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dc.contributor.authorFriedrich, Lucas
dc.contributor.authorWinters, Andrew R.
dc.contributor.authorFernández, David C. Del Rey
dc.contributor.authorGassner, Gregor J.
dc.contributor.authorParsani, Matteo
dc.contributor.authorCarpenter, Mark H.
dc.date.accessioned2018-01-15T06:10:39Z
dc.date.available2018-01-15T06:10:39Z
dc.date.issued2017-12-29
dc.identifier.urihttp://hdl.handle.net/10754/626745
dc.description.abstractThis work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre-Gauss-Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between nonconforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h/p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1712.10234v1
dc.relation.urlhttp://arxiv.org/pdf/1712.10234v1
dc.rightsArchived with thanks to arXiv
dc.titleAn Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentExtreme Computing Research Center
dc.eprint.versionPre-print
dc.contributor.institutionMathematical Institute, University of Cologne, Cologne, Germany
dc.contributor.institutionNational Institute of Aerospace and Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA, USA
dc.contributor.institutionComputational AeroSciences Branch, NASA Langley Research Center, Hampton, VA, USA
dc.identifier.arxividarXiv:1712.10234
kaust.personParsani, Matteo
refterms.dateFOA2018-06-13T19:21:33Z


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