics of floods, storm surges and |
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134 | tsunami. These hazards are modelled using the conservative shallow |
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135 | water equations which are described in section~\ref{sec:model}. In |
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136 | ANUGA these equations are solved using a finite volume method as |
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137 | described in section~\ref{sec:model}. A more complete discussion of the |
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138 | method can be found in \citet{Nielsen2005} where the model and solution |
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139 | technique is validated on a standard tsunami benchmark data set |
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140 | or in \citet{Roberts2007} where the numerical method and parallelisation |
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141 | of ANUGA is discussed. |
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142 | This modelling capability is part of |
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143 | Geoscience Australia's ongoing research effort to model and |
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144 | understand the potential impact from natural hazards in order to |
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145 | reduce their impact on Australian communities \citep{Nielsen2006}. |
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146 | ANUGA is currently being trialled for flood |
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147 | modelling \citep{Rigby2008}. |
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148 | |
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149 | The validity of other hydrodynamic models have been reported |
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150 | elsewhere, with \citet{Hubbard02} providing an |
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151 | excellent review of 1D and 2D models and associated validation |
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152 | tests. They described the evolution of these models from fixed, nested |
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153 | to adaptive grids and the ability of the solvers to cope with the |
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154 | moving shoreline. They highlighted the difficulty in verifying the |
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155 | nonlinear shallow water equations themselves as the only standard |
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156 | analytical solution is that of \citet{Carrier58} that is strictly for |
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157 | non-breaking waves. Further, |
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158 | whilst there is a 2D analytic solution from \citet{Thacker81}, it appears |
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159 | that the circular island wave tank example of Briggs et al will become |
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160 | the standard data set to verify the equations. |
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161 | |
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162 | This paper will describe the validation outputs in a similar way to |
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163 | \citet{Hubbard02} to |
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164 | present an exhaustive validation of the numerical model. |
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165 | Further to these tests, we will |
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166 | incorporate a test to verify friction values. The tests reported in |
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167 | this paper are: |
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168 | \begin{itemize} |
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169 | \item Verification against the 1D analytical solution of Carrier and |
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170 | Greenspan (p~\pageref{sec:carrier}) |
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171 | \item Testing against 1D (flume) data sets to verify wave height and |
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172 | velocity (p~\pageref{sec:stage and velocity}) |
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173 | \item Determining friction values from 1D flume data sets |
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174 | (p~\pageref{sec:friction}) |
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175 | \item Validation against a genuinely 2D analytical |
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176 | solution of the model equations (p~\ref{sec:XXX}) |
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177 | \item Testing against the 2D Okushiri benchmark problem |
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178 | (p~\pageref{sec:okushiri}) |
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179 | \item Testing against the 2D data sets modelling wave run-up around a circular island by Briggs et al. |
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180 | (p~\pageref{sec:circular island}) |
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181 | \end{itemize} |
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182 | |
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183 | |
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184 | Throughout the paper, qualitative comparisons will be drawn against |
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185 | other models. Moreover, all source code necessary to reproduce the |
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186 | results reported in this paper is available as part of the ANUGA |
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187 | distribution in the form of a test suite. It is thus possible for |
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188 | anyone to readily verify that the implementation meets the |
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189 | requirements set out by these benchmarks. |
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190 | |
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191 | |
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192 | %Hubbard and Dodd's model, OTT-2D, has some similarities to ANUGA, and |
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193 | %whilst the mesh can be refined, it is based on rectangular mesh. |
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194 | |
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195 | %The ANUGA model and numerical scheme is briefly described in |
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196 | %section~\ref{sec:model}. A more detailed description of the numerical |
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197 | %scheme and software implementation can be found in \citet{Nielsen2005} and |
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198 | %\citet{Roberts2007}. |
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199 | The six case studies to validation and verify ANUGA |
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200 | will be presented in section~\ref{sec:validation}, with the |
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201 | conclusions outlined in section~\ref{sec:conclusions}. |
