Analysis of the artificial viscosity in the smoothed particle hydrodynamics modelling of regular waves

ABSTRACT This paper considers the effect of artificial viscosity in smoothed particle hydrodynamics (SPH) computations of six different regular waves. The purpose is to improve the modelling of physically real effects and thereby make SPH a more attractive modelling option. The essence of the proposed method is to avoid running the simulation with different values of the empirical coefficient used in artificial viscosity in order to find the optimum value of this parameter for a given problem. Thorough calibration of the SPH's numerical parameters is performed through the comparison between numerical and experimental data. Among the various parameters involved, the smoothing length and the particle resolution are important in shaping the results. The analysis confirms that when the ratio of particle spacing to smoothing length and the particle resolution useful for different computational domains have been defined, the empirical coefficient depends only on the type of wave breaking in term of the Irribarren number.

[1]  Damien Violeau,et al.  Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview , 2007 .

[2]  R. A. Dalrymple,et al.  SPH Simulations of Regular and Irregular Waves and their Comparison with Experimental Data , 2009 .

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

[4]  P. Stansby,et al.  Kinematics and depth-integrated terms in surf zone waves from laboratory measurement , 2005, Journal of Fluid Mechanics.

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

[6]  M. Mossa,et al.  Experimental study on the hydrodynamics of regular breaking waves , 2006 .

[7]  J. Monaghan,et al.  A Switch to Reduce SPH Viscosity , 1997 .

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

[9]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[10]  Stefano Sibilla,et al.  3D SPH modelling of hydraulic jump in a very large channel , 2013 .

[11]  Jean-Paul Vila,et al.  ON PARTICLE WEIGHTED METHODS AND SMOOTH PARTICLE HYDRODYNAMICS , 1999 .

[12]  M. G. Cimoroni,et al.  NUMERICAL SIMULATION OF FLUID STRUCTURE INTERACTION , 1994 .

[13]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .

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

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

[16]  C. Antoci,et al.  Numerical simulation of fluid-structure interaction by SPH , 2007 .

[17]  Robert A. Dalrymple,et al.  3D SPH Simulation of large waves mitigation with a dike , 2007 .

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

[19]  S. Attaway,et al.  Smoothed particle hydrodynamics stability analysis , 1995 .

[20]  Joseph P. Morris,et al.  A Study of the Stability Properties of Smooth Particle Hydrodynamics , 1996, Publications of the Astronomical Society of Australia.

[21]  M. Dumbser,et al.  A New Stable Version of the SPH Method in Lagrangian Coordinates , 2008 .

[22]  M. Lastiwka,et al.  Truncation error in mesh‐free particle methods , 2006 .

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

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

[25]  Rui Xu,et al.  Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method , 2008, J. Comput. Phys..

[26]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[27]  Robert G. Dean,et al.  Water wave mechanics for engineers and scientists , 1983 .

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

[29]  Hitoshi Gotoh,et al.  On particle-based simulation of a dam break over a wet bed , 2010 .

[30]  D. Balsara.  von Neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms , 1995 .

[31]  S. Shao,et al.  Corrected Incompressible SPH method for accurate water-surface tracking in breaking waves , 2008 .

[32]  B. Rogers,et al.  State-of-the-art of classical SPH for free-surface flows , 2010 .

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

[34]  Robert A. Dalrymple,et al.  Modeling Dam Break Behavior over a Wet Bed by a SPH Technique , 2008 .

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

[36]  J. Michael Owen,et al.  A tensor artificial viscosity for SPH , 2004 .

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

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

[39]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[40]  Omar M. Knio,et al.  SPH Modelling of Water Waves , 2001 .

[41]  Andrea Colagrossi,et al.  A set of canonical problems in sloshing, Part I: Pressure field in forced roll-comparison between experimental results and SPH , 2009 .

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

[43]  Mario Gallati,et al.  SPH Simulation of Sediment Flushing Induced by a Rapid Water Flow , 2012 .

[44]  J. Monaghan.  On the problem of penetration in particle methods , 1989 .

[45]  Dennis W. Quinn,et al.  An Analysis of 1-D Smoothed Particle Hydrodynamics Kernels , 1996 .

[46]  G. Dilts.  MOVING-LEAST-SQUARES-PARTICLE HYDRODYNAMICS-I. CONSISTENCY AND STABILITY , 1999 .

[47]  Abbas Khayyer,et al.  Modified Moving Particle Semi-implicit methods for the prediction of 2D wave impact pressure , 2009 .

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

[49]  R. Issa,et al.  Modelling a Plunging Breaking Solitary Wave with Eddy-Viscosity Turbulent SPH Models , 2008 .

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

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

[52]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

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