[Simulation numérique directe tridimensionnelle du déferlement plongeant]
Une étude du déferlement tridimensionelle est présentée sur la base de résultats obtenus par simulation numérique directe des équations de Navier–Stokes diphasiques. Le suivi de l'interface est réalisé par l'utilisation du schéma TVD Lax–Wendroff (Total Variation Diminishing) qui permet de gérer les reconnexions de l'interface. Le déferlement est obtenu à partir de l'initialisation dans un domaine semi-périodique d'une onde sinusoidale instable. Après présentation des équations et des méthodes numériques employées, une comparaison est effectuée entre deux simulations tridimensionelles et une discussion est menée quant à la nécessité d'utiliser une perturbation afin de destabiliser la symétrie du calcul. Les résultats obtenus sont alors commentés.
The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed.
Accepté le :
Publié le :
Mot clés : Mécanique des fluides, Navier–Stokes, Déferlement plongeant, Simulation numérique
Pierre Lubin 1 ; Stéphane Vincent 1 ; Jean-Paul Caltagirone 1 ; Stéphane Abadie 2
@article{CRMECA_2003__331_7_495_0,
author = {Pierre Lubin and St\'ephane Vincent and Jean-Paul Caltagirone and St\'ephane Abadie},
title = {Fully three-dimensional direct numerical simulation of a plunging breaker},
journal = {Comptes Rendus. M\'ecanique},
pages = {495--501},
publisher = {Elsevier},
volume = {331},
number = {7},
year = {2003},
doi = {10.1016/S1631-0721(03)00108-6},
language = {en},
}
TY - JOUR AU - Pierre Lubin AU - Stéphane Vincent AU - Jean-Paul Caltagirone AU - Stéphane Abadie TI - Fully three-dimensional direct numerical simulation of a plunging breaker JO - Comptes Rendus. Mécanique PY - 2003 SP - 495 EP - 501 VL - 331 IS - 7 PB - Elsevier DO - 10.1016/S1631-0721(03)00108-6 LA - en ID - CRMECA_2003__331_7_495_0 ER -
%0 Journal Article %A Pierre Lubin %A Stéphane Vincent %A Jean-Paul Caltagirone %A Stéphane Abadie %T Fully three-dimensional direct numerical simulation of a plunging breaker %J Comptes Rendus. Mécanique %D 2003 %P 495-501 %V 331 %N 7 %I Elsevier %R 10.1016/S1631-0721(03)00108-6 %G en %F CRMECA_2003__331_7_495_0
Pierre Lubin; Stéphane Vincent; Jean-Paul Caltagirone; Stéphane Abadie. Fully three-dimensional direct numerical simulation of a plunging breaker. Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 495-501. doi : 10.1016/S1631-0721(03)00108-6. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00108-6/
[1] Breaking waves on beaches, Ann. Rev. Fluid Mech., Volume 15 (1983), pp. 149-178
[2] Vertical variation of the flow across the surf zone, Coastal Eng., Volume 45 (2002), pp. 169-198
[3] Efficient solving method for unsteady incompressible interfacial flow problems, Int. J. Numer. Meth. Fluids, Volume 30 (1999), pp. 795-811
[4] A one cell local multigrid method for solving unsteady incompressible multi-phase flows, J. Comput. Phys., Volume 163 (2000), pp. 172-215
[5] A continuum method for modeling surface tension, J. Comput. Phys., Volume 100 (1992), pp. 335-354
[6] Mécanisme de génération du jet secondaire ascendant dans un déferlement plongeant, C. R. Acad. Sci. Paris, Sér. IIb, Volume 326 (1998), pp. 553-559
[7] P. Lubin, S. Vincent, J.-P. Caltagirone, S. Abadie, Fully three-dimensional direct numerical simulation of plunging breaking waves, in: Coastal Engineering 2003, 6th International Conference on Computer Modelling and Experimental Measurements of Seas and Coastal Regions, Cadiz, Spain, 2003, accepted
[8] Numerical simulation of breaking waves, J. Adv. Water Resource, Volume 4 (1981), pp. 77-82
[9] Two-dimensional Navier–Stokes simulation of breaking waves, Phys. Fluid, Volume 11 (1999), pp. 121-133
[10] Numerical modelling of the flow generated by plunging breakers, Proceedings Coastal Dynamics, Lund, Sweden, 2001, pp. 202-211
[11] Geometric propertries or deep-water breaking waves, J. Fluid Mech., Volume 209 (1989), pp. 405-433
[12] Role of vortices in surf zone prediction: sedimentation and wave forces, Soc. Econ. Paleontol. Mineral. Spec. Publ., Volume 24 (1976), pp. 92-114
[13] Vortex formation in plunging breaker, Proc. of the 20th ICCE, 1986, pp. 711-723
[14] Three-dimensional large eddy simulation of breaking waves, Coastal Eng. J. Japan, Volume 3–4 (1999), pp. 281-301
[15] Large eddy simulation of breaking waves, Coastal Eng., Volume 42 (2001), pp. 53-86
Cité par Sources :
Commentaires - Politique