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

International audienceThis 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