Entropy conserving and kinetic energy preserving numerical methods for the euler equations using summation-by-parts operators

Abstract

Summation-by-parts operators can be used in the context of finite difference and discontinuous Galerkin methods to create discretisations mimicking properties given at the continuous level such as entropy conservation. Recently, there has been some interest in schemes for the Euler equations that additionally preserve the kinetic energy. However, some these methods resulted in undesired and unexpected changes of the kinetic energy in numerical experiments of Gassner et al. (J Comput Phys 327:39–66, 2016). Here, analytical insights into kinetic energy preservation are given and new entropy conservative and kinetic energy preserving numerical fluxes are proposed.