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Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations

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arxiv 1701.02264 v2 pith:GSTVEMPT submitted 2017-01-09 math.NA cs.NA

Hendrik Ranocha This is my paper
classification math.NAcs.NA
keywords fluxesentropynumericalconservativedifferencingdissipationenhancedfirstly
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Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux differencing form of Fisher and Carpenter (2013) and secondly (enhanced by dissipation) as numerical surface fluxes in finite volume like schemes. The purpose of this article is threefold. Firstly, the flux differencing theory is extended, guaranteeing high-order for general symmetric and consistent numerical fluxes and investigating entropy stability in a generalised framework of summation-by-parts operators applicable to multiple dimensions and simplex elements. Secondly, a general procedure to construct affordable entropy conservative fluxes is described explicitly and used to derive several new fluxes. Finally, robustness properties of entropy stable numerical fluxes are investigated and positivity preservation is proven for several entropy conservative fluxes enhanced with local Lax-Friedrichs type dissipation operators. All these theoretical investigations are supplemented with numerical experiments.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods

    math.NA 2025-08 accept novelty 7.0 of 10

    The authors derive an entropy-conservative two-point flux for the ultra-relativistic Euler equations, prove its consistency, and validate an entropy-stable DG scheme against 1D radial reference solutions in 2D and 3D.

  2. Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws

    math.NA 2026-07 accept novelty 6.0 of 10

    Entropy-conservative diagonal-norm SBP flux-differencing schemes converge at order p to smooth solutions of general entropy-symmetrizable hyperbolic systems under periodic boundaries.

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