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Numerical simulation of plunging wave breaking by the weakly compressible smoothed particle hydrodynamic method

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Abstract

In this paper, a numerical meshless method called the weakly compressible smoothed particle hydrodynamic (WCSPH) method, which is a two-dimensionalmodel of a weakly compressible fluid, is applied to simulate the plunging wave breaking process. This model solves the viscous fluid equations to obtain the velocity and density fields and also solves the equation of state to obtain the pressure field. The WCSPH method is demonstrated to have a higher computational efficiency than the basic SPH model. To simulate the turbulent behavior of the fluid flow in the wave breaking procedure, a sub particle scale (SPS) model is used, which is obtained from the Large eddy simulation (LES) theory. To consider the accuracy of the standard WCSPH model (WCSPH model without considering the turbulent effect), a dam break test is performed, and model results are compared with available experimental data.

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References

  1. M. J. F. Stive, “Energy Dissipation in Waves Breaking on Gentle Slopes,” Coastal Eng. 8(2), 99–127 (1984).

    Article  Google Scholar 

  2. D. J. Skyner, C. Gray, and C. A. Greated, “A Comparison of Time-Stepping Numerical Predictions with Whole-Field Flow Measurement in Breaking Waves,” NATO ASI Ser., Ser. E: Appl. Sci. 178, 490–508 (1990).

    Google Scholar 

  3. J. C. Lin and D. Rockwell, “Evolution of a Quasi-Steady Breaking Wave,” J. Fluid Mech. 302, 29–44 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  4. F. C. K. Ting and J. T. Kirby, “Dynamics of Surf-Zone Turbulence in a Spilling Breaker,” Coastal Eng. 27(3/4), 131–160 (1996).

    Article  Google Scholar 

  5. P. Hull and G. Müller, “An Investigation of Breaker Heights, Shapes and Pressures,” Ocean Eng. 29(1), 59–79 (2002).

    Article  Google Scholar 

  6. F. Harlow and E. Welch, “Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface,” Phys. Fluids 8(12), 2182–2189 (1965).

    Article  ADS  MATH  Google Scholar 

  7. C. W. Hirt and B. D. Nichols, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys. 39(1), 201–225 (1981).

    Article  ADS  MATH  Google Scholar 

  8. R. K. C. Chan and R. L. Street, “A Computer Study of Finite-Amplitude Water Waves,” J. Comput. Phys. 6(1), 68–94 (1970).

    Article  ADS  MATH  Google Scholar 

  9. P. Lin and P. L. F. Liu, “A Numerical Study of Breaking Waves in the Surf Zone,” J. Fluid Mech. 359(1), 239–264 (1998).

    Article  ADS  MATH  Google Scholar 

  10. L. Lucy, “A Numerical Approach to Testing the Fission Hypothesis,” Astronom. J. 82(12), 1013–1024 (1977).

    Article  ADS  Google Scholar 

  11. R. A. Gingold and J. J. Monaghan, “Smoothed Particle Hydrodynamics-Theory and Application to Non-Spherical Stars,” Monthly Notices Roy. Astronom. Soc. 181, 375–389 (1977).

    ADS  MATH  Google Scholar 

  12. J. J. Monaghan, “Smoothed Particle Hydrodynamics,” Annual Rev. Astronomy Astrophys. 30, 543–574 (1992).

    Article  ADS  Google Scholar 

  13. J. P. Morris, P. J. Fox, and Y. Zhu, “Modeling Low Reynolds Number Incompressible Flows using SPH,” J. Comput. Phys. 136(1), 214–226 (1997).

    Article  ADS  MATH  Google Scholar 

  14. J. J. Monaghan and A. Kos, “Solitary Waves on a Cretan Beach,” J. Waterway Port, Coast. Ocean Eng. 125(3), 145–154 (1999).

    Article  Google Scholar 

  15. A. Colagrossi and M. Landrini, “Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics,” J. Comput. Phys. 191(2), 448–475 (2003).

    Article  ADS  MATH  Google Scholar 

  16. S. Shao and H. Gotoh, “Turbulence Particle Models for Tracking Free Surfaces,” J. Hydraul. Res. 43(3), 276–289 (2005).

    Article  Google Scholar 

  17. J. J. Monaghan, “Smoothed Particle Hydrodynamics,” Rep. Prog. Phys. 68, 1703–1759 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  18. D. Violeau and R. Issa, “Numerical Modelling of Complex Turbulent Free-Surface Flows with the SPH Method: An Overview,” Int. J. Numer. Methods Fluids. 53(2), 277–304 (2007).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. S. Shao, C. Ji, D. I. Graham, et al. “Simulation of Wave Overtopping by an Incompressible SPH Model,” Coastal Eng. 53(9), 723–735 (2006).

