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

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 adaptivemesh 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 adaptivemesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.