Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems

By Eitan Tadmor. Acta Numerica, 2003

542 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e8da9a5701d15fa89002f8fca711157c9ec99dca

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains (2013, methodology): “Other authors [6,13,14] have noted that an entropy that makes the hyperbolic matrices symmetric will not necessarily make the diffusive coefficient matrix symmetric.”
Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces (2014, methodology): “Tadmor [41] developed a pointwise relation between adjoining solution and flux-point data that satisfies (3.11); the relation is given by the expression (wi+1 − wi)T f̄i = ψi+1 − ψi.”
Review of summation-by-parts schemes for initial-boundary-value problems (2013, background): “A successful way to prove non-linear stability for conservation laws is reviewed in [124].”
A review of numerical methods for nonlinear partial differential equations (2012, background): “As examples we mention the conservation of mass, which is the basic framework for modern “shock-capturing” methods, the class of conservative schemes in the sense of Lax–Wendroff [134]; Energy conservative schemes which are advocated in long-term calculations of weather prediction using the global c”
Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws (2012, methodology): “Even higher-order accurate entropy conservative fluxes were proposed in [19, 31].”
Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations (2012, background): “Tadmor [26,27] introduced the idea of an entropy conservative numerical flux which should satisfy the following condition (vj+1−vj)·fj+ (1)2 =ψj+1−ψj.”
Numerical Methods for High-Speed Flows (2011, background): “More general expressions for the numerical flux of entropy-consistent schemes can be found in Tadmor (2003).”