Comptes Rendus
no. 4
On the Navier–Stokes equations simulation of the head-on collision between two surface solitary waves
[Sur la collision frontale de deux ondes solitaires par simulation des équations de Navier–Stokes]

Présenté par : Michel Combarnous

Pierre Lubin1  ; Stéphane Vincent1  ; Jean-Paul Caltagirone1
1 Transferts, ecoulements, fluides, energétique (TREFLE), UMR CNRS 8508, site École nationale supérieure de chimie et de physique de Bordeaux (ENSCPB), université Bordeaux 1, 16, avenue Pey-Berland, 33607 Pessac cedex, France
Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 351-357.

Ce travail est consacré à l'étude numérique de la collision bidimensionnelle frontale de deux ondes solitaires par simulation numérique des équations de Navier–Stokes en formulation diphasique. L'intérêt de cette étude réside dans la démonstration de la capacité de l'outil numérique original à traiter efficacement ce problème d'onde hautement non-linéaire. Dans cette Note, les résultats numériques sont comparés aux résultats disponibles dans la littérature. Une première investigation de l'hydrodynamique de l'écoulement général est proposée. Il est ainsi démontré que cette configuration est d'une très grande utilité pour valider un code de simulation de mécanique des fluides numérique.

The scope of this Note is to show the results obtained for simulating the two-dimensional head-on collision of two solitary waves by solving the Navier–Stokes equations in air and water. The work is dedicated to the numerical investigation of the hydrodynamics associated to this highly nonlinear flow configuration, the first numerical results being analyzed. The original numerical model is proved to be efficient and accurate in predicting the main features described in experiments found in the literature. This Note also outlines the interest of this configuration to be considered as a test-case for numerical models dedicated to computational fluid mechanics.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2005.02.005
Keywords: Computational fluid mechanics, Two-phase flow, Head-on collision, Solitary waves
Mot clés : Mécanique des fluides numérique, Écoulement diphasique, Collision frontale, Ondes solitaires
Pierre Lubin 1 ; Stéphane Vincent 1 ; Jean-Paul Caltagirone 1

1 Transferts, ecoulements, fluides, energétique (TREFLE), UMR CNRS 8508, site École nationale supérieure de chimie et de physique de Bordeaux (ENSCPB), université Bordeaux 1, 16, avenue Pey-Berland, 33607 Pessac cedex, France 
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Pierre Lubin; Stéphane Vincent; Jean-Paul Caltagirone. On the Navier–Stokes equations simulation of the head-on collision between two surface solitary waves. Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 351-357. doi : 10.1016/j.crme.2005.02.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.02.005/

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[11] S. Vincent; J.-P. Caltagirone; P. Lubin; T.N. Randrianarivelo An adaptative augmented Lagrangian method for three-dimensional multi-material flows, Comput. Fluids, Volume 33 (2004), pp. 1273-1289

[12] S. Vincent; J.-P. Caltagirone Efficient solving method for unsteady incompressible interfacial flow problems, Int. J. Numer. Methods Fluids, Volume 30 (1999), pp. 795-811

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[14] P. Lubin; S. Vincent; J.-P. Caltagirone; S. Abadie Fully three-dimensional direct simulation of a plunging breaker, C. R. Mecanique, Volume 331 (2003), pp. 495-501

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