This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.
Mots-clés : wave breaking, finite volumes, low Mach compressible flows, multiphase flow
@article{M2AN_2005__39_3_591_0, author = {Helluy, Philippe and Golay, Fr\'ed\'eric and Caltagirone, Jean-Paul and Lubin, Pierre and Vincent, St\'ephane and Drevard, Deborah and Marcer, Richard and Frauni\'e, Philippe and Seguin, Nicolas and Grilli, Stephan and Lesage, Anne-C\'ecile and Dervieux, Alain and Allain, Olivier}, title = {Numerical simulations of wave breaking}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {591--607}, publisher = {EDP-Sciences}, volume = {39}, number = {3}, year = {2005}, doi = {10.1051/m2an:2005024}, mrnumber = {2157152}, zbl = {1130.76023}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an:2005024/} }
TY - JOUR AU - Helluy, Philippe AU - Golay, Frédéric AU - Caltagirone, Jean-Paul AU - Lubin, Pierre AU - Vincent, Stéphane AU - Drevard, Deborah AU - Marcer, Richard AU - Fraunié, Philippe AU - Seguin, Nicolas AU - Grilli, Stephan AU - Lesage, Anne-Cécile AU - Dervieux, Alain AU - Allain, Olivier TI - Numerical simulations of wave breaking JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 591 EP - 607 VL - 39 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2005024/ DO - 10.1051/m2an:2005024 LA - en ID - M2AN_2005__39_3_591_0 ER -
%0 Journal Article %A Helluy, Philippe %A Golay, Frédéric %A Caltagirone, Jean-Paul %A Lubin, Pierre %A Vincent, Stéphane %A Drevard, Deborah %A Marcer, Richard %A Fraunié, Philippe %A Seguin, Nicolas %A Grilli, Stephan %A Lesage, Anne-Cécile %A Dervieux, Alain %A Allain, Olivier %T Numerical simulations of wave breaking %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 591-607 %V 39 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2005024/ %R 10.1051/m2an:2005024 %G en %F M2AN_2005__39_3_591_0
Helluy, Philippe; Golay, Frédéric; Caltagirone, Jean-Paul; Lubin, Pierre; Vincent, Stéphane; Drevard, Deborah; Marcer, Richard; Fraunié, Philippe; Seguin, Nicolas; Grilli, Stephan; Lesage, Anne-Cécile; Dervieux, Alain; Allain, Olivier. Numerical simulations of wave breaking. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Low Mach Number Flows Conference, Tome 39 (2005) no. 3, pp. 591-607. doi : 10.1051/m2an:2005024. http://archive.numdam.org/articles/10.1051/m2an:2005024/
[1] Practical computation of axisymmetrical multifluid flows. Internat. J. Finite Volumes 1 (2003) 1-34.
, and ,[2] Numerical Simulations of Three-dimensional Wave Breaking by Coupling of a VOF Method and A Boundary Element Method, in Proc. 13th Offshore and Polar Engrg. Conf., ISOPE03, Honolulu, USA (May 2003) 333-339.
, and ,[3] Zbl
, , and , 3D two phase flows numerical simulations by SL-VOF method. Internat. J. Numer. Methods Fluids 45 (2004) 581-604. |[4] A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335-354. | Zbl
, and ,[5] Pseudo compressibility method for incompressible flow calculation, in 4th Int. Symposium on computational Fluid Dynamics, Davis, California, 9-12 September (1991).
, , and ,[6] Résolution de problèmes à frontière libre. Thesis, Paris VI (1981).
,[7] Some approximate godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479-513. | Zbl
, and ,[8] Fully Nonlinear Potential Flow Models used for Long Wave Runup Prediction, in Long-Wave Runup Models, H. Yeh, P. Liu and C. Synolakis Eds., World Scientific Pub (1997) 116-180.
,[9] Numerical modeling of wave breaking induced by fixed or moving boundaries. Comput. Mech. 17 (1996) 374-391. | Zbl
and ,[10] Corner problems and global accuracy in the boundary element solution of nonlinear wave flows. Engrg. Analysis Boundary Elements 7 (1990) 178-195.
and ,[11] A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, Internat. J. Numer. Methods Fluids 35 (2001) 829-867. | Zbl
, and ,[12] The Breaking of a Solitary Wave over a Step: Modeling and Experiments, in Proc. 4th Intl. Conf. on Hydraulic Engineering Software (HYDROSOFT92, Valencia, Spain, July 92), W.R. Blain and E. Cabrera Eds., Elsevier, Applied Science, Fluid Flow Modelling, Computational Mechanics Publications 1992575-586 (1992).
