Energy balance numerical schemes for shallow water equations with discontinuous topography

Authors:
J. Murillo;P. García-Navarro
Affiliations:
-;-
Venue:
Journal of Computational Physics
Year:
2013

Citing 11
Cited 1

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Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry

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Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

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A Riemann solver for unsteady computation of 2D shallow flows with variable density

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Efficient well-balanced hydrostatic upwind schemes for shallow-water equations

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Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications

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Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property

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Abstract

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.