Formulation of entropy-conservative discretizations for compressible flows of thermally perfect gases

TL;DR

This paper introduces a new discretization method for the compressible Euler equations that ensures entropy conservation for thermally perfect gases, improving accuracy and robustness over existing methods.

Contribution

It develops a novel entropy-conserving discretization scheme specifically for thermally perfect gases, extending previous approaches to more realistic gas models.

Findings

Enhanced accuracy compared to existing schemes

Improved robustness in simulations

Preservation of linear invariants and kinetic energy

Abstract

This study proposes a novel spatial discretization procedure for the compressible Euler equations that guarantees entropy conservation at a discrete level for thermally perfect gases. The procedure is based on a locally conservative formulation, and extends the entropy-conserving schemes to the more realistic case of thermally perfect gases, while still guaranteeing preservation of both linear invariants and kinetic energy. The proposed methodology, which can also be extended to multicomponent gases and to an Asymptotically Entropy-Conservative formulation, shows advantages in terms of accuracy and robustness when compared to existing similar approaches.