Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state Article Swipe

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Euler equations Mathematics Compressibility Invariant (physics) Backward Euler method Applied mathematics Euler's formula Entropy (arrow of time) Domain (mathematical analysis) Mathematical analysis Compressible flow Physics Thermodynamics Mathematical physics Quantum mechanics

Bennett Clayton , Jean‐Luc Guermond , Matthias Maier , Bojan Popov , Eric Tovar ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2207.12832 · OA: W4288099495

This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature.