Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

Abstract EN

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids.

We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method.

Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.