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202 | |
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203 | NOTE: This is just a brain dump at the moment and needs to be incorporated properly |
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204 | in the text somewhere. |
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205 | |
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206 | Need some discussion on Bousssinesq type models - Boussinesq equations get the |
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207 | nonlinearity and dispersive effects to a high degree of accuracy |
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208 | |
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209 | moving wet-dry boundary algorithms - applicability to coastal engineering |
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210 | |
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211 | Fuhrman and Madesn 2008 \cite{Fuhrman2008}do validation - they have a Boussinesq type |
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212 | model, finite |
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213 | difference (therefore needing a supercomputer), 4th order, four stage RK time stepping |
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214 | scheme. |
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215 | |
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216 | their tests are (1) nonlinear run-up on periodic and transient waves on a sloping |
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217 | beach with excellent comparison to analytic solutions (2) 2d parabolic basin |
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218 | (3) solitary wave evolution through 2d triangular channel (4) solitary wave evolution on |
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219 | conical island (we need to compare to their computation time and note they use a |
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220 | vertical exaggeration for their images) |
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221 | |
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222 | excellent accuracy mentioned - but what is it - what does it mean? |
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223 | |
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224 | of interest is that they mention mass conservation and calculate it throughout the simulations |
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225 | |
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226 | Kim et al \cite{DaiHong2007} use Riemann solver - talk about improved accuracy by using 2nd order upwind |
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227 | scheme. Use finite volume on a structured mesh. Do parabolic basic and circular island. Needed? |
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228 | |
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229 | Delis et all 2008 \cite{Delis2008}- finite volume, Godunov-type explicit scheme coupled with Roe's |
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230 | approximate Riemann solver. It accurately describes breaking waves as bores or hydraulic jumps |
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231 | and conserves volume across flow discontinuties - is this just a result of finite volume? |
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232 | |
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233 | They also show mass conservation for most of the simulations |
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234 | |
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235 | similar range of validation tests that compare well - our job to compare to these as well |
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236 | |
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237 | \section{Mathematical model, numerical scheme and implementation} |
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238 | \label{sec:model} |
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239 | |
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240 | The ANUGA model is based on the shallow water wave equations which are |
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241 | widely regarded as suitable for modelling 2D flows subject to the |
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242 | assumptions that horizontal scales (e.g. wave lengths) greatly exceed |
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243 | the depth, vertical velocities are negligible and the fluid is treated |
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244 | as inviscid and incompressible. See e.g. the classical texts |
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245 | \citet{Stoker57} and \citet{Peregrine67} for the background or |
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246 | \citet{Roberts1999} for more details on the mathematical model |
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247 | used by ANUGA. |
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248 | |
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249 | The conservation form of the shallow water wave |
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250 | equations used in ANUGA are: |
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251 | \[ |
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252 | \frac{\partial \UU}{\partial t}+\frac{\partial \EE}{\partial |
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253 | x}+\frac{\partial \GG}{\partial y}=\SSS |
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254 | \] |
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255 | where $\UU=\left[ {{\begin{array}{*{20}c} |
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256 | h & {uh} & {vh} \\ |
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257 | \end{array} }} \right]^T$ is the vector of conserved quantities; water depth |
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258 | $h$, $x$-momentum $uh$ and $y$-momentum $vh$. Other quantities |
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259 | entering the system are bed elevation $z$ and stage (absolute water |
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260 | level above a reference datum such as Mean Sea Level) $w$, |
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261 | where the relation $w = z + h$ holds true at all times. |
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262 | The fluxes in the $x$ and $y$ directions, $\EE$ and $\GG$ are given |
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263 | by |
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264 | \[ |
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265 | \EE=\left[ {{\begin{array}{*{20}c} |
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266 | {uh} \hfill \\ |
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267 | {u^2h+gh^2/2} \hfill \\ |
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268 | {uvh} \hfill \\ |
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269 | \end{array} }} \right]\mbox{ and }\GG=\left[ {{\begin{array}{*{20}c} |
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270 | {vh} \hfill \\ |
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271 | {vuh} \hfill \\ |
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272 | {v^2h+gh^2/2} \hfill \\ |
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273 | \end{array} }} \right] |
