Using the Dafermos entropy rate criterion in numerical schemes

The following work concerns the construction of an entropy dissipative finite volume solver based on the convex combination of an entropy conservative and an entropy dissipative flux. We aim to construct a semidiscrete scheme that is entropy stable in the sense of the entropy criterion of Dafermos a...

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Bibliographic Details
Published inBIT Vol. 62; no. 4; pp. 1673 - 1701
Main Author Klein, Simon-Christian
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2022
Springer Nature B.V
Subjects
Computational Mathematics and Numerical Analysis
Criteria
Dissipation
Entropy
Mathematics
Mathematics and Statistics
Numeric Computing
76L05
High-order methods
65M08
Entropy stability
35L03
35L45
35L67
Finite-volume methods
65M12
35L65
65M20
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Summary:The following work concerns the construction of an entropy dissipative finite volume solver based on the convex combination of an entropy conservative and an entropy dissipative flux. We aim to construct a semidiscrete scheme that is entropy stable in the sense of the entropy criterion of Dafermos as well as in the classical sense entropy dissipative. The proposed semidiscrete scheme shows nice properties like 2 p order accuracy in smooth regions as well as a non-oscillatory behavior around shocks.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-022-00927-x