Parallel Fully Adaptive Tsunami Simulations

Abstract

We present our framework for parallel simulations of hyperbolic partial differential equations on triangular grids. As a proofof- concept, we implemented the shallow water equations using a finite volume method together with the Riemann solvers of LeVeque and George [1] and multi-resolution geoinformation datasets. The results show a parallel fully adaptive simulation applied to the 2011 Tohoku tsunami fieldbenchmark.

Efficient adaptivity is realized by grid-traversals which follow the Sierpiński space filling curve. A stack- and stream-based approach accounts for locality and cache efficiency by arranging the data exchange among cells. For tsunamis we used the normalized height mass exchange as adaptivity criterion in every time step. Therefore, if a certain refinement threshold is exceeded, the corresponding cells are refined by newest vertex bisection. Values falling below a coarsening threshold result in a merge of the respective triangles.