Show simple item record

dc.contributor.authorRanocha, Hendrik
dc.contributor.authorGassner, Gregor J
dc.date.accessioned2020-10-05T08:15:33Z
dc.date.available2020-10-05T08:15:33Z
dc.date.issued2020-09-28
dc.identifier.urihttp://hdl.handle.net/10754/665437
dc.description.abstractRecently, 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).
dc.description.sponsorshipResearch reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Gregor Gassner is supported by the European Research Council (ERC) under the European Union’s Eights Framework Program Horizon 2020 with the research project Extreme, ERC grant agreement no. 714487.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2009.13139
dc.rightsArchived with thanks to arXiv
dc.titlePreventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Mathematics and Computer Science, Center for Data and Simulation Science, University of Cologne, Germany.
dc.identifier.arxivid2009.13139
kaust.personRanocha, Hendrik
refterms.dateFOA2020-10-05T08:16:17Z


Files in this item

Thumbnail
Name:
Preprintfile1.pdf
Size:
1.308Mb
Format:
PDF
Description:
Pre-print

This item appears in the following Collection(s)

Show simple item record