Adaptive Mesh Refinement Method Applied to Shallow Water Model: A Mass Conservative Projection
Résumé
In the tsunami waves context, efficient numerical methods are necessary to simulate multiscales events. One way to reduce the computational cost is to use an adaptive mesh refinement method on unstructured meshes. This approach is used in this paper with a finite volume scheme solving the multi-dimensional Saint-Venant system. The adaptive mesh refinement method follows a block-based decomposition (called BB-AMR), which allows quick meshing and easy parallelization. One step of the AMR method is the so-called projection step where the new mesh values have to be defined from the old ones. For vertically integrated model the bathymetry variation during the projection step plays a crucial role on the mass conservation. To avoid large deficit or excess of mass a special attention is given to the projection step. Finally a 3D test case simulation is compared to experimental results to illustrated the quasi conservation of the mass with an appropriated projection method.
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