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dc.contributor.authorParsani, Matteo
dc.contributor.authorCarpenter, Mark H.
dc.contributor.authorFisher, Travis C.
dc.contributor.authorNielsen, Eric J.
dc.date.accessioned2016-11-21T09:15:11Z
dc.date.available2016-11-21T09:15:11Z
dc.date.issued2016-10-04
dc.identifier.citationParsani M, Carpenter MH, Fisher TC, Nielsen EJ (2016) Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations. SIAM Journal on Scientific Computing 38: A3129–A3162. Available: http://dx.doi.org/10.1137/15M1043510.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/15M1043510
dc.identifier.urihttp://hdl.handle.net/10754/621846
dc.description.abstractStaggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
dc.description.sponsorshipThis work was partially supported by King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1043510
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.subjecthigh-order accurate discontinuous methods
dc.subjectentropy stability
dc.subjectSBP-SAT
dc.subjectcompressible Navier--Stokes
dc.subjectstaggered grid
dc.subjectconservation
dc.titleEntropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentExtreme Computing Research Center
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionComputational AeroSciences Branch (CASB), NASA Langley Research Center (LaRC), Hampton, VA 23681
dc.contributor.institutionComputational Thermal and Fluid Mechanics, Sandia National Labs, Albuquerque, NM 871
dc.contributor.institutionCASB, NASA LaRC, Hampton, VA 23681
kaust.personParsani, Matteo
refterms.dateFOA2018-06-14T02:26:56Z
dc.date.published-online2016-10-04
dc.date.published-print2016-01


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