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274 | \] |
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275 | and the source term (which includes gravity and friction) is given |
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276 | by |
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277 | \[ |
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278 | \SSS=\left[ {{\begin{array}{*{20}c} |
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279 | 0 \hfill \\ |
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280 | -{gh(z_{x} + S_{fx} )} \hfill \\ |
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281 | -{gh(z_{y} + S_{fy} )} \hfill \\ |
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282 | \end{array} }} \right] |
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283 | \] |
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284 | where $S_f$ is the bed friction. The friction term is modelled using |
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285 | Manning's resistance law |
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286 | \[ |
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287 | S_{fx} =\frac{u\eta ^2\sqrt {u^2+v^2} }{h^{4/3}}\mbox{ and }S_{fy} |
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288 | =\frac{v\eta ^2\sqrt {u^2+v^2} }{h^{4/3}} |
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289 | \] |
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290 | in which $\eta$ is the Manning resistance coefficient. |
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291 | |
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292 | %%As demonstrated in our papers, \cite{modsim2005,Roberts1999} these |
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293 | %%equations provide an excellent model of flows associated with |
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294 | %%inundation such as dam breaks and tsunamis. Question - how do we |
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295 | %%know it is excellent? |
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296 | |
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297 | ANUGA uses a finite-volume method as |
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298 | described in \citet{Roberts2007} where the study area is represented by an |
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299 | unstructured triangular mesh in which the vector of conserved quantities |
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300 | $\UU$ is maintained and updated over time. The flexibility afforded by |
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301 | allowing unstructed meshes rather than fixed resolution grids |
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302 | is the ability for the user to refine the mesh in areas of interest |
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303 | while leaving other areas coarse and thereby conserving computational |
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304 | resources. |
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305 | |
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306 | |
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307 | The approach used in ANUGA are distinguished from many |
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308 | other implementations (e.g. \citet{Hubbard02} or \citet{Zhang07}) by the |
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309 | following features: |
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310 | \begin{itemize} |
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311 | \item The fluxes across each edge are computed using the semi-discrete |
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312 | central-upwind scheme for approximating the Riemann problem |
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313 | proposed by \citet{KurNP2001}. This scheme deals with different |
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314 | flow regimes such as shocks, rarefactions and sub to super |
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315 | critical flow transitions using one general approach. We have |
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316 | found this scheme to be pleasingly simple, robust and efficient. |
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317 | \item ANUGA does not employ a shoreline detection algorithm as the |
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318 | central-upwind scheme is capable of resolving fluxes arising between |
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319 | wet and dry cells. ANUGA does optionally bypass unnecessary |
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320 | computations for dry-dry cell boundaries purely to improve performance. |
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321 | \item ANUGA employs a second order spatial reconstruction of triangles |
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322 | to produce a piece-wise linear function construction of the conserved |
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323 | quantities. This function is allowed to be discontinuous across the |
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324 | edges of the cells, but the slope of this function is limited to avoid |
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325 | artificially introduced oscillations. This approach provides good |
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326 | approximation of steep gradients in the solution. However, |
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327 | where the depths are very small compared to the bed-slope a linear |
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328 | combination between second order and first order reconstructions is |
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329 | employed to guarantee numerical stability that may arise form very |
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330 | small depths. |
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331 | \end{itemize} |
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332 | |
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333 | In the computations presented in this paper we use an explicit Euler |
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334 | time stepping method with variable timestepping subject to the |
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335 | CFL condition: |
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336 | \[ |
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337 | \delta t = \min_k \frac{r_k}{v_k} |
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338 | \] |
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339 | where $r_k$ refers to the radius of the inscribed circle of triangle |
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340 | $k$, $v_k$ refers to the maximal velocity calculated from fluxes |
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341 | passing in or out of triangle $k$ and $\delta t$ is the resulting |
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342 | 'safe' timestep to be used for the next iteration. |
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343 | |
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344 | |
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345 | ANUGA utilises a general velocity limiter described in the |
