Entropy stable schemes on two-dimensional unstructured grids

Abstract

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. The scheme is constructed using a judicious combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a piecewise linear reconstruction procedure satisfying a suitable sign property. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.