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Journal of Scientific Computing

Erschienen in:

04.05.2019

Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities

verfasst von: Christophe Berthon, Arnaud Duran, Françoise Foucher, Khaled Saleh, Jean De Dieu Zabsonré

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2019

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Abstract

This work is devoted to the derivation of an energy estimate to be satisfied by numerical schemes when approximating the weak solutions of the shallow water model. More precisely, here we adopt the well-known hydrostatic reconstruction technique to enforce the adopted Finite-Volume scheme to be well-balanced; namely to exactly preserve the lake at rest stationary solution. Such a numerical approach is known to get a semi-discrete (continuous in time) entropy inequality. However, a semi-discrete energy estimation turns, in general, to be insufficient to claim the required stability. In the present work, we adopt the artificial numerical viscosity technique to increase the desired stability and then to recover a fully discrete energy estimate. Several numerical experiments illustrate the relevance of the designed viscous hydrostatic reconstruction scheme.

Vorheriger Artikel New Analysis of Galerkin FEMs for Miscible Displacement in Porous Media

Nächster Artikel Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data

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Titel: Improvement of the Hydrostatic Reconstruction Scheme to Get Fully Discrete Entropy Inequalities
verfasst von: Christophe Berthon
Arnaud Duran
Françoise Foucher
Khaled Saleh
Jean De Dieu Zabsonré
Publikationsdatum: 04.05.2019
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-00961-y

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