Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces | Zendy

Mark H. Carpenter | Zendy; Travis C. Fisher | Zendy; Eric J. Nielsen | Zendy; Steven H. Frankel | Zendy

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Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces

Author(s) -

Mark H. Carpenter,

Travis C. Fisher,

Eric J. Nielsen,

Steven H. Frankel

Publication year - 2014

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/130932193

Subject(s) - mathematics , discontinuous galerkin method , euler equations , navier–stokes equations , spectral element method , mathematical analysis , nonlinear system , spectral method , entropy (arrow of time) , dissipative system , backward euler method , compressibility , finite element method , mixed finite element method , physics , quantum mechanics , thermodynamics

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible Navier--Stokes equations. The new methods are similar to strong form, nodal discontinuous Galerkin spectral elements but conserve entropy for the Euler equations and are entropy stable for the Navier--Stokes equations. Shock capturing follows immediately by combining them with a dissipative companion operator via a comparison approach. Smooth and discontinuous test cases are presented that demonstrate their efficacy.

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