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346 | manual which guarantees a gradual compression of computed velocities |
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347 | in the presence of very shallow depths: |
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348 | \begin{equation} |
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349 | \hat{u} = \frac{\mu}{h + h_0/h}, \bigskip \hat{v} = \frac{\nu}{h + h_0/h}, |
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350 | \end{equation} |
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351 | where $h_0$ is a regularisation parameter that controls the minimal |
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352 | magnitude of the denominator. The default value is $h_0 = 10^{-6}$. |
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353 | |
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354 | |
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355 | ANUGA is mostly written in the object-oriented programming |
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356 | language Python with computationally intensive parts implemented |
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357 | as highly optimised shared objects written in C. |
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358 | |
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359 | Python is known for its clarity, elegance, efficiency and |
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360 | reliability. Complex software can be built in Python without undue |
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361 | distractions arising from idiosyncrasies of the underlying software |
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362 | language syntax. In addition, Python's automatic memory management, |
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363 | dynamic typing, object model and vast number of libraries means that |
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364 | ANUGA scripts can be produced quickly and can be adapted fairly easily to |
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365 | changing requirements. |
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366 | |
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367 | |
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368 | |
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369 | \section{Validation} |
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370 | \label{sec:validation} Validation is an ongoing process and the purpose of this paper |
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371 | is to describe a range of tests that validate ANUGA as a hydrodynamic model. |
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372 | This section will describe the six tests outlined in section~\ref{sec:intro}. |
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373 | Run times where specified measure the model time only and exclude model setup, |
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374 | data conversions etc. All examples were timed on a a 2GHz 64-bit |
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375 | Dual-Core AMD Opteron(tm) series 2212 Linux server. %This is a tornado compute node (cat /proc/cpuinfo). |
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376 | |
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377 | |
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378 | \subsection{1D analytical validation} |
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379 | |
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380 | Tom Baldock has done something here for that NSW report |
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381 | |
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382 | \subsection{Stage and Velocity Validation in a Flume} |
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383 | \label{sec:stage and velocity} |
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384 | This section will describe tilting flume tank experiments that were |
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385 | conducted at the Gordon McKay Hydraulics Laboratory at the University of |
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386 | Queensland that confirm ANUGA's ability to estimate wave height |
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387 | and velocity. The same flume tank simulations were also used |
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388 | to explore Manning's friction and this will be described in the next section. |
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389 | |
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390 | The flume was set up for dam-break experiments, having a |
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391 | water reservior at one end. The flume was glass-sided, 3m long, 0.4m |
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392 | in wide, and 0.4m deep, with a PVC bottom. The reservoir in the flume |
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393 | was 0.75m long. For this experiment the reservoir water was 0.2m |
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394 | deep. At time zero the reservoir gate is manually opened and the water flows |
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395 | into the other side of the flume. The water ran up a flume slope of |
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396 | 0.03 m/m. To accurately model the bed surface a Manning's friction |
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397 | value of 0.01, representing PVC was used. |
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398 | |
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399 | % Neale, L.C. and R.E. Price. Flow characteristics of PVC sewer pipe. |
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400 | % Journal of the Sanitary Engineering Division, Div. Proc 90SA3, ASCE. |
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401 | % pp. 109-129. 1964. |
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402 | |
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403 | Acoustic displacement sensors that produced a voltage that changed |
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404 | with the water depth was positioned 0.4m from the reservoir gate. The |
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405 | water velocity was measured with an Acoustic Doppler Velocimeter 0.45m |
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406 | from the reservoir gate. This sensor only produced reliable results 4 |
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407 | seconds after the reservoir gate opened, due to limitations of the sensor. |
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408 | |
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409 | |
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410 | % Validation UQ flume |
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411 | % at X:\anuga_validation\uq_sloped_flume_2008 |
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412 | % run run_dam.py to create sww file and .csv files |
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413 | % run plot.py to create graphs heere automatically |
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414 | % The Coasts and Ports '2007 paper is in TRIM d2007-17186 |
