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Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow

Martin Parisot 1
1 ANGE - Numerical Analysis, Geophysics and Ecology
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : This work is devoted to the numerical resolution in multidimensional framework of a hierarchy of reduced models of the free surface Euler equations, also called water waves equations. The current paper, the first in a series of two, focuses on a hierarchy of monolayer dispersive models, such is the Serre-Green-Naghdi model. A particular attention is given to the dissipation of the mechanical energy at the discrete level, i.e. to design an entropy-satisfying scheme. To illustrate the accuracy and the robustness of the strategy, several numerical experiments are performed. In particular, the strategy is able to deal with dry areas without particular treatment.
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Submitted on : Thursday, July 25, 2019 - 10:57:18 AM
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Martin Parisot. Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow. International Journal for Numerical Methods in Fluids, Wiley, 2019, ⟨10.1002/fld.4766⟩. ⟨hal-01242128v4⟩

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