    Article  Google Scholar 

  20. J. J. Monaghan and J. C. Lattanzio, “A Refined Method for Astrophysical Problems,” Astronom. Astrophys. 149, 135–143 (1985).

    ADS  MATH  Google Scholar 

  21. G. R. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method, Ed. by G. R. Liu and M. B. Liu (World Sci., S. l., 2003).

  22. B. D. Rogers and R. A. Dalrymple, “A SPH Modeling of Breaking Waves,” Coastal Eng. 1–4, 415–427 (2004).

    Google Scholar 

  23. M. J. Ketabdari and H. Saghi, “Large Eddy Simulation of Laminar and Turbulent Flow on Collocated and Staggered Grids,” ISRN Mech. Eng. 1, 1–13 (2011).

    Article  Google Scholar 

  24. A. Yoshizawa, “Statistical Theory for Compressible Turbulent Shear Flows, with the Application to Subgrid Modeling,” Phys. Fluids 29, 2152–2164 (1986).

    Article  ADS  MATH  Google Scholar 

  25. L. Blin, A. Hadjadj, and L. Vervisch, “Large Eddy Simulation of Turbulent Flows in Reversing Systems,” J. Turbulence, No. 4, 1–12 (2003).

    Google Scholar 

  26. J. Smagorinsky, “General Circulation Experiments with the Primitive Equations,” Monthly Weather Rev. 91(3), 99–164 (1963).

    Article  ADS  Google Scholar 

  27. R. A. Dalrymple and B. D. Rogers, “Numerical Modeling of Water Waves with the SPH Method,” Coastal Eng. 53(2/3), 141–147 (2006).

    Article  Google Scholar 

  28. E. Y. M. Lo and S. Shao, “Simulation of Near-Shore Solitary Wave Mechanics by an Incompressible SPH Method,” Appl. Ocean Res. 24(5), 275–286 (2002).

    Article  Google Scholar 

  29. G. K. Batchelor, Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge, 1967).

    MATH  Google Scholar 

  30. J. J. Monaghan, “On the Problem of Penetration in Particle Methods,” J. Comput. Phys. 82(1), 1–15 (1989).

    Article  ADS  MATH  Google Scholar 

  31. R. A. Dalrymple and O. Knio, “SPH Modeling of Water Waves,” Proc. Coastal Dynamics (ACSE), Lund, Sweden (2001), pp. 779–787.

    Google Scholar 

  32. A. J. C. Crespo, M. Gómez-Gesteira, and R. A. Dalrymple, “Boundary Conditions Generated by Dynamic Particles in SPH Methods,” Computers, Materials, Continua. 5(3), 173–184 (2007).

    MathSciNet  MATH  Google Scholar 

  33. M. J. Ketabdari, M. R. H. Nobari, and M. Moradi Larmaei, “Simulation of Waves Group Propagation and Breaking in Coastal Zone using a Navier-Stokes Solver with an Improved VOF Free Surface Treatment,” Appl. Ocean Res. 30(2), 130–143 (2008).

    Article  Google Scholar 

  34. J. C. Martin and W. J. Moyce, “Pt 4. An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane,” Philos. Trans. Roy. Soc. London, Ser. A: Math. Phys. Sci. 244(882), 312–324 (1952).

    Article  MathSciNet  ADS  Google Scholar 

  35. R. Issa, Numerical Assessment of the Smoothed Particle Hydrodynamics Gridless Method for Incompressible Flows and Its Extension to Turbulent Flows (Univ. Manchester Inst. of Sci. and Technol., Manchester, 2005).

    Google Scholar 

  36. R. G. Dean, Water Wave Mechanics for Engineers and Scientists, (Ed. by R. G. Dean, R. A. Dalrymple World Sci., S. l., 1991).

  37. T. Vinje and P. Brevig, “Numerical Simulation of Breaking Waves,” J. Advance Water Resources 4, 77–82 (1981).

    Article  Google Scholar 

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Correspondence to M. J. Ketabdari.

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Original Russian Text © M.J. Ketabdari, A.N. Roozbahani.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 3, pp. 155–165, May–June, 2013.

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Ketabdari, M.J., Roozbahani, A.N. Numerical simulation of plunging wave breaking by the weakly compressible smoothed particle hydrodynamic method. J Appl Mech Tech Phy 54, 477–486 (2013). https://doi.org/10.1134/S0021894413030188

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  • DOI: https://doi.org/10.1134/S0021894413030188

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