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415 | \begin{figure}[htbp] |
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416 | \centerline{\includegraphics[width=4in]{uq-flume-depth}} |
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417 | \caption{Comparison of wave tank and ANUGA water height at .4 m |
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418 | from the gate}\label{fig:uq-flume-depth} |
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419 | \end{figure} |
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420 | |
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421 | \begin{figure}[htbp] |
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422 | \centerline{\includegraphics[width=4in]{uq-flume-velocity}} |
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423 | \caption{Comparison of wave tank and ANUGA water velocity at .45 m |
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424 | from the gate}\label{fig:uq-flume-velocity} |
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425 | \end{figure} |
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426 | |
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427 | Figure~\ref{fig:uq-flume-depth} shows that ANUGA predicts the actual |
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428 | water depth very well, although there is an initial drop in water depth |
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429 | within the first second that is not simulated by ANUGA. |
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430 | Water depth and velocity are coupled as described by the nonlinear |
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431 | shallow water equations, thus if one of these quantities accurately |
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432 | estimates the measured values, we would expect the same for the other |
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433 | quantity. This is demonstrated in Figure~\ref{fig:uq-flume-velocity} |
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434 | where the water velocity is also predicted accurately. Sediment |
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435 | transport studies rely on water velocity estimates in the region where |
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436 | the sensors cannot provide this data. With water velocity being |
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437 | accurately predicted, studies such as sediment transport can now use |
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438 | reliable estimates. |
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439 | |
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440 | |
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441 | \subsection{Okushiri Wavetank Validation} |
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442 | \label{sec:okushiri} |
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443 | As part of the Third International Workshop on Long-wave Runup |
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444 | Models in 2004 (\url{http://www.cee.cornell.edu/longwave}), four |
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445 | benchmark problems were specified to allow the comparison of |
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446 | numerical, analytical and physical models with laboratory and field |
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447 | data. One of these problems describes a wave tank simulation of the |
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448 | 1993 Okushiri Island tsunami off Hokkaido, Japan \cite{MatH2001}. A |
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449 | significant feature of this tsunami was a maximum run-up of 32~m |
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450 | observed at the head of the Monai Valley. This run-up was not |
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451 | uniform along the coast and is thought to have resulted from a |
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452 | particular topographic effect. Among other features, simulations of |
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453 | the Hokkaido tsunami should capture this run-up phenomenon. |
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454 | |
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455 | This dataset has been used by to validate tsunami models by |
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456 | a number of tsunami scientists. Examples include Titov ... lit review |
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457 | here on who has used this example for verification (Leharne?) |
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458 | |
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459 | \begin{figure}[htbp] |
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460 | %\centerline{\includegraphics[width=4in]{okushiri-gauge-5.eps}} |
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461 | \centerline{\includegraphics[width=4in]{ch5.png}} |
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462 | \centerline{\includegraphics[width=4in]{ch7.png}} |
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463 | \centerline{\includegraphics[width=4in]{ch9.png}} |
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464 | \caption{Comparison of wave tank and ANUGA water stages at gauge |
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465 | 5,7 and 9.}\label{fig:val} |
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466 | \end{figure} |
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467 | |
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468 | |
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469 | \begin{figure}[htbp] |
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470 | \centerline{\includegraphics[width=4in]{okushiri-model.jpg}} |
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471 | \caption{Complex reflection patterns and run-up into Monai Valley |
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472 | simulated by ANUGA and visualised using our netcdf OSG |
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473 | viewer.}\label{fig:run} |
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474 | \end{figure} |
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475 | |
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476 | The wave tank simulation of the Hokkaido tsunami was used as the |
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477 | first scenario for validating ANUGA. The dataset provided |
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478 | bathymetry and topography along with initial water depth and the |
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479 | wave specifications. The dataset also contained water depth time |
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480 | series from three wave gauges situated offshore from the simulated |
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481 | inundation area. The ANUGA model comprised $41404$ triangles |
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482 | and took about $1330$ s to run on the test platform described in |
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483 | Section~\ref{sec:validation}. |
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484 | |
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485 | The script to run this example is available in the ANUGA distribution in the subdirectory |
