A Non-Hydrostatic Shallow Water Model on Triangular Meshes in Sam(oa) Guided Research Project

For the simulation of tsunamis, the hydrostatic shallow water equations have established as a sound mathematical basis. However, due to the hydrostatic assumption, not all relevant physical effects—especially in coastal areas—can be modelled accurately. In this paper, we therefore show how to extend the PDE-framemwork sam(oa)2 towards modified non-hydrostatic shallow water equations. We use the finite volume method based on Riemann solvers to solve the hydrostatic shallow water equations and a fractional step method for the inclusion of non-hydrostatic effects. After having explained the general numerical approach, we develop a dual grid discretization of the non-hydrostatic pressure equation on dynamically adaptive triangular grids. This will allow for a matrix-free solution of the corresponding system of linear equations. Finally, we show the validity of the new model based on four common test cases for non-hydrostatic shallow water models.