An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property

Handle URI:
http://hdl.handle.net/10754/626745
Title:
An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property
Authors:
Friedrich, Lucas; Winters, Andrew R.; Fernández, David C. Del Rey; Gassner, Gregor J.; Parsani, Matteo ( 0000-0001-7300-1280 ) ; Carpenter, Mark H.
Abstract:
This 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Extreme Computing Research Center
Publisher:
arXiv
Issue Date:
29-Dec-2017
ARXIV:
arXiv:1712.10234
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1712.10234v1; http://arxiv.org/pdf/1712.10234v1
Appears in Collections:
Other/General Submission; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFriedrich, Lucasen
dc.contributor.authorWinters, Andrew R.en
dc.contributor.authorFernández, David C. Del Reyen
dc.contributor.authorGassner, Gregor J.en
dc.contributor.authorParsani, Matteoen
dc.contributor.authorCarpenter, Mark H.en
dc.date.accessioned2018-01-15T06:10:39Z-
dc.date.available2018-01-15T06:10:39Z-
dc.date.issued2017-12-29en
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.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1712.10234v1en
dc.relation.urlhttp://arxiv.org/pdf/1712.10234v1en
dc.rightsArchived with thanks to arXiven
dc.titleAn Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Propertyen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.eprint.versionPre-printen
dc.contributor.institutionMathematical Institute, University of Cologne, Cologne, Germanyen
dc.contributor.institutionNational Institute of Aerospace and Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA, USAen
dc.contributor.institutionComputational AeroSciences Branch, NASA Langley Research Center, Hampton, VA, USAen
dc.identifier.arxividarXiv:1712.10234en
kaust.authorParsani, Matteoen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.