Stabilizing DG Methods Using Dafermos' Entropy Rate Criterion: III -- Unstructured Grids

Abstract

The approach presented in the second installment of this series is extended to multidimensional systems of conservation laws that are approximated via a Discontinuous Galerkin method on unstructured (triangular) grids. Special attention is paid to predicting the entropy dissipation from boundaries. The resulting schemes are free of tunable viscosity parameters and tested on the Euler equations. The trinity of testcases is the spreading of thermal energy from a point source, transsonic and supersonic flows around airfoils, and supersonic air inlets.