Numerical simulations of wave breaking

Philippe Helluy; Frédéric Golay; Jean-Paul Caltagirone; Pierre Lubin; Stéphane Vincent; Deborah Drevard; Richard Marcer; Philippe Fraunié; Nicolas Seguin; Stephan Grilli; Anne-Cécile Lesage; Alain Dervieux; Olivier Allain

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 39, Issue: 3, page 591-607
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Helluy, Philippe, et al. "Numerical simulations of wave breaking." ESAIM: Mathematical Modelling and Numerical Analysis 39.3 (2010): 591-607. <http://eudml.org/doc/194277>.

@article{Helluy2010,
abstract = { 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. },
author = {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},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Wave breaking; finite volumes; low Mach compressible flows; multiphase flow.},
language = {eng},
month = {3},
number = {3},
pages = {591-607},
publisher = {EDP Sciences},
title = {Numerical simulations of wave breaking},
url = {http://eudml.org/doc/194277},
volume = {39},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 3
SP - 591
EP - 607
AB - 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.
LA - eng
KW - Wave breaking; finite volumes; low Mach compressible flows; multiphase flow.
UR - http://eudml.org/doc/194277
ER -

References

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  1. T. Barberon, P. Helluy and S. Rouy, Practical computation of axisymmetrical multifluid flows. Internat. J. Finite Volumes1 (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 Fluids45 (2004) 581–604.  
  4. J.U. Brackbill, B.D. Kothe and C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys.100 (1992) 335–354.  
  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. Fluids32 (2003) 479–513.  
  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.  
  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 Elements7 (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 Fluids35 (2001) 829–867.  
  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 Elements6 (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 Fluids20 (2001) 57–74.  
  20. H. Guillard and C. Viozat, On the behavior of upwind schemes in the low Mach number limit. Comput. Fluids28 (1999) 63–86.  
  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.  
  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).  
  24. P. Lubin, S. Vincent, J. Caltagirone and S. Abadie, Fully three-dimensional numerical simulation of a plunging breaker. C. R. Mécanique331 (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 Exhibition3 (2004) 306–312.  
  26. S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York (2002).  
  27. P. Sagaut, Large eddy simulation for incompressible flows. Springer-Verlag, New York (1998).  
  28. R. Saurel and R. Abgrall, A simple method for compressible multifluid flows. SIAM J. Sci. Comput.21 (1999) 1115–1145.  
  29. J.A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences. Cambridge University Press (1996).  
  30. M. Tanaka, The stability of solitary waves. Phys. Fluids29 (1986) 650–655.  
  31. E. Turkel, Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys.72 (1987) 277–298.  
  32. E. Turkel, Review of preconditioning methods for fluid dynamics. Appl. Numer. Math.12 (1993) 257–284.  
  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 Fluids30 (1999) 795–811.  
  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.  
  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.  
  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).  
  38. H. Viviand, Analysis of pseudo-compressibility systems for compressible and incompressible flows. Technical report, Comput. Fluids Dynamics Rev. (1995).  
  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.  

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