A Family of Entropy-Conservative Flux Functions for the Euler Equations

Abstract

Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such entropy-conservative flux functions. The proposed flux functions are solutions to quadratic optimization problems and admit closed-form, computationally affordable expressions. We establish the properties of the flux functions including their continuous differentiability, which is necessary for high-order discretizations.

Further numerical tests revealed that the flux is not high-order accurate (it is limited to 2nd order) despite the theoretical results. The source of this problem is believed to be related to finite-precision arithmetic, but further study is needed