Geodesic
Simulation of complex free surface flows
Krisztian Benyo1 ; Ayoub Charhabil2 ; Mohamed-Ali Debyaoui3 ; Yohan Penel4
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
ESAIM. Proceedings, Tome 70 (2021), pp. 45-67.

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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].
DOI : 10.1051/proc/202107004

Krisztian Benyo 1 ; Ayoub Charhabil 2 ; Mohamed-Ali Debyaoui 3 ; Yohan Penel 4

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 
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     author = {Krisztian Benyo and Ayoub Charhabil and Mohamed-Ali Debyaoui and Yohan Penel},
     title = {Simulation of complex free surface flows},
     journal = {ESAIM. Proceedings},
     pages = {45--67},
     publisher = {mathdoc},
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     year = {2021},
     doi = {10.1051/proc/202107004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202107004/}
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Krisztian Benyo; Ayoub Charhabil; Mohamed-Ali Debyaoui; Yohan Penel. Simulation of complex free surface flows. ESAIM. Proceedings, Tome 70 (2021), pp. 45-67. doi : 10.1051/proc/202107004. http://geodesic.mathdoc.fr/articles/10.1051/proc/202107004/

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