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486 | \code{anuga_validation/automated_validation_tests/okushiri_tank_validation}. |
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487 | |
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488 | |
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489 | Figure~\ref{fig:val} compares the observed wave tank and modelled |
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490 | ANUGA water depth (stage height) at one of the gauges. The plots |
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491 | show good agreement between the two time series, with ANUGA |
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492 | closely modelling the initial draw down, the wave shoulder and the |
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493 | subsequent reflections. The discrepancy between modelled and |
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494 | simulated data in the first 10 seconds is due to the initial |
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495 | condition in the physical tank not being uniformly zero. Similarly |
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496 | good comparisons are evident with data from the other two gauges. |
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497 | Additionally, ANUGA replicates exceptionally well the 32~m Monai |
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498 | Valley run-up, and demonstrates its occurrence to be due to the |
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499 | interaction of the tsunami wave with two juxtaposed valleys above |
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500 | the coastline. The run-up is depicted in Figure~\ref{fig:run}. |
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501 | |
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502 | This successful replication of the tsunami wave tank simulation on a |
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503 | complex 3D beach is a positive first step in validating the ANUGA |
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504 | modelling capability. |
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505 | |
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506 | \subsection{Runup of solitary wave on circular island wavetank validation} |
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507 | \label{sec:circular island} |
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508 | This section will describe the ANUGA results for the experiments |
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509 | conducted by Briggs et al (1995). Here, a 30x25m basin with a conical |
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510 | island is situated near the centre and a directional wavemaker is used |
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511 | to produce planar solitary waves of specified crest lenghts and |
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512 | heights. A series of gauges were distributed within the experimental |
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513 | setup. As described by Hubbard and Dodd \cite{Hubbard02}, a number of |
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514 | researchers have used this benchmark problem to test their numerical |
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515 | models. {\bf Jane: check whether these results are now avilable as |
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516 | they were not in 2002}. Hubbard and Dodd \cite{Hubbard02} note that a |
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517 | particular 3D model appears to obtain slightly better results than the |
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518 | 2D ones reported but that 3D models are unlikely to be competitive in |
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519 | terms of computing power for applications in coastal engineering at |
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520 | least. Choi et al \cite{Choi07} use a 3D RANS model (based on the |
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521 | Navier-Stokes equations) for the same problem and find a very good |
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522 | comparison with laboratory and 2D numerical results. An obvious |
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523 | advantage of the 3D model is its ability to investigate the velocity |
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524 | field and Choi et al also report on the limitation of depth-averaged |
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525 | 2D models for run-up simulations of this type. |
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526 | |
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527 | Once results are availble, need to compare to Hubbard and Dodd and |
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528 | draw any conclusions from nested rectangular grid vs unstructured |
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529 | gird. Figure \ref{fig:circular screenshots} shows a sequence of |
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530 | screenshots depicting the evolution of the solitary wave as it hits |
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531 | the circular island. |
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532 | |
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533 | \begin{figure}[htbp] |
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534 | \centerline{ |
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535 | \includegraphics[width=5cm]{circular1.png} |
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536 | \includegraphics[width=5cm]{circular2.png}} |
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537 | \centerline{ |
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538 | \includegraphics[width=5cm]{circular3.png} |
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539 | \includegraphics[width=5cm]{circular4.png}} |
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540 | \centerline{ |
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541 | \includegraphics[width=5cm]{circular5.png} |
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542 | \includegraphics[width=5cm]{circular6.png}} |
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543 | \centerline{ |
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544 | \includegraphics[width=5cm]{circular7.png} |
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545 | \includegraphics[width=5cm]{circular8.png}} |
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546 | \centerline{ |
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547 | \includegraphics[width=5cm]{circular9.png} |
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548 | \includegraphics[width=5cm]{circular10.png}} |
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549 | \caption{Screenshots of the evolution of solitary wave around circular island.} |
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550 | \label{fig:circular screenshots} |
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551 | \end{figure} |
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552 | |
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553 | |