, and ,[13] Characteristics of solitary wave breaking induced by breakwaters, J. Waterway Port Coastal Ocean Engrg. 120 (1994) 74-92.
, and ,[14] An Efficient Boundary Element Method for Nonlinear Water Waves. Engrg. Analysis Boundary Elements 6 (1989) 97-107.
, and ,[15] Breaking criterion and characteristics for solitary waves on slopes. J. Waterway Port Coastal Ocean Engrg. 123 (1997) 102-112.
, and ,[16] Closure of: Breaking criterion and characteristics for solitary waves on slopes. J. Waterway Port Coastal Ocean Engrg. 124 (1997) 333-335.
, and ,[17] Shoaling of solitary waves on plane beaches. J. Waterway Port Coastal Ocean Engrg. 120 (1994) 609-628.
, , and ,[18] Computation of Shoaling and Breaking Waves in Nearshore Areas by the Coupling of BEM and VOF Methods, in Proc. 9th Offshore and Polar Engng. Conf., ISOPE99, Brest, France 3 (May 1999) 304-309.
, , and ,[19] Solitary wave breaking on sloping beaches: 2D two phase flow numerical simulation by SL-VOF method. Eur. J. Mech. B Fluids 20 (2001) 57-74. | Zbl
, , , and ,[20] On the behavior of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63-86. | Zbl
and ,[21] Volume of fluid method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 323-345. | Zbl
and ,[22] Modeling of Breaking and Post-breaking Waves on Slopes by Coupling of BEM and VOF methods, in Proc. 13th Offshore and Polar Engng. Conf., ISOPE03, Honolulu, USA (May 2003) 353-359.
, , , and ,[23] Piecewise linear interface calculation. Technical report, Fascicule B-Mecanique, C. R. Acad. Sci. Paris Ser. II. (1995). | Zbl
,[24] Fully three-dimensional numerical simulation of a plunging breaker. C. R. Mécanique 331 (2003) 495-501.
, , and ,[25] Large eddy simulation of vortices induced by plunging breaking waves, in Proc. ISOPE 2004, 14th Intl. Offshore and Polar Enginering Conference and Exhibition 3 (2004) 306-312.
, , and ,[26] Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York (2002). | MR | Zbl
and ,[27] Large eddy simulation for incompressible flows. Springer-Verlag, New York (1998). | Zbl
,[28] A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21 (1999) 1115-1145. | Zbl
and ,[29] Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences. Cambridge University Press (1996). | MR | Zbl
,[30] The stability of solitary waves. Phys. Fluids 29 (1986) 650-655. | Zbl
,[31] Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72 (1987) 277-298. | Zbl
,[32] Review of preconditioning methods for fluid dynamics. Appl. Numer. Math. 12 (1993) 257-284. | Zbl
,[33] Modélisation d'écoulements incompressibles de fluides non-miscibles. Université Bordeaux I (1999).
,[34] Efficient solving method for unsteady incompressible interfacial flow problems. Internat. J. Numer. Methods Fluids 30 (1999) 795-811. | Zbl
and ,[35] A one cell local multigrid method for solving unsteady incompressible multi-phase flows. J. Comput. Phys. 163 (2000) 172-215. | Zbl
and , , , and , an adaptative augmented Lagrangian method for three-dimensional multi-material flows. Comput. Fluids (2004), under press. |[37] Pseudo-unsteady methods for transonic flow computations, in 19th Int. Conf. on Numerical Methods in Fluid Dynamics, Stanford, Springer-Verlag, New-York 141 (1980). | MR
,[38] Analysis of pseudo-compressibility systems for compressible and incompressible flows. Technical report, Comput. Fluids Dynamics Rev. (1995). | Zbl
,[39] Kinematic of overtuning solitary waves and their relations to breaker types. Coastal Engrg. 29 (1997) 317-346.
, and ,Cité par Sources :