Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics

Handle URI:
http://hdl.handle.net/10754/622194
Title:
Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics
Authors:
Carpenter, M.H.; Fisher, T.C.; Nielsen, E.J.; Parsani, Matteo ( 0000-0001-7300-1280 ) ; Svärd, M.; Yamaleev, N.
Abstract:
A systematic approach based on a diagonal-norm summation-by-parts (SBP) framework is presented for implementing entropy stable (SS) formulations of any order for the compressible Navier–Stokes equations (NSE). These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy equality for smooth problems. They are also valid for discontinuous flows provided sufficient dissipation is added at shocks and discontinuities to satisfy an entropy inequality. Admissible SBP operators include all centred diagonal-norm finite-difference (FD) operators and Legendre spectral collocation-finite element methods (LSC-FEM). Entropy stable multiblock FD and FEM operators follows immediately via nonlinear coupling operators that ensure conservation, accuracy and preserve the interior entropy estimates. Nonlinearly stable solid wall boundary conditions are also available. Existing SBP operators that lack a stability proof (e.g. weighted essentially nonoscillatory) may be combined with an entropy stable operator using a comparison technique to guarantee nonlinear stability of the pair. All capabilities extend naturally to a curvilinear form of the NSE provided that the coordinate mappings satisfy a geometric conservation law constraint. Examples are presented that demonstrate the robustness of current state-of-the-art entropy stable SBP formulations.
KAUST Department:
Extreme Computing Research Center
Citation:
Carpenter MH, Fisher TC, Nielsen EJ, Parsani M, Svärd M, et al. (2016) Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics. Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues: 495–524. Available: http://dx.doi.org/10.1016/bs.hna.2016.09.014.
Publisher:
Elsevier BV
Journal:
Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues
Issue Date:
9-Nov-2016
DOI:
10.1016/bs.hna.2016.09.014
Type:
Book Chapter
ISSN:
1570-8659
Additional Links:
http://www.sciencedirect.com/science/article/pii/S1570865916300230
Appears in Collections:
Extreme Computing Research Center; Book Chapters

Full metadata record

DC FieldValue Language
dc.contributor.authorCarpenter, M.H.en
dc.contributor.authorFisher, T.C.en
dc.contributor.authorNielsen, E.J.en
dc.contributor.authorParsani, Matteoen
dc.contributor.authorSvärd, M.en
dc.contributor.authorYamaleev, N.en
dc.date.accessioned2017-01-02T08:42:37Z-
dc.date.available2017-01-02T08:42:37Z-
dc.date.issued2016-11-09en
dc.identifier.citationCarpenter MH, Fisher TC, Nielsen EJ, Parsani M, Svärd M, et al. (2016) Entropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics. Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues: 495–524. Available: http://dx.doi.org/10.1016/bs.hna.2016.09.014.en
dc.identifier.issn1570-8659en
dc.identifier.doi10.1016/bs.hna.2016.09.014en
dc.identifier.urihttp://hdl.handle.net/10754/622194-
dc.description.abstractA systematic approach based on a diagonal-norm summation-by-parts (SBP) framework is presented for implementing entropy stable (SS) formulations of any order for the compressible Navier–Stokes equations (NSE). These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy equality for smooth problems. They are also valid for discontinuous flows provided sufficient dissipation is added at shocks and discontinuities to satisfy an entropy inequality. Admissible SBP operators include all centred diagonal-norm finite-difference (FD) operators and Legendre spectral collocation-finite element methods (LSC-FEM). Entropy stable multiblock FD and FEM operators follows immediately via nonlinear coupling operators that ensure conservation, accuracy and preserve the interior entropy estimates. Nonlinearly stable solid wall boundary conditions are also available. Existing SBP operators that lack a stability proof (e.g. weighted essentially nonoscillatory) may be combined with an entropy stable operator using a comparison technique to guarantee nonlinear stability of the pair. All capabilities extend naturally to a curvilinear form of the NSE provided that the coordinate mappings satisfy a geometric conservation law constraint. Examples are presented that demonstrate the robustness of current state-of-the-art entropy stable SBP formulations.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S1570865916300230en
dc.subjectNonlinear stabilityen
dc.subjectEntropy analysisen
dc.subjectCompressible Navier–Stokesen
dc.subjectHigh-order summation-by-partsen
dc.subjectSimultaneous-approximation-termen
dc.subjectWENOen
dc.subjectContravariant stabilityen
dc.titleEntropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamicsen
dc.typeBook Chapteren
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalHandbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issuesen
dc.contributor.institutionNASA Langley Research Center, Hampton, VA, United Statesen
dc.contributor.institutionSandia National Laboratories, Albuquerque, NM, United Statesen
dc.contributor.institutionUniversity of Bergen, Bergen, Norwayen
dc.contributor.institutionOld Dominion University, Norfolk, VA, United Statesen
kaust.authorParsani, Matteoen
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