Changeset 2871
- Timestamp:
- May 16, 2006, 11:03:53 AM (18 years ago)
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
documentation/experimentation/smf.tex
r2869 r2871 53 53 in inundation modelling} 54 54 55 Geoscience Australia (GA) is a federal government agency playing a 56 critical role in enabling government and the community to make 57 informed decisions about exploration of resources, the management 58 of the environment, the safety of critical infrastructure and the 59 resultant wellbeing of all Australians. GA does this by producing 60 first-class geoscientific information and knowledge. 61 62 The Risk Research Group (RRG) within GA is researching natural and 63 human-caused hazards to enhance Australia's risk mitigation 64 capabilities through policy and decision-maker support. The group is 65 working with other agencies to develop and collect information on 66 natural disasters, and develop risk models for forecasting the 67 impact of future hazard events. 68 69 The risks posed by tsunamis is one of the natural hazards areas which 70 the RRG is investigating. GA can model the propagation of an event 71 generated by a submarine earthquake 72 through to inundation ashore. Currently, we are 73 employing the Method of Splitting Tsunami (MOST) [1] for the event 74 and subsequent propagation in deep water, and then use ANUGA [2] to 75 propagate the resultant waves in shallow water and onshore. 76 77 ANUGA has been developed by GA and ANU to solve the nonlinear shallow water 78 wave equation using the finite volume technique. 79 An advantage of this technique is that the cell resolution can be changed 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. 55 We work at Geoscience Australia (GA) in the Risk Research Group 56 researching risks posed by a range of natural hazards 57 (http://www.ga.gov.au/urban/projects/risk/index.jsp). 58 Due to recent 59 events, we are investigating the tsunami risk to Australia. To understand 60 impact ashore, we have developed in conjunction 61 with the Australian National University, a hydrodynamic model called 62 ANUGA which uses the finite volume technique, [1]. 84 63 85 64 A recent tsunami inundation study called for the tsunami source to 86 65 be a slump and as such, we implemented the surface elevation 87 function as described in equation 14 of Watts et al 2005, [3]. The reason 88 then for our contact is that we have some questions and a request 89 in regard to this methodology. 66 function as described in Watts et al 2005, [3]. We found this a useful 67 way to incorporate another tsunami-genic event to our understanding 68 of tsunami risk. In trying 69 to implement this function however, we had some questions. 90 70 91 71 {\bf Question 1:} Is there a physical explanation to why the total volume 92 72 of the surface elevation function should not be zero? 73 74 {\bf Question 2:} Is the substitution of $x_g$ into the elevation function realistic? 93 75 94 76 Investigating the long term behaviour of the … … 96 78 the slump was added to the system. Further investigation showed that 97 79 the depressed volume was greater than the volume displaced above the 98 water surface with approximately 2-3 \% loss. Figure 2 of [3] shows 99 surface elevation functions $\eta(x,y)$ for various parameters 100 which indicate that the total volume is not conserved. 80 water surface with approximately 2-3 \% loss. You can see from 81 Figure 2 of [3] that the 82 surface elevation function $\eta(x,y)$ indicates that 83 the total volume is not conserved. 101 84 102 Setting the integral of the elevation function to zero will 103 ensure that volume is conserved. Solving for $\kappa'$ yields the result, 85 However, we can alleviate this issue by finding the appropriate set of parameters which 86 will conserve volume. Setting the integral of the elevation function to zero and 87 solving for $\kappa'$ yields the result, 104 88 105 89 $$\kappa' = [ … … 108 92 ]_{x_{\rm min}}^{x_{\rm max}} \ .$$ 109 93 110 \noindent Figure \ref{fig:vol_cons} shows the relationship between111 $\kappa'$ and $\Delta x$. It must be noted, that whilst94 \noindent The relationship between $\kappa'$ and $\Delta x$ is shown in 95 Figure \ref{fig:vol_cons}. It must be noted, that whilst 112 96 $\kappa'$ is technically less than 1 for $\Delta x < 5.93$ it is 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 $\Delta x$.97 effectively equal to 1 for those values. From this calculation, it would 98 seem then that there would be no appropriate $\Delta x$ for $\kappa'$ = 0.83 99 (a parameter used in [2]). 