An entropy stable spacetime discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations

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dc.contributor.authorHiltebrand, Andreas
dc.contributor.authorMay, Sandra
dc.date.accessioned2017-08-03T11:16:29Z
dc.date.available2017-08-03T11:16:29Z
dc.date.issued2017-07
dc.description.abstractIn this paper, we present an entropy stable scheme for solving the compressible Navier-Stokes equations in two space dimensions. Our scheme uses entropy variables as degrees of freedom. It is an extension of an existing spacetime discontinuous Galerkin method for solving the compressible Euler equations. The physical diffusion terms are incorporated by means of the symmetric (SIPG) or nonsymmetric (NIPG) interior penalty method, resulting in the two versions ST-SDSC-SIPG and ST-SDSC-NIPG. The streamline diffusion and shock-capturing terms from the original scheme have been kept, but have been adjusted appropriately. This guarantees that the new scheme essentially reduces to the original scheme for the compressible Euler equations in regions with underresolved physical diffusion. We show entropy stability for both versions under suitable assumptions. We also present numerical results confirming the accuracy and robustness of our schemes.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/36039
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-18056
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;574
dc.subjectdiscontinuous Galerkin methoden
dc.subjectcompressible Navier-Stokes equationsen
dc.subjectentropy stabilityen
dc.subjectentropy variablesen
dc.subjectinterior penalty methoden
dc.subjectwall boundary conditionsen
dc.subject.ddc610
dc.titleAn entropy stable spacetime discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equationsen
dc.typeText
dc.type.publicationtypepreprint
dcterms.accessRightsopen access

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