Turbulence particle models for tracking free surfaces

Two numerical particle models, the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods, coupled with a sub-particle scale (SPS) turbulence model, are presented to simulate free surface flows. Both SPH and MPS methods have the advantages in that the governing Navier-Stokes equations are solved by Lagrangian approach and no grid is needed in the computation. Thus the free surface can be easily and accurately tracked by particles without numerical diffusion. In this paper different particle interaction models for SPH and MPS methods are summarized and compared. The robustness of two models is validated through experimental data of a dam-break flow. In addition, a series of numerical runs are carried out to investigate the order of convergence of the models with regard to the time step and particle spacing. Finally the efficiency of the incorporated SPS model is further demonstrated by the computed turbulence patterns from a breaking wave. It is shown that both SPH and MPS models provide a useful tool for simulating free surface flows.

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

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

[3]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

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

[5]  Patrick J. Fox,et al.  A pore‐scale numerical model for flow through porous media , 1999 .

[6]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

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

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

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

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

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

[12]  Wang Guangqian,et al.  Simulation of fan formation using a debris mass model , 2002 .

[13]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[14]  Erik Damgaard Christensen,et al.  Large eddy simulation of breaking waves , 2001 .

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

[16]  Yoshiaki Oka,et al.  A Mesh-Free Numerical Method for Direct Simulation of Gas-Liquid Phase Interface , 1999 .

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

[18]  Kuang-An Chang,et al.  Runup and Rundown of Solitary Waves on Sloping Beaches , 1999 .

[19]  J. Monaghan,et al.  A refined particle method for astrophysical problems , 1985 .

[20]  J. C. Martin.  An experimental study of the collapse of liquid column on a rigid horizontal plane , 1952 .

[21]  C. K. Thornhill,et al.  Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , 1952, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

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

[23]  John T. Batina,et al.  A gridless Euler/Navier-Stokes solution algorithm for complex-aircraft applications , 1993 .

[24]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

[25]  梶島 岳夫.  乱流の数値シミュレーション = Numerical simulation of turbulent flows , 2003 .

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

[27]  Yoshiaki Oka,et al.  Numerical analysis of fragmentation mechanisms in vapor explosions , 1999 .