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• W2111072571 abstract "We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented." @default.
• W2111072571 created "2016-06-24" @default.
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• W2111072571 date "2011-06-01" @default.
• W2111072571 modified "2023-10-11" @default.
• W2111072571 title "Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography" @default.
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• W2111072571 doi "https://doi.org/10.1016/j.jcp.2011.03.042" @default.
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