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

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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:
CreatorsEmailORCIDORCID Put Code
Gassner, Gregor J.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Winters, Andrew R.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kopriva, David A.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
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
Uncontrolled Keywords:
KeywordsLanguage
NAVIER-STOKES EQUATIONS; FINITE-DIFFERENCE METHODS; VOLUME WENO SCHEMES; HYPERBOLIC SYSTEMS; MOVING WATER; SUMMATION; PARTS; SEMIIMPLICIT; STABILITY; BOUNDARYMultiple languages
Mathematics, AppliedMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/29363

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