Changeset 2865
- Timestamp:
- May 15, 2006, 2:01:49 PM (18 years ago)
- Location:
- documentation/experimentation
- Files:
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- 2 edited
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smf.tex (modified) (7 diffs)
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volume_conservation.png (modified) (previous)
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documentation/experimentation/smf.tex
r2853 r2865 55 55 Geoscience Australia (GA) is a federal government agency playing a 56 56 critical role in enabling government and the community to make 57 inform ationdecisions about exploration of resources, the management57 informed decisions about exploration of resources, the management 58 58 of the environment, the safety of critical infrastructure and the 59 59 resultant wellbeing of all Australians. GA does this by producing … … 69 69 The risks posed by tsunamis is one of the natural hazards areas which 70 70 the RRG is investigating. GA can model the propagation of an event 71 generated througha submarine earthquake71 generated by a submarine earthquake 72 72 through to inundation ashore. Currently, we are 73 73 employing the Method of Splitting Tsunami (MOST) [1] for the event 74 and subsequent propagation in deep water, and then use ANUGA to74 and subsequent propagation in deep water, and then use ANUGA [2] to 75 75 propagate the resultant waves in shallow water and onshore. 76 76 77 77 ANUGA has been developed by GA and ANU to solve the nonlinear shallow water 78 wave equation using the finite volume technique (described in [2]).78 wave equation using the finite volume technique. 79 79 An advantage of this technique is that the cell resolution can be changed 80 according to areas of interest. ANUGA is under constant development and 81 validation investigations. 80 according to areas of interest 81 and that wetting and drying is treated robustly as part of the numerical 82 scheme. ANUGA is continually being developed and 83 validated. 82 84 83 85 A recent tsunami inundation study called for the tsunami source to 84 86 be a slump and as such, we implemented the surface elevation 85 87 function as described in equation 14 of Watts et al 2005, [3]. The reason 86 then for our contact is that we have some questions and a request. 87 88 {\bf Question 1:} Is there a physical explanation to why the volume 88 then for our contact is that we have some questions and a request 89 in regard to this methodology. 90 91 {\bf Question 1:} Is there a physical explanation to why the total volume 89 92 of the surface elevation function should not be zero? 90 93 … … 94 97 the depressed volume was greater than the volume displaced above the 95 98 water surface with approximately 2-3 \% loss. Figure 2 of [3] shows 96 a series of the surface elevation functionsfor various parameters97 which indicate that volume is not conserved.99 surface elevation functions $\eta(x,y)$ for various parameters 100 which indicate that the total volume is not conserved. 98 101 99 102 Setting the integral of the elevation function to zero will 100 ensure that volume is conserved. As aresult,103 ensure that volume is conserved. Solving for $\kappa'$ yields the result, 101 104 102 105 $$\kappa' = [ … … 106 109 107 110 \noindent Figure \ref{fig:vol_cons} shows the relationship between 108 $\kappa $ and $\Delta x$. It must be noted, that whilst111 $\kappa'$ and $\Delta x$. It must be noted, that whilst 109 112 $\kappa'$ is technically less than 1 for $\Delta x < 5.93$ it is 110 effectively equal to 1 for $0 \le \Delta x \approx 5.93$. Therefore 111 it is not possible for $\kappa' = 0.83$; a parameter chosen in [1]. 113 effectively equal to 1 for those values. 114 Choosing $\kappa'$ = 0.83, as suggested in [1], will therefore 115 not guarantee conservation of volumen for any value of $\Delta x$. 112 116 113 117 Figure 2 in [3] … … 143 147 maximum inundation depth in some locations. 144 148 145 {\bf Question:} Is the substitution of $x_g$ into the elevation function 146 a realistic one? 149 {\bf Question 2:} Is the substitution of $x_g$ into the elevation function realistic? 147 150 148 151 Watts et al [3] provide additional information on the value of … … 162 165 163 166 We are continuing to seek out validation data sets to improve the 164 accuracy of our model. We recently had goodsuccess in validating167 accuracy of our model. We recently had success in validating 165 168 the model against the Benchmark Problem #2 Tsunami Run-up 166 169 onto a complex 3-dimensional beach, as provided to the 3rd … … 173 176 be very interested in comparing our finite volume model using the 174 177 approximated surface elevation function with your 175 experimental results. Would it therefore be possible for you to release the178 experimental results. Would it therefore be possible for you to provide the 176 179 experimental time series for comparison with ANUGA? 177 180
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