Numerical simulations of wave breaking

Philippe Helluy; Frédéric Golay; Jean-Paul Caltagirone[1]; Pierre Lubin; Stéphane Vincent; Deborah Drevard[2]; Richard Marcer[3]; Philippe Fraunié; Nicolas Seguin[4]; Stephan Grilli[5]; Anne-Cécile Lesage[6]; Alain Dervieux; Olivier Allain[7]

  • [1] TREFLE - ENSCPB - UMR CNRS 8508, Bordeaux, France.
  • [2] LSEET, Université de Toulon, BP 132F, La Garde Cedex, France.
  • [3] Principia Z.I. Athélia 13705 La Ciotat Cedex, France.
  • [4] Laboratoire J.-L. Lions, Université Paris VI, France.
  • [5] Department of Ocean Engineering, University of Rhode Island, Narragansett, RI 02882, USA.
  • [6] INRIA, Sophia Antipolis, France.
  • [7] Société Lemma, La Roquette-Sur-Siagne, France.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

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

Abstract

top
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

top

Helluy, Philippe, et al. "Numerical simulations of wave breaking." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.3 (2005): 591-607. <http://eudml.org/doc/244970>.

@article{Helluy2005,
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.},
affiliation = {TREFLE - ENSCPB - UMR CNRS 8508, Bordeaux, France.; LSEET, Université de Toulon, BP 132F, La Garde Cedex, France.; Principia Z.I. Athélia 13705 La Ciotat Cedex, France.; Laboratoire J.-L. Lions, Université Paris VI, France.; Department of Ocean Engineering, University of Rhode Island, Narragansett, RI 02882, USA.; INRIA, Sophia Antipolis, France.; Société Lemma, La Roquette-Sur-Siagne, France.},
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {wave breaking; finite volumes; low Mach compressible flows; multiphase flow},
language = {eng},
number = {3},
pages = {591-607},
publisher = {EDP-Sciences},
title = {Numerical simulations of wave breaking},
url = {http://eudml.org/doc/244970},
volume = {39},
year = {2005},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2005
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/244970
ER -

References

top
  1. [1] T. Barberon, P. Helluy and S. Rouy, Practical computation of axisymmetrical multifluid flows. Internat. J. Finite Volumes 1 (2003) 1–34. 
  2. [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. [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. Zbl1085.76548
  4. [4] J.U. Brackbill, B.D. Kothe and C. Zemach, A continuum method for modeling surface tension. J. Comput. Phys. 100 (1992) 335–354. Zbl0775.76110
  5. [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. [6] A. Dervieux, Résolution de problèmes à frontière libre. Thesis, Paris VI (1981). 
  7. [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. Zbl1084.76540
  8. [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. [9] S.T. Grilli and R. Subramanya, Numerical modeling of wave breaking induced by fixed or moving boundaries. Comput. Mech. 17 (1996) 374–391. Zbl0851.76043
  10. [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. [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. Zbl1039.76043
  12. [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. [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. [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. [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. [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. [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. [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. [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. Zbl0983.76059
  20. [20] H. Guillard and C. Viozat, On the behavior of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63–86. Zbl0963.76062
  21. [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. Zbl0462.76020
  22. [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. [23] J. Li, Piecewise linear interface calculation. Technical report, Fascicule B-Mecanique, C. R. Acad. Sci. Paris Ser. II. (1995). Zbl0826.76065
  24. [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. Zbl1177.76237
  25. [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. [26] S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York (2002). Zbl1026.76001MR1939127
  27. [27] P. Sagaut, Large eddy simulation for incompressible flows. Springer-Verlag, New York (1998). Zbl0964.76002
  28. [28] R. Saurel and R. Abgrall, A simple method for compressible multifluid flows. SIAM J. Sci. Comput. 21 (1999) 1115–1145. Zbl0957.76057
  29. [29] J.A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Materials Sciences. Cambridge University Press (1996). Zbl0859.76004MR1409367
  30. [30] M. Tanaka, The stability of solitary waves. Phys. Fluids 29 (1986) 650–655. Zbl0605.76025
  31. [31] E. Turkel, Preconditioned methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72 (1987) 277–298. Zbl0633.76069
  32. [32] E. Turkel, Review of preconditioning methods for fluid dynamics. Appl. Numer. Math. 12 (1993) 257–284. Zbl0770.76048
  33. [33] S. Vincent, Modélisation d’écoulements incompressibles de fluides non-miscibles. Université Bordeaux I (1999). 
  34. [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. Zbl0944.76043
  35. [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. Zbl0991.76058
  36. [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. Zbl1079.76047MR2092435
  37. [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). MR625683
  38. [38] H. Viviand, Analysis of pseudo-compressibility systems for compressible and incompressible flows. Technical report, Comput. Fluids Dynamics Rev. (1995). Zbl0875.76554
  39. [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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.