Issue |
ESAIM: ProcS
Volume 70, 2021
CEMRACS 2019 - Geophysical Fluids, Gravity Flows
|
|
---|---|---|
Page(s) | 45 - 67 | |
DOI | https://doi.org/10.1051/proc/202107004 | |
Published online | 01 June 2021 |
Simulation of complex free surface flows
1 Laboratoire d’Hydraulique Saint-Venant, EDF R&D, ENPC
2 Laboratoire Analyse, Géométrie et Applications, Université Paris 13
3 IMATH - Institut de Mathématiques de Toulon
4 INRIA Paris — Sorbonne Université — CNRS (LJLL), team ANGE, 2 rue Simone Iff, CS 42112, 75589 Paris cedex 12
We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].
Résumé
L’objet de l’étude est le système de Serre-Green-Naghdi afin de modéliser des écoulements incompressibles à surface libre en eaux peu profondes, tout en tenant compte les effets de la pression non-hydrostatique et les phénomènes dispersifs qui jouent un rôle important en particulier en océanographie côtière. Plusieurs schémas numériques sont présentés, basés sur une méthode de splitting, en séparant la partie hyperbolique et la partie non-hydrostatique. Les algorithmes sont comparés à travers des simulations avec des ondes solitaires. Le modèle est également validé avec des données expérimentales concernant les ondes de Favre [12].
© EDP Sciences, SMAI 2021
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