Development of CMPS Method for Accurate Water-Surface Tracking in Breaking Waves

A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.

[1]  Terry R. Healy,et al.  Completeness, conservation and error in SPH for fluids , 2008 .

[2]  Yoshiaki Oka,et al.  Hamiltonian moving-particle semi-implicit (HMPS) method for incompressible fluid flows , 2007 .

[3]  APPLICABILITY OF MPS METHOD TO BREAKING AND POST-BREAKING OF SOLITARY WAVES , 2007 .

[4]  D. Graham,et al.  Simulation of wave overtopping by an incompressible SPH model , 2006 .

[5]  Songdong Shao.  Simulation of breaking wave by SPH method coupled with k-ε model , 2006 .

[6]  Benedict D. Rogers,et al.  Numerical Modeling of Water Waves with the SPH Method , 2006 .

[7]  Hitoshi Gotoh,et al.  Key issues in the particle method for computation of wave breaking , 2006 .

[8]  Shigeo Wada,et al.  A particle method for blood flow simulation: application to flowing red blood cells and platelets , 2006 .

[9]  Hitoshi Gotoh,et al.  Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall , 2005 .

[10]  Hitoshi Gotoh,et al.  Turbulence particle models for tracking free surfaces , 2005 .

[11]  Hitoshi Gotoh,et al.  Simulating Coupled Motion of Progressive Wave and Floating Curtain Wall by SPH-LES Model , 2004 .

[12]  Sivakumar Kulasegaram,et al.  Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems , 2004 .

[13]  Hitoshi Gotoh,et al.  SPH-LES Model for Numerical Investigation of Wave Interaction with Partially Immersed Breakwater , 2004 .

[14]  T. Sakai,et al.  Numerical Model of Wave Breaking by Lagrangian Particle Method with Sub-Particle-Scale Turbulence Model , 2004 .

[15]  Matthias Müller,et al.  Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. , 2004, Technology and health care : official journal of the European Society for Engineering and Medicine.

[16]  A. Colagrossi,et al.  Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .

[17]  Nader A. Issa,et al.  Fluid motion generated by impact , 2003 .

[18]  S. Shao,et al.  INCOMPRESSIBLE SPH METHOD FOR SIMULATING NEWTONIAN AND NON-NEWTONIAN FLOWS WITH A FREE SURFACE , 2003 .

[19]  Ying Li,et al.  Energy Balance Model for Breaking Solitary Wave Runup , 2003 .

[20]  Stephan T. Grilli,et al.  Modeling of Breaking and Post-breaking Waves on Slopes by Coupling of BEM and VOF Methods , 2003 .

[21]  Edmond Y.M. Lo,et al.  Simulation of near-shore solitary wave mechanics by an incompressible SPH method , 2002 .

[22]  S. Hess,et al.  Viscoelastic flows studied by smoothed particle dynamics , 2002 .

[23]  Ying Li.  Non-breaking and breaking solitary wave run-up , 2000, Journal of Fluid Mechanics.

[24]  T. Yabe,et al.  The constrained interpolation profile method for multiphase analysis , 2001 .

[25]  Yoshiaki Oka,et al.  A particle method for elastic and visco-plastic structures and fluid-structure interactions , 2001 .

[26]  S. Koshizuka.  Application of Moving Particle Semi-implicit Method to Nuclear Reactor Safety , 2001 .

[27]  Hitoshi Gotoh,et al.  Sub-particle-scale turbulence model for the MPS method , 2001 .

[28]  J. K. Chen,et al.  A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems , 2000 .

[29]  Sivakumar Kulasegaram,et al.  Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations , 2000 .

[30]  J. Bonet,et al.  Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations , 1999 .

[31]  Hitoshi Gotoh,et al.  LAGRANGIAN SIMULATION OF BREAKING WAVES USING PARTICLE METHOD , 1999 .

[32]  S. Cummins,et al.  An SPH Projection Method , 1999 .

[33]  J. Monaghan,et al.  Solitary Waves on a Cretan Beach , 1999 .

[34]  Ted Belytschko,et al.  ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS , 1998 .

[35]  S. Koshizuka,et al.  International Journal for Numerical Methods in Fluids Numerical Analysis of Breaking Waves Using the Moving Particle Semi-implicit Method , 2022 .

[36]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[37]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[38]  T. Belytschko,et al.  Consistent pseudo-derivatives in meshless methods , 1997 .

[39]  I. A. Svendsen,et al.  BREAKING CRITERION AND CHARACTERISTICS FOR SOLITARY WAVES ON SLOPES , 1997 .

[40]  Anthony Peter Whitworth,et al.  A new prescription for viscosity in smoothed particle hydrodynamics. , 1996 .

[41]  G. R. Johnson,et al.  NORMALIZED SMOOTHING FUNCTIONS FOR SPH IMPACT COMPUTATIONS , 1996 .

[42]  S. Koshizuka,et al.  Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid , 1996 .

[43]  Yoshiaki Oka,et al.  A particle method for calculating splashing of incompressible viscous fluid , 1995 .

[44]  Wing Kam Liu,et al.  Reproducing kernel particle methods for structural dynamics , 1995 .

[45]  J. Monaghan,et al.  SPH simulation of multi-phase flow , 1995 .

[46]  Wing Kam Liu,et al.  Reproducing kernel particle methods , 1995 .

[47]  S. Koshizuka.  A particle method for incompressible viscous flow with fluid fragmentation , 1995 .

[48]  S. Miyama,et al.  Numerical Simulation of Viscous Flow by Smoothed Particle Hydrodynamics , 1994 .

[49]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[50]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[51]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver , 1991 .

[52]  Takashi Yabe,et al.  A universal solver for hyperbolic equations by cubic-polynomial interpolation. II, Two- and three-dimensional solvers , 1991 .

[53]  Larry D. Libersky,et al.  Smooth particle hydrodynamics with strength of materials , 1991 .

[54]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[55]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[56]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[57]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .