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A well balanced and...
A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations
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- Gassner, Gregor J (författare)
- Mathematical Institute, University of Cologne, Germany
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- Winters, Andrew Ross (författare)
- Mathematical Institute, University of Cologne, Germany
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- Kopriva, David A (författare)
- Department of Mathematics, The Florida State University Weyertal, Cologne Germany, USA
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(creator_code:org_t)
- Elsevier, 2016
- 2016
- Engelska.
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 272:2, s. 291-308
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Geovetenskap och miljövetenskap -- Oceanografi, hydrologi och vattenresurser (hsv//swe)
- NATURAL SCIENCES -- Earth and Related Environmental Sciences -- Oceanography, Hydrology and Water Resources (hsv//eng)
Nyckelord
- skew-symmetric shallow water equations
- discontinuous Galerkin spectral element method
- Gauss-Lobatto Legendre
- summation-by-parts
- entropy conservation
- well balanced
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