Artificial Viscosity to Get Both Robustness and Discrete Entropy Inequalities

In the present work, we consider the numerical approximation of the weak solutions of first-order system of evolution laws supplemented with entropy inequalities. The systems under consideration are hyperbolic as soon as a conservation form is satisfied, but such stability property may be lost for n...

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Veröffentlicht in:Journal of scientific computing Jg. 97; H. 3; S. 65
Hauptverfasser: Berthon, Christophe, Castro Díaz, Manuel J., Duran, Arnaud, Morales de Luna, Tomás, Saleh, Khaled
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.12.2023
Springer Nature B.V
Springer Verlag
Schlagworte:
Algorithms
Analysis of PDEs
Approximation
Computational Mathematics and Numerical Analysis
Conservation laws
Eigenvalues
Entropy
Fluid mechanics
Inequalities
Inequality
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Mathematics and Statistics
Mechanics
Numerical Analysis
Physics
Robustness (mathematics)
Stability
Theoretical
Viscosity
65M08
Discrete entropy inequalities
CFL-like condition
Robustness
Evolution laws
Finite volume schemes
65M12
robustness
discrete entropy inequalities
finite volume schemes
ISSN:0885-7474, 1573-7691
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Beschreibung
Zusammenfassung:In the present work, we consider the numerical approximation of the weak solutions of first-order system of evolution laws supplemented with entropy inequalities. The systems under consideration are hyperbolic as soon as a conservation form is satisfied, but such stability property may be lost for non-conservative systems. Here, we show that the robustness and the entropy stability of any finite volume numerical scheme can be restored by introducing a suitable artificial numerical viscosity.
Bibliographie:ObjectType-Article-1
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02385-1