Entropy stable spectral collocation schemes for the Navier-Stokes Equations: Discontinuous interfaces

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

doi:10.1137/130932193

Entropy stable spectral collocation schemes for the Navier-Stokes Equations: Discontinuous interfaces

Mark H. Carpenter, Travis C. Fisher, Eric J. Nielsen, Steven H. Frankel

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	B835-B867
Journal	SIAM Journal on Scientific Computing
Volume	36
Issue number	5
DOIs	https://doi.org/10.1137/130932193
State	Published - 2014
Externally published	Yes

Keywords

Conservation
Entropy stability
High-order finite-element methods
Navier-Stokes
SBP-SAT
Skew-symmetric

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/130932193

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title = "Entropy stable spectral collocation schemes for the Navier-Stokes Equations: Discontinuous interfaces",

abstract = "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.",

keywords = "Conservation, Entropy stability, High-order finite-element methods, Navier-Stokes, SBP-SAT, Skew-symmetric",

author = "Carpenter, {Mark H.} and Fisher, {Travis C.} and Nielsen, {Eric J.} and Frankel, {Steven H.}",

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AU - Carpenter, Mark H.

AU - Fisher, Travis C.

AU - Nielsen, Eric J.

AU - Frankel, Steven H.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Conservation

KW - Entropy stability

KW - High-order finite-element methods

KW - Navier-Stokes

KW - SBP-SAT

KW - Skew-symmetric

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Entropy stable spectral collocation schemes for the Navier-Stokes Equations: Discontinuous interfaces

Abstract

Keywords

ASJC Scopus subject areas

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