A hierarchy of non-hydrostatic layer-averaged approximation of Euler equations for free surface flows

Enrique D. Fernandez-Nieto (1) , Martin Parisot (2) , Yohan Penel (3, 2) , Jacques Sainte-Marie (2, 3)

1 IMUS - Departamento de Matemática Aplicada I
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 Cerema Direction Centre-Est - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Centre-Est

Free surface flows were mainly simulated in the literature by means of shallow water models derived from simplifying assumptions. Research however lead to find out a better balance between physical relevance and computational efficiency. The present work aims at deriving a hierarchy of models corresponding to semi-discretisations with respect to the vertical variable of the Euler equations. More precisely, the resulting semi-discrete systems are multilayer models involving both hydrostatic and non-hydrostatic parts of the pressure field. The hierarchy is parametrised by the order of accuracy. Models are proven to satisfy an energy inequality and are assessed by studying the exact dispersion relation for linear waves and the influence of the number of layers.

Mots clés: Free-surface flows; Euler Equations; Non-hydrostatic pressure; Semi-discrete model

Domaines: Modélisation et simulation

Enrique D. Fernandez-Nieto, Martin Parisot, Yohan Penel, Jacques Sainte-Marie. A hierarchy of non-hydrostatic layer-averaged approximation of Euler equations for free surface flows. 2017. ⟨hal-01324012v1⟩