116 100 117 Figure 2 in [3]118 could then be reproducedfor appropriate values of $\kappa'$ and $\Delta x$ to101 We've reproduced Figure 2 in [3] 102 for appropriate values of $\kappa'$ and $\Delta x$ to 119 103 ensure volume conservation within the system. Using the above 120 104 formulation, the values of interest shown in Figure 2 of [3] would … … 140 124 \end{figure} 141 125 142 The next question is then how this alteration affects the impact onshore? 143 It is of course expected to increase the inundation depth 144 due to the increased volume of water which can 145 be propagated ashore. In one investigation, we saw little 146 change to the inundation extent, but some significant increases in 147 maximum inundation depth in some locations. 126 For our particular test case, changing the surface elevation function 127 in this way increases the inundation depth ashore by a factor greater than 128 the water loss. 148 129 149 {\bf Question 2:} Is the substitution of $x_g$ into the elevation function realistic? 150 151 Watts et al [3] provide additional information on the value of 152 $\Delta x$; $x_0 - \Delta x \approx x_g$, where$x_g$ is formulated130 Our next question is whether it was appropriate to substitute 131 the formulation for $x_g$ into the surface elevation function using 132 $x_0 - \Delta x \approx x_g$. 133 ($x_g$ is formulated 153 134 as $x_g = d/\tan \theta + T/ \sin \theta$ (described as a gauge 154 located above the SMF initial submergence location in [4]). Here $d$155 represents the depth at where the SMF is situated, $T$ the thickness156 and $\theta$ the slope of the bed. As a result, $\kappa'$ can be 157 recast as 135 located above the SMF initial submergence location in [4]).) 136 In this 137 way, $\kappa'$ as described above would not 138 be dependent on $\Delta x$; 158 139 159 140 $$\kappa' \approx {\rm erf} ( \frac{x - x_0}{\sqrt\lambda_0} ) / … … 161 142 - x_g}{\sqrt \lambda_0 } )$$ 162 143 163 \noindent thereby eliminating $\Delta x$ from the surface elevation164 function, $\eta(x,y)$.165 144 166 145 We are continuing to seek out validation data sets to improve the … … 168 147 the model against the Benchmark Problem #2 Tsunami Run-up 169 148 onto a complex 3-dimensional beach, as provided to the 3rd 170 International Workshop on Long Wave Run-up in 2004, see [ 2].171 We note in [ 5] your proposal for others to employ the benchmark149 International Workshop on Long Wave Run-up in 2004, see [1]. 150 We note in [4] your proposal for others to employ the benchmark 172 151 cases described there for experimental or numerical work. 173 152 Your model has been compared with the laboratory experiments in 2003 [5] and … … 181 160 \parindent 0pt 182 161 183 We look forward to your response regarding the questions and the request.162 We look forward to your response. 184 163 185 164 Yours sincerely, … … 191 170 {\bf References} 192 171 193 [1] 194 Titov, V.V., and F.I. Gonzalez (1997), Implementation and testing of 195 the Method of Splitting Tsunami (MOST) model, NOAA Technical Memorandum 196 ERL PMEL-112. 197 198 [2] Nielsen, O., S. Robers, D. Gray, A. McPherson, and A. Hitchman (2005) 172 [1] Nielsen, O., S. Robers, D. Gray, A. McPherson, and A. Hitchman (2005) 199 173 Hydrodynamic modelling of coastal inundation, MODSIM 2005 International 200 174 Congress on Modelling and Simulation. Modelling and Simulation Society … … 202 176 http://www.msanz.org.au/modsim05/papers/nielsen.pdf (CHECK THIS!!) 203 177 204 [ 3] Watts, P., Grilli, S.T., Tappin, D.R. and Fryer, G.J. (2005),178 [2] Watts, P., Grilli, S.T., Tappin, D.R. and Fryer, G.J. (2005), 205 179 Tsunami generation by submarine mass failure Part II: Predictive 206 180 equations and case studies, Journal of Waterway, Port, Coastal, and 207 181 Ocean Engineering, 131, 298 - 310. 208 182 209 [ 4] Grilli, S.T. and Watts, P. (2005), Tsunami generation by183 [3] Grilli, S.T. and Watts, P. (2005), Tsunami generation by 210 184 submarine mass failure Part I: Modeling, experimental validation, 211 185 and sensitivity analyses, Journal of Waterway, Port, Coastal, and 212 186 Ocean Engineering, 131, 283 - 297. 213 187 214 [ 5] Watts, P., Imamura, F. and Grilli, S. (2000)215 Comparting Model Simulations of three Benchmark Tsunami Generation,188 [4] Watts, P., Imamura, F. and Grilli, S. (2000) 189 Comparting Model Simulations of Three Benchmark Tsunami Generation, 216 190 Science of Tsunami Hazards, 18, 2, 107-123. 217 191 218 [ 6] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for192 [5] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for 219 193 Tsunamis Generated by Underwater Landslides: Comparison with Numerical Modeling, 220 194 Proceedings of the Thirteenth (2003) International Offshore and
Note: See TracChangeset
for help on using the changeset viewer.