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dc.contributor.authorCarpenter, M.H.
dc.contributor.authorFisher, T.C.
dc.contributor.authorNielsen, E.J.
dc.contributor.authorParsani, Matteo
dc.contributor.authorSvärd, M.
dc.contributor.authorYamaleev, N.
dc.date.accessioned2017-01-02T08:42:37Z
dc.date.available2017-01-02T08:42:37Z
dc.date.issued2016-11-09
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.
dc.identifier.issn1570-8659
dc.identifier.doi10.1016/bs.hna.2016.09.014
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.
dc.publisherElsevier BV
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S1570865916300230
dc.subjectNonlinear stability
dc.subjectEntropy analysis
dc.subjectCompressible Navier–Stokes
dc.subjectHigh-order summation-by-parts
dc.subjectSimultaneous-approximation-term
dc.subjectWENO
dc.subjectContravariant stability
dc.titleEntropy Stable Summation-by-Parts Formulations for Compressible Computational Fluid Dynamics
dc.typeBook Chapter
dc.contributor.departmentExtreme Computing Research Center
dc.identifier.journalHandbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues
dc.contributor.institutionNASA Langley Research Center, Hampton, VA, United States
dc.contributor.institutionSandia National Laboratories, Albuquerque, NM, United States
dc.contributor.institutionUniversity of Bergen, Bergen, Norway
dc.contributor.institutionOld Dominion University, Norfolk, VA, United States
kaust.personParsani, Matteo


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