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A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
Mathematical Institute, University of Cologne, Germany.
Mathematical Institute, University of Cologne, Germany.ORCID iD: 0000-0002-5902-1522
Department of Mathematics, The Florida State University Weyertal, Cologne Germany, USA.
2016 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 272, no 2, p. 291-308Article in journal (Refereed) Published
Abstract [en]

In this work, we design an arbitrary high order accurate nodal discontinuous Galerkin spectral element type method for the one dimensional shallow water equations. The novel method uses a skew-symmetric formulation of the continuous problem. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, we show that combined with a special numerical interface flux function, the method exactly preserves the entropy, which is also the total energy for the shallow water equations. Finally, we prove that the surface fluxes, the skew-symmetric volume integrals, and the source term are well balanced. Numerical tests are performed to demonstrate the theoretical findings.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 272, no 2, p. 291-308
Keywords [en]
skew-symmetric shallow water equations, discontinuous Galerkin spectral element method, Gauss-Lobatto Legendre, summation-by-parts, entropy conservation, well balanced
National Category
Computational Mathematics Oceanography, Hydrology and Water Resources
Identifiers
URN: urn:nbn:se:liu:diva-156863DOI: 10.1016/j.amc.2015.07.014ISI: 000364538800005Scopus ID: 2-s2.0-84947039180OAI: oai:DiVA.org:liu-156863DiVA, id: diva2:1315753
Available from: 2019-05-14 Created: 2019-05-14 Last updated: 2019-05-23Bibliographically approved

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