DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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Entropy-stable flux from positive-semidefinite entropy-variable dissipation

Definition

Let $(η, q)$ be an entropy pair with entropy variable $v$ and potential $ψ$ , and let $F^{e c}$ be a consistent entropy-conservative flux as in Tadmor entropy-conservative two-point flux. For each pair $(U_{L}, U_{R}) \in A^{2}$ , choose a symmetric positive-semidefinite matrix $D (U_{L}, U_{R}) \in R^{m \times m}$ . The associated entropy-stable dissipative flux is $F^{e s} (U_{L}, U_{R}) : = F^{e c} (U_{L}, U_{R}) - \frac{1}{2} D (U_{L}, U_{R}) (v (U_{R}) - v (U_{L})) .$ Positive semidefinite means $z^{T} D (U_{L}, U_{R}) z \geq 0$ for every $z \in R^{m}$ . No fully discrete time-step property is included.

Depends on

Tadmor entropy-conservative two-point flux

Used by

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

E. Tadmor, Entropy Stable Schemes for Hyperbolic Conservation Laws, Handbook of Numerical Methods for Hyperbolic Problems, Vol. 17 (standard reference, not scraped)
R. Bürger, P. E. Méndez, and C. Parés, On Entropy Stable Schemes for Degenerate Parabolic Multispecies Kinematic Flow Models (standard reference, not scraped)