Energy balance numerical schemes for shallow water equations with discontinuous topography

The well-balanced property that ensures quiescent equilibrium when solving the shallow-water equations with varying topography is extended in this work to ensure numerically a constant level of energy in steady cases with velocity when necessary. This is done in the context of augmented solvers that...

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Bibliographic Details
Published in:Journal of computational physics 2013-03, Vol.236, p.119-142
Main Authors: Murillo, J., García-Navarro, P.
Format: Article
Language:English
Subjects:
Computation
Energy balance
Godunov-type scheme
HLL solver
Integrals
Mathematical analysis
Resonant regime
Riemann solver
Roe solver
Shallow water
Shallow water equations
Solvers
Topography
Weak solutions
Well-balanced approach
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Summary:The well-balanced property that ensures quiescent equilibrium when solving the shallow-water equations with varying topography is extended in this work to ensure numerically a constant level of energy in steady cases with velocity when necessary. This is done in the context of augmented solvers that consider in their definition the presence of a discontinuous bed. In order to guarantee a constant energy state a proper integral approach of the bed source term is presented. This approach is systematically assessed via a series of steady test cases and Riemann problems including the resonance regime.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.11.003