Entropy-stable schemes for relativistic hydrodynamics equations

Abstract

In this article, we propose high-order finite difference schemes for the equations of relativistic hydrodynamics, which are entropy stable. The crucial components of these schemes are a computationally efficient entropy conservative flux and suitable high-order entropy dissipative operators. We first design a higher-order entropy conservative flux. For the construction of appropriate entropy dissipative operators, we derive entropy scaled right eigenvectors. This is then used with ENO-based sign-preserving reconstruction of scaled entropy variables, which results in higher-order entropy-stable schemes. Several numerical results are presented up to fourth order to demonstrate entropy stability and performance of these schemes.