Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state

Alessandro Aiello; Carlo De Michele; Gennaro Coppola

doi:10.1016/j.jcp.2025.113836

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arXiv · 2408.01235

Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state

Alessandro Aiello·Carlo De Michele·Gennaro Coppola

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Abstract

This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation by parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state.

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Alessandro Aiello, Carlo De Michele, Gennaro Coppola. 2025-09-23. Entropy conservative discretization of compressible Euler equations with an arbitrary equation of state. https://doi.org/10.1016/j.jcp.2025.113836

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