Universität zu Köln

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:	Creators Email ORCID ORCID Put Code Gassner, Gregor J. ggassner@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hindenlang, Florian J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Kopriva, David A. UNSPECIFIED UNSPECIFIED UNSPECIFIED
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
Date:	25 January 2019
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Discontinuous Galerkin English Bassi and Rebay English viscous terms English linearized Navier-Stokes equations English compressible Navier-Stokes English energy stability English skew-symmetry English entropy-stability English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9270