Universität zu Köln

Gassner, Gregor J., Winters, Andrew R., Hindenlang, Florian J. and Kopriva, David A. (2018). The BR1 Scheme is Stable for the Compressible Navier-Stokes Equations. J. Sci. Comput., 77 (1). S. 154 - 201. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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Abstract

In this work we prove that the original (Bassi and Rebay in J Comput Phys 131:267-279, 1997) scheme (BR1) for the discretization of second order viscous terms within the discontinuous Galerkin collocation spectral element method (DGSEM) with Gauss Lobatto nodes is stable. More precisely, we prove in the first part that the BR1 scheme preserves energy stability of the skew-symmetric advection term DGSEM discretization for the linearized compressible Navier-Stokes equations (NSE). In the second part, we prove that the BR1 scheme preserves the entropy stability of the recently developed entropy stable compressible Euler DGSEM discretization of Carpenter et al. (SIAM J Sci Comput 36:B835-B867, 2014) for the non-linear compressible NSE, provided that the auxiliary gradient equations use the entropy variables. Both parts are presented for fully three-dimensional, unstructured curvilinear hexahedral grids. Although the focus of this work is on the BR1 scheme, we show that the proof naturally includes the Local DG scheme of Cockburn and Shu.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gassner, Gregor J. UNSPECIFIED 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:38-172178
DOI:	10.1007/s10915-018-0702-1
Journal or Publication Title:	J. Sci. Comput.
Volume:	77
Number:	1
Page Range:	S. 154 - 201
Date:	2018
Publisher:	SPRINGER/PLENUM PUBLISHERS
Place of Publication:	NEW YORK
ISSN:	1573-7691
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DISCONTINUOUS GALERKIN METHODS; SPECTRAL ELEMENT DISCRETIZATION; CONSERVATION-LAWS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/17217