Modeling Incompressible Fluids by Means of the SPH Method: Surface Tension and Viscosity

The adaptations of the SPH method for simulating incompressible fluids which focuse on two features: the surface tension and artificial viscosity, are presented in this article. The background and principles of the SPH method are explained and its application to incompressible fluids simulations is discussed. The methodology and implementation of artificial viscosity in the SPH method are presented. The modification for surface tension simulation, which relies on incorporating additional forces into the model, as well as the methodology are suggested. Also, the new equations for artificial viscosity are presented, which are able to simulate a flow of non-newtonian fluids. The results obtained with the method are presented and discussed.

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

[2]  J. Morris.  Simulating surface tension with smoothed particle hydrodynamics , 2000 .

[3]  Paul Meakin,et al.  Modeling of surface tension and contact angles with smoothed particle hydrodynamics. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[5]  L. Hernquist,et al.  TREESPH: A Unification of SPH with the Hierarchical Tree Method , 1989 .

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

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

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

[9]  David A. Yuen,et al.  Parallel implementation of the fluid particle model for simulating complex fluids in the mesoscale , 2002, Concurr. Comput. Pract. Exp..

[10]  H. Posch,et al.  Liquid drops and surface tension with smoothed particle applied mechanics , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

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

[13]  P. Wróblewski,et al.  SPH - a comparison of neighbor search methods based on constant number of neighbors and constant cut-off radius , 2007 .

[14]  F. N. van de Vosse,et al.  The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. , 1999, Journal of biomechanics.

[15]  Stuart L. Shapiro,et al.  Tests of Spurious Transport in Smoothed Particle Hydrodynamics , 1999 .

[16]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .