Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations

Handle URI:
http://hdl.handle.net/10754/621846
Title:
Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations
Authors:
Parsani, Matteo ( 0000-0001-7300-1280 ) ; Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.
Abstract:
Staggered 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).
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Extreme Computing Research Center
Citation:
Parsani 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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
4-Oct-2016
DOI:
10.1137/15M1043510
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was partially supported by King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia
Additional Links:
http://epubs.siam.org/doi/10.1137/15M1043510
Appears in Collections:
Articles; 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.authorParsani, Matteoen
dc.contributor.authorCarpenter, Mark H.en
dc.contributor.authorFisher, Travis C.en
dc.contributor.authorNielsen, Eric J.en
dc.date.accessioned2016-11-21T09:15:11Z-
dc.date.available2016-11-21T09:15:11Z-
dc.date.issued2016-10-04en
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.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/15M1043510en
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).en
dc.description.sponsorshipThis work was partially supported by King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabiaen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1043510en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjecthigh-order accurate discontinuous methodsen
dc.subjectentropy stabilityen
dc.subjectSBP-SATen
dc.subjectcompressible Navier--Stokesen
dc.subjectstaggered griden
dc.subjectconservationen
dc.titleEntropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equationsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionComputational AeroSciences Branch (CASB), NASA Langley Research Center (LaRC), Hampton, VA 23681en
dc.contributor.institutionComputational Thermal and Fluid Mechanics, Sandia National Labs, Albuquerque, NM 871en
dc.contributor.institutionCASB, NASA LaRC, Hampton, VA 23681en
kaust.authorParsani, Matteoen
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