Efficient Entropy Stable Gauss Collocation Methods

The construction of high-order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently gene...

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Bibliographic Details
Published inJournal of computational physics Vol. 41; no. 5
Main Authors Chan, Jesse, Fernandez, David C Del Rey, Carpenter, Mark H
Format Journal Article
LanguageEnglish
Published Langley Research Center Elsevier 01.01.2019
Subjects
Numerical Analysis
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Summary:The construction of high-order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semidiscrete, entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest 8 that the use of Gauss points significantly improves accuracy on curved meshes.
Bibliography:NF1676L-32194
Langley Research Center
LaRC
ISSN:0021-9991
DOI:10.1137/18M1209234