Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Handle URI:
http://hdl.handle.net/10754/600892
Title:
Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics
Authors:
Carpenter, Mark H.; Parsani, Matteo ( 0000-0001-7300-1280 ) ; Nielsen, Eric J.; Fisher, Travis C.
Abstract:
Nonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.
KAUST Department:
Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Carpenter, M.H., Parsani, M., Nielsen, E.J. and Fisher, T.C., 2016. Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics. In 54th AIAA Aerospace Sciences Meeting (p. 1058).
Publisher:
American Institute of Aeronautics and Astronautics (AIAA)
Journal:
54th AIAA Aerospace Sciences Meeting
Conference/Event name:
54th AIAA Aerospace Sciences Meeting
Issue Date:
4-Jan-2016
DOI:
10.2514/6.2016-1058
Type:
Conference Paper
Sponsors:
Special thanks are extended to Dr. Mujeeb R. Malik for funding this work as part of the “Revolutionary Computational Aerosciences” project.
Additional Links:
http://arc.aiaa.org/doi/10.2514/6.2016-1058
Appears in Collections:
Conference Papers; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorCarpenter, Mark H.en
dc.contributor.authorParsani, Matteoen
dc.contributor.authorNielsen, Eric J.en
dc.contributor.authorFisher, Travis C.en
dc.date.accessioned2016-03-08T13:32:11Zen
dc.date.available2016-03-08T13:32:11Zen
dc.date.issued2016-01-04en
dc.identifier.citationCarpenter, M.H., Parsani, M., Nielsen, E.J. and Fisher, T.C., 2016. Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics. In 54th AIAA Aerospace Sciences Meeting (p. 1058).en
dc.identifier.doi10.2514/6.2016-1058en
dc.identifier.urihttp://hdl.handle.net/10754/600892en
dc.description.abstractNonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.en
dc.description.sponsorshipSpecial thanks are extended to Dr. Mujeeb R. Malik for funding this work as part of the “Revolutionary Computational Aerosciences” project.en
dc.publisherAmerican Institute of Aeronautics and Astronautics (AIAA)en
dc.relation.urlhttp://arc.aiaa.org/doi/10.2514/6.2016-1058en
dc.rightsArchived with thanks to 54th AIAA Aerospace Sciences Meetingen
dc.titleTowards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamicsen
dc.typeConference Paperen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal54th AIAA Aerospace Sciences Meetingen
dc.conference.date4-8 January 2016en
dc.conference.name54th AIAA Aerospace Sciences Meetingen
dc.conference.locationSan Diego, California, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionComput. AeroSciences Branch (CASB) NASA LaRC, Hampton, VA 23681, USAen
dc.contributor.institutionSandia National Laboratories, Albuquerque, NM 87123, USAen
dc.contributor.institutionCASB, NASA LaRC, Hampton, VA 23681, USAen
kaust.authorParsani, Matteoen
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