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554 | \subsection{Flume tank validation before and after breaking waves} |
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555 | |
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556 | To explicitly determine if ANUGA can model waves after breaking |
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557 | several experiments were conducted at the Monash University Institute for |
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558 | Sustainable Water Resources using a wave flume. The experiments were |
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559 | designed to produce a variety of breaking waves. The experiments were |
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560 | conducted on a 2.5$^\circ$ and a 1.5$^\circ$ plane beach slope set-up |
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561 | in a glass-sided wave flume of 40m in length, 1.0m wide and 1.6m deep. |
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562 | The wave generator can generate waves up to 0.6m in height, with a |
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563 | period range of 0.3 - 7.0 seconds. |
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564 | |
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565 | Four scenarios with different combinations of wave height and wave period |
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566 | were used, with each test being repeated. |
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567 | |
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568 | A variety of measurements were taken during each test. Mid-depth |
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569 | water velocity and wave height were measured on the approach section. |
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570 | The water height at several points along the flume were measured using |
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571 | pressure transducers. The wave profile was video recorded, this |
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572 | determined the location of breaking waves. All the tests produced 4 to |
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573 | 7 waves. Generally the first wave did not break, with subsequent |
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574 | waves breaking; accept for scenario 2, for which the first 3 waves did |
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575 | not break. Scenario 1 produced plunging breakers. Scenario 3 |
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576 | produced collapsing breakers. All other scenarios produced spilling |
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577 | breakers. Details of the tests performed are given in Table |
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578 | \ref{tab:hinwoodSummary}. |
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579 | |
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580 | \begin{table} |
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581 | \caption{Details of the Monash University experiments.} % Can't get right |
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582 | \begin{center} |
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583 | \begin{tabular}{ c p{3cm} p{3cm} p{3cm} } |
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584 | |
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585 | \hline |
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586 | Test Name & Beach slope nominal, \emph{degrees} & Water depth offshore, |
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587 | \emph{mm } & Wave frequency nominal, \emph{Hz} \\ \hline |
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588 | S1R1 & 3.5 & 400 & 0.200 \\ \hline |
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589 | S1R2 & 3.5 & 400 & 0.200 \\ \hline |
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590 | S2R1 & 3.5 & 400 & 0.125 \\ \hline |
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591 | S2R2 & 3.5 & 400 & 0.125 \\ \hline |
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592 | S3R1 & 1.5 & 336 & 0.200 \\ \hline |
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593 | S3R2 & 1.5 & 336 & 0.200 \\ \hline |
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594 | S4R1 & 1.5 & 336 & 0.125 \\ \hline |
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595 | S4R2 & 1.5 & 336 & 0.125 \\ \hline |
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596 | |
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597 | % Mapping of new names to old names |
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598 | % S1R2 T1R3 |
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599 | % S1R1 T1R5 |
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600 | % S2R1 T2R7 |
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601 | % S2R2 T2R8 |
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602 | % S3R2 T3R28 |
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603 | % S3R1 T3R29 |
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604 | % S4R2 T4R31 |
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605 | % S4R1 T4R32 |
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606 | |
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607 | |
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608 | |
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609 | \end{tabular} |
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610 | \label{tab:hinwoodSummary} |
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611 | |
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612 | \end{center} |
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613 | \end{table} |
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614 | |
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615 | All of these tests were simulated using ANUGA. The Mid-depth water |
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616 | velocity and wave height measured on the approach section were used as |
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617 | boundary conditions for the ANUGA simulations. The origin of the z |
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618 | coordinate was the still water line, positive upwards. The origin of |
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619 | the x coordinate was the toe of the beach, x measured positive |
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620 | shorewards A Manning's friction coefficient of zero was used. To |
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621 | quantify the difference between the simulated stage and the |
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622 | experimental stage the Root Mean Square Deviation (RMSD) |
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623 | (\cite{Kobayshi2000}) was used |
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624 | |
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625 | \[ |
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626 | RMSD =\sqrt {\frac{1 }{n} \displaystyle\sum_{i=1}^{n}{(x_i - y_i)}^2} |
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627 | \] |
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628 | |
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629 | Figures \ref{fig:S1-rmsd} to \ref{fig:S4-rmsd} show the RMSD of each |
---|
630 | sensor for all tests and the location where each wave broke. The |
