Accurate numerical methods for free-surface flows

PIs: Enrique D. Fernández Nieto and Yohal Penel

Abstract: The objective is to develop new numerical methods to simulate free surface flows. A hierarchy of dispersive models was built from a Galerkin type formalism: a semi-discretization according to the vertical (reinterpretation of the multi-layer formalism) makes it possible to reduce the dimension of the problem by working on averages per layer. The hierarchy of models corresponds to distinct choices of degree of polynomial approximation in each layer for each variable (vertical speed, transverse speed, dynamic pressure). Within the framework of this project, we are therefore interested in the simulation of models obtained through different numerical strategies. Several criteria make it possible to discriminate these approaches: the calculation time / precision ratio, the preservation of equilibrium states (conventional or not), the positivity of the water height and the properties of stability (entropy, … ).