Numerical simulations of wave breaking
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) no. 3, p. 591-607
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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {3},
     year = {2005},
     pages = {591-607},
     doi = {10.1051/m2an:2005024},
     zbl = {1130.76023},
     mrnumber = {2157152},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) no. 3, pp. 591-607. doi : 10.1051/m2an:2005024. http://www.numdam.org/item/M2AN_2005__39_3_591_0/

[1] T. Barberon, P. Helluy and S. Rouy, Practical computation of axisymmetrical multifluid flows. Internat. J. Finite Volumes 1 (2003) 1-34.

[2] B. Biausser, S.T. Grilli and P. Fraunié, 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.

[3] B. Biausser, S. Guignard, R. Marcer and P. Fraunié, 3D two phase flows numerical simulations by SL-VOF method. Internat. J. Numer. Methods Fluids 45 (2004) 581-604. | Zbl 1085.76548

[4] J.U. Brackbill, B.D. Kothe and C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335-354. | Zbl 0775.76110

[5] C. De Jouëtte, H. Viviand, S. Wormon and J.M. Le Gouez, Pseudo compressibility method for incompressible flow calculation, in 4th Int. Symposium on computational Fluid Dynamics, Davis, California, 9-12 September (1991).

[6] A. Dervieux, Résolution de problèmes à frontière libre. Thesis, Paris VI (1981).

[7] T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479-513. | Zbl 1084.76540

[8] S.T. Grilli, 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] S.T. Grilli and R. Subramanya, Numerical modeling of wave breaking induced by fixed or moving boundaries. Comput. Mech. 17 (1996) 374-391. | Zbl 0851.76043

[10] S.T. Grilli and I.A. Svendsen, Corner problems and global accuracy in the boundary element solution of nonlinear wave flows. Engrg. Analysis Boundary Elements 7 (1990) 178-195.

[11] S.T. Grilli, P. Guyenne and F. Dias, A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, Internat. J. Numer. Methods Fluids 35 (2001) 829-867. | Zbl 1039.76043

[12] S.T. Grilli, M.A. Losada and F. Martin, 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).

[13] S.T. Grilli, M.A. Losada and F. Martin, Characteristics of solitary wave breaking induced by breakwaters, J. Waterway Port Coastal Ocean Engrg. 120 (1994) 74-92.

[14] S.T. Grilli, J. Skourup and I.A. Svendsen, An Efficient Boundary Element Method for Nonlinear Water Waves. Engrg. Analysis Boundary Elements 6 (1989) 97-107.

[15] S.T. Grilli, I.A. Svendsen and R. Subramanya, Breaking criterion and characteristics for solitary waves on slopes. J. Waterway Port Coastal Ocean Engrg. 123 (1997) 102-112.

[16] S.T. Grilli, I.A. Svendsen and R. Subramanya, Closure of: Breaking criterion and characteristics for solitary waves on slopes. J. Waterway Port Coastal Ocean Engrg. 124 (1997) 333-335.

[17] S.T. Grilli, R. Subramanya, I.A. Svendsen and J. Veeramony, Shoaling of solitary waves on plane beaches. J. Waterway Port Coastal Ocean Engrg. 120 (1994) 609-628.

[18] S. Guignard, S.T. Grilli, R. Marcer and V. Rey, 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.

[19] S. Guignard, R. Marcer, V. Rey, C. Kharif and P. Fraunié, 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 0983.76059

[20] H. Guillard and C. Viozat, On the behavior of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63-86. | Zbl 0963.76062

[21] C.W. Hirt and B.D. Nichols, Volume of fluid method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 323-345. | Zbl 0462.76020

[22] C. Lachaume, B. Biausser, S.T. Grilli, P. Fraunié and S. Guignard, 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.

[23] J. Li, Piecewise linear interface calculation. Technical report, Fascicule B-Mecanique, C. R. Acad. Sci. Paris Ser. II. (1995). | Zbl 0826.76065

[24] P. Lubin, S. Vincent, J. Caltagirone and S. Abadie, Fully three-dimensional numerical simulation of a plunging breaker. C. R. Mécanique 331 (2003) 495-501.

[25] P. Lubin, S. Vincent, J. Caltagirone and S. Abadie, 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.

[26] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York (2002). | MR 1939127 | Zbl 1026.76001

[27] P. Sagaut, Large eddy simulation for incompressible flows. Springer-Verlag, New York (1998). | Zbl 0964.76002

[28] R. Saurel and R. Abgrall, A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21 (1999) 1115-1145. | Zbl 0957.76057

[29] J.A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences. Cambridge University Press (1996). | MR 1409367 | Zbl 0859.76004

[30] M. Tanaka, The stability of solitary waves. Phys. Fluids 29 (1986) 650-655. | Zbl 0605.76025

[31] E. Turkel, Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72 (1987) 277-298. | Zbl 0633.76069

[32] E. Turkel, Review of preconditioning methods for fluid dynamics. Appl. Numer. Math. 12 (1993) 257-284. | Zbl 0770.76048

[33] S. Vincent, Modélisation d'écoulements incompressibles de fluides non-miscibles. Université Bordeaux I (1999).

[34] S. Vincent and J.P. Caltagirone, Efficient solving method for unsteady incompressible interfacial flow problems. Internat. J. Numer. Methods Fluids 30 (1999) 795-811. | Zbl 0944.76043

[35] S. Vincent and J.P. Caltagirone, A one cell local multigrid method for solving unsteady incompressible multi-phase flows. J. Comput. Phys. 163 (2000) 172-215. | Zbl 0991.76058

[36] S. Vincent, J.P. Caltagirone, P. Lubin and T.N. Randrianarivelo, an adaptative augmented Lagrangian method for three-dimensional multi-material flows. Comput. Fluids (2004), under press. | MR 2092435 | Zbl 1079.76047

[37] H. Viviand, 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 625683

[38] H. Viviand, Analysis of pseudo-compressibility systems for compressible and incompressible flows. Technical report, Comput. Fluids Dynamics Rev. (1995). | Zbl 0875.76554

[39] T. Yasuda, H. Mutsuda and N. Mizutani, Kinematic of overtuning solitary waves and their relations to breaker types. Coastal Engrg. 29 (1997) 317-346.