Using the Dafermos Entropy Rate Criterion in Numerical Schemes

Abstract

The following work concerns the construction of an entropy dissipative finite volume solver based on the convex combination of an entropy conservative and an entropy dissipative flux. We aim to construct a semidiscrete scheme that is entropy stable in the sense of the entropy criterion of Dafermos as well as in the classical sense entropy dissipative. The proposed semidiscrete scheme shows nice properties like $2p$ order accuracy in smooth regions as well as a non-oscillatory behavior around shocks.