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631 | RMSD is calculated over the time of the experiment. |
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632 | |
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633 | % To create these figures goto \anuga_work\development\Hinwood_2008 |
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634 | % do python validation_graphs.py |
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635 | \begin{figure}[htbp] |
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636 | \centerline{\includegraphics[width=4in]{S1-rmsd}} |
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637 | \caption{RMSD of stage between the wave tank and ANUGA for S1R1 and |
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638 | S1R2. Horizontal lines represent the x location of breaking waves.} |
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639 | \label{fig:S1-rmsd} |
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640 | \end{figure} |
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641 | |
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642 | |
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643 | \begin{figure}[htbp] |
---|
644 | \centerline{\includegraphics[width=4in]{S2-rmsd}} |
---|
645 | \caption{RMSD of stage between the wave tank and ANUGA for S2R1 and |
---|
646 | S2R2. Horizontal lines represent the x location of breaking waves.} |
---|
647 | \label{fig:S2-rmsd} |
---|
648 | \end{figure} |
---|
649 | |
---|
650 | \begin{figure}[htbp] |
---|
651 | \centerline{\includegraphics[width=4in]{S3-rmsd}} |
---|
652 | \caption{RMSD of stage between the wave tank and ANUGA for S3R1 and |
---|
653 | S3R2. Horizontal lines represent the x location of breaking waves. |
---|
654 | The circles represent gauges shown in \ref{fig:S3-stage-compares}} |
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655 | % More, circles represent gauges shown in |
---|
656 | %\protect{\ref{fig:S3-stage-compares}} Again, circles represent gauges |
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657 | %shown in \ref{fig:S3-stage-compares}} |
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658 | \label{fig:S3-rmsd} |
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659 | \end{figure} |
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660 | |
---|
661 | \begin{figure}[htbp] |
---|
662 | \centerline{\includegraphics[width=4in]{S4-rmsd}} |
---|
663 | \caption{RMSD of stage between the wave tank and ANUGA for S4R1 and |
---|
664 | S4R2. Horizontal lines represent the x location of breaking waves.} |
---|
665 | \label{fig:S4-rmsd} |
---|
666 | \end{figure} |
---|
667 | |
---|
668 | For a more direct comparision between the simulation and the |
---|
669 | experiment the water stages at three gauges, generally the initial, final |
---|
670 | and worst fit, were compared in Figures \ref{fig:S1-stage-compare} to |
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671 | \ref{fig:S4-stage-compare}. |
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672 | |
---|
673 | \begin{figure}[htbp] |
---|
674 | \centerline{\includegraphics[width=5in]{S1-stage-compare}} |
---|
675 | \caption{Comparison of wave tank (solid line) and ANUGA (broken line) |
---|
676 | water stages at three gauges for S1R1.} |
---|
677 | \label{fig:S1-stage-compare} |
---|
678 | \end{figure} |
---|
679 | |
---|
680 | \begin{figure}[htbp] |
---|
681 | \centerline{\includegraphics[width=5in]{S2-stage-compare}} |
---|
682 | \caption{Comparison of wave tank (solid line) and ANUGA (broken line) |
---|
683 | water stages at three |
---|
684 | gauges for S2R1.} |
---|
685 | \label{fig:S2-stage-compare} |
---|
686 | \end{figure} |
---|
687 | |
---|
688 | \begin{figure}[htbp] |
---|
689 | \centerline{\includegraphics[width=5in]{S3-stage-compare}} |
---|
690 | \caption{Comparison of wave tank (solid line) and ANUGA (broken line) |
---|
691 | water stages at three |
---|
692 | gauges for S3R1.} |
---|
693 | \label{fig:S3-stage-compare} |
---|
694 | \end{figure} |
---|
695 | |
---|
696 | \begin{figure}[htbp] |
---|
697 | \centerline{\includegraphics[width=5in]{S4-stage-compare}} |
---|
698 | \caption{Comparison of wave tank (solid line) and ANUGA (broken line) |
---|
699 | water stages at three |
---|
700 | gauges for S4R1.} |
---|
701 | \label{fig:S4-stage-compare} |
---|
702 | \end{figure} |
---|
703 | |
---|
704 | Overall these results show an excellent level of agreement between |
---|
705 | predicted and measured stage. The RMSD figures generally show a |
---|
706 | decrease in accuracy, the further the gauge is from the initial |
---|
707 | condition, untill wave breaking. Generally after wave breaking the |
---|
708 | RMSD value decreases. This is a clear indication of ANUGA accurately |
---|
709 | predicting the stage after the wave has broken. There are |
---|
710 | several points worth emphasising here. Overall all of the RMSD values |
---|
711 | are good. There is not much difference between the worst and best |
---|
712 | gauges (-0.7 m and 5.6m) for S1R1, for example. A decrease in RMSD |
---|
713 | does not necesarily mean the accuracy of ANUGA is improving. For |
---|
714 | example, in S4R1 the drop in RMSD between gauges 7.6 and 11.6 is partially due |
---|
715 | to vertical water motion effecting gauge 7.6 and a decrease in the |
---|
716 | time period where waves are being measured, as oppossed to still |
---|
717 | water, for gauge 11.6. Additionally, sensors near the wave run-up |
---|
718 | have a lower amplitude than the wave at breaking, which can result in |
---|
719 | a low RMSD, which may not be the case if the results were relative, |
---|
720 | see gauge 5.6 and 7.6 \ref{fig:S1-stage-compare}. |
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721 | |
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722 | |
---|
723 | |
---|
724 | |
---|
725 | |
---|
726 | \label{sec:Hinwood} |
---|
727 | |
---|
728 | |
---|
729 | |
---|
730 | |
---|
731 | \clearpage |
---|
732 | |
---|
733 | \section{Conclusions} |
---|
734 | \label{sec:conclusions} |
---|
735 | ANUGA is a flexible and robust modelling system |
---|
736 | that simulates hydrodynamics by solving the shallow water wave |
---|
737 | equation in a triangular mesh. It can model the process of wetting |
---|
738 | and drying as water enters and leaves an area and is capable of |
---|
739 | capturing hydraulic shocks due to the ability of the finite-volume |
---|
740 | method to accommodate discontinuities in the solution. |
---|
741 | ANUGA can take as input bathymetric and topographic datasets and |
---|
742 | simulate the behaviour of riverine flooding, storm surge, |
---|
743 | tsunami or even dam breaks. |
---|
744 | Initial validation using wave tank data supports ANUGA's |
---|
745 | ability to model complex scenarios. Further validation will be |
---|
746 | pursued as additional datasets become available. |
---|
747 | The ANUGA source code and validation case studies reported here are available |
---|
748 | at \url{http://sourceforge.net/projects/anuga}. |
---|
749 | |
---|
750 | something about use on flood modelling community and their validation initiatives |
---|
751 | |
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752 | |
---|
753 | %\bibliographystyle{plainnat} |
---|
754 | \bibliographystyle{elsart-harv} |
---|
755 | \bibliography{anuga-bibliography} |
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756 | |
---|
757 | \end{document} |
---|