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dc.contributor.authorRanocha, Hendrik
dc.contributor.authorSayyari, Mohammed
dc.contributor.authorDalcin, Lisandro
dc.contributor.authorParsani, Matteo
dc.contributor.authorKetcheson, David I.
dc.date.accessioned2020-12-08T09:09:53Z
dc.date.available2019-11-11T09:37:24Z
dc.date.available2020-12-08T09:09:53Z
dc.date.issued2020-03-12
dc.date.submitted2019-05-22
dc.identifier.citationRanocha, H., Sayyari, M., Dalcin, L., Parsani, M., & Ketcheson, D. I. (2020). Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations. SIAM Journal on Scientific Computing, 42(2), A612–A638. doi:10.1137/19m1263480
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/19m1263480
dc.identifier.urihttp://hdl.handle.net/10754/659959
dc.description.abstractThe framework of inner product norm preserving relaxation Runge-Kutta methods [D. I. Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850-2870] is extended to general convex quantities. Conservation, dissipation, or other solution properties with respect to any convex functional are enforced by the addition of a relaxation parameter that multiplies the Runge-Kutta update at each step. Moreover, other desirable stability (such as strong stability preservation) and efficiency (such as low storage requirements) properties are preserved. The technique can be applied to both explicit and implicit Runge-Kutta methods and requires only a small modification to existing implementations. The computational cost at each step is the solution of one additional scalar algebraic equation for which a good initial guess is available. The effectiveness of this approach is proved analytically and demonstrated in several numerical examples, including applications to high order entropy-conservative and entropy-stable semidiscretizations on unstructured grids for the compressible Euler and Navier-Stokes equations.
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST).
dc.description.sponsorshipWe are thankful for the computing resources of the Supercomputing Laboratory and the Extreme Computing Research Center at King Abdullah University of Science and Technology
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/19M1263480
dc.relation.urlhttp://arxiv.org/pdf/1905.09129
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1905.09129
dc.titleRelaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
dc.typeArticle
dc.contributor.departmentKing Abdullah University of Science and Technology (KAUST), Extreme Computing Research Center (ECRC), Computer Electrical and Mathematical Science and Engineering Division (CEMSE), Thuwal, 23955-6900, Saudi Arabia
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionTU Braunschweig, Institute Computational Mathematics, Universitatsplatz 2, 38106 Braunschweig, Germany
dc.identifier.volume42
dc.identifier.issue2
dc.identifier.pagesA612-A638
dc.identifier.arxivid1905.09129
kaust.personSayyari, Mohammed
kaust.personDalcin, Lisandro
kaust.personParsani, Matteo
kaust.personKetcheson, David I.
dc.date.accepted2019-11-06
dc.identifier.eid2-s2.0-85084494434
refterms.dateFOA2019-11-11T09:37:53Z
kaust.acknowledged.supportUnitSupercomputing Laboratory
kaust.acknowledged.supportUnitExtreme Computing Research Center


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