Parallel Tsunami Simulations With Block - Structured Adaptive Mesh Refinement

Due to the catastrophic effects of tsunamis, tsunami simulations are desired to increase the understanding of the phenomena, as well as to serve as mitigation and early warning systems for the affected areas. Even with the advent of supercomputers, the latter one is far out of reach due to the contradicting need for accuracy and speed. A common solution to this problem are adaptively refined grids, which use a fine discretisation in the regions of interest where a higher accuracy is needed, such as the shoreline or around the tsunami wave, and a coarser resolution in the rest of the domain. Therefore, adaptively refined grids offer a compromise between accuracy and time and memory efficiency. However, they raise a number of algorithmic challenges. The group at the Scientific Computing Chair in TUM is working on the SWE package, a code that implements the governing equations of tsunami simulations, the shallow water equations, with several parallelisation strategies. This project augments the SWE package with a blockstructured adaptive mesh refinement. The "block-structured" term means that the adaptive refinement is done at block level, to avoid the possible overhead that cell-level refinement involves. For this, coarsening and refining strategies were implemented, as well as two timeintegration schemes, namely global time-stepping and local time-stepping. Different interpolation schemes, which use time or space interpolation for the ghost layer exchange, are also available. An analytical benchmark was employed for validation and accuracy analysis, and it was noticed that the local time-stepping gives better results than the global time-stepping scheme. Another goal of this project was to adapt the MPI implementation to accommodate adaptive mesh refinement. An analysis showing how much the domain resolution can be increased, and how that affects the parallel performance, is included in this thesis.