Universität zu Köln

Ranocha, Hendrik ORCID: 0000-0002-3456-2277 and Gassner, Gregor J. ORCID: 0000-0002-1752-1158 (2020). Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes. Technical Report.

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Abstract

Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible Euler equations. The issue is related to missing local linear stability, i.e. the stability of the discretization towards perturbations added to a stable base flow. This is strongly related to an anti-diffusion mechanism, that is inherent in entropy-conserving two-point fluxes, which are a key ingredient for the high-order discontinuous Galerkin extension. In this paper, we investigate if pressure equilibrium preservation is a remedy to these recently found local linear stability issues of entropy-conservative/dissipative high-order split-form discontinuous Galerkin methods for the compressible Euler equations. Pressure equilibrium preservation describes the property of a discretization to keep pressure and velocity constant for pure density wave propagation. We present the full theoretical derivation, analysis, and show corresponding numerical results to underline our findings. The source code to reproduce all numerical experiments presented in this article is available online (DOI: 10.5281/zenodo.4054366).

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Ranocha, Hendrik UNSPECIFIED orcid.org/0000-0002-3456-2277 UNSPECIFIED Gassner, Gregor J. ggassner@math.uni-koeln.de orcid.org/0000-0002-1752-1158 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-121986
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2020,7
Date:	1 October 2020
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language entropy conservation English kinetic energy preservation English pressure equilibrium preservation English compressible Euler equations English summation-by-parts English UNSPECIFIED English UNSPECIFIED English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/12198