Gassner, Gregor J., Winters, Andrew R., Hindenlang, Florian J. and Kopriva, David A. (2019). The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. Technical Report.

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Abstract

We show how to modify the original Bassi and Rebay scheme (BR1)[F. Bassi and S. Rebay, A High Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations, Journal of Computational Physics, 131:267–279, 1997] to get a provably stable discontinuous Galerkin collocation spectral element method (DGSEM) with Gauss-Lobatto (GL) nodes for the compressible Navier-Stokes equations (NSE) on three dimensional curvilinear meshes. Specifically, we show that the BR1 scheme can be provably stable if the metric identities are discretely satisfied, a two-point average for the metric terms is used for the contravariant fluxes in the volume, an entropy conserving split form is used for the advective volume integrals, the auxiliary gradients for the viscous terms are computed from gradients of entropy variables, and the BR1 scheme is used for the interface fluxes. Our analysis shows that even with three dimensional curvilinear grids, the BR1 fluxes do not add artificial dissipation at the interior element faces. Thus, the BR1 interface fluxes preserve the stability of the discretization of the advection terms and we get either energy stability or entropy-stability for the linear or nonlinear compressible NSE, respectively.

Item Type: Preprints, Working Papers or Reports (Technical Report)
Creators:
CreatorsEmailORCID
Gassner, Gregor J.ggassner@math.uni-koeln.deUNSPECIFIED
Winters, Andrew R.UNSPECIFIEDUNSPECIFIED
Hindenlang, Florian J.UNSPECIFIEDUNSPECIFIED
Kopriva, David A.UNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-92709
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2019,1
Subjects: Data processing Computer science
Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
Discontinuous GalerkinEnglish
Bassi and RebayEnglish
viscous termsEnglish
linearized Navier-Stokes equationsEnglish
compressible Navier-StokesEnglish
energy stabilityEnglish
skew-symmetryEnglish
entropy-stabilityEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Central Institutions / Interdisciplinary Research Centers > Center for Data and Simulation Science
Language: English
Date: 25 January 2019
URI: http://kups.ub.uni-koeln.de/id/eprint/9270

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