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

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

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This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured Glass Filler Stations 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 Warm-Ups 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.