Gassner, Gregor J., Winters, Andrew R. and Kopriva, David A. (2016). A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. Appl. Math. Comput., 272. S. 291 - 309. NEW YORK: ELSEVIER SCIENCE INC. ISSN 1873-5649
Full text not available from this repository.Abstract
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 discretisadon 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. (C) 2015 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-293630 | ||||||||||||||||
DOI: | 10.1016/j.amc.2015.07.014 | ||||||||||||||||
Journal or Publication Title: | Appl. Math. Comput. | ||||||||||||||||
Volume: | 272 | ||||||||||||||||
Page Range: | S. 291 - 309 | ||||||||||||||||
Date: | 2016 | ||||||||||||||||
Publisher: | ELSEVIER SCIENCE INC | ||||||||||||||||
Place of Publication: | NEW YORK | ||||||||||||||||
ISSN: | 1873-5649 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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Refereed: | Yes | ||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/29363 |
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