Dynamic particle refinement in SPH: application to free surface flow and non-cohesive soil simulations

In this paper, we present a dynamic refinement algorithm for the smoothed particle Hydrodynamics (SPH) method. An SPH particle is refined by replacing it with smaller daughter particles, which positions are calculated by using a square pattern centered at the position of the refined particle. We determine both the optimal separation and the smoothing distance of the new particles such that the error produced by the refinement in the gradient of the kernel is small and possible numerical instabilities are reduced. We implemented the dynamic refinement procedure into two different models: one for free surface flows, and one for post-failure flow of non-cohesive soil. The results obtained for the test problems indicate that using the dynamic refinement procedure provides a good trade-off between the accuracy and the cost of the simulations.

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

[2]  S. Kitsionas,et al.  Smoothed Particle Hydrodynamics with particle splitting, applied to self-gravitating collapse , 2002, astro-ph/0203057.

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

[4]  Joseph John Monaghan,et al.  The dynamics of interstellar cloud complexes , 1988 .

[5]  D. Roose,et al.  Particle refinement for fluid flow simulations with SPH , 2011 .

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

[7]  Anthony Peter Whitworth,et al.  High resolution simulations of clump-clump collisions using SPH with Particle Splitting , 2001 .

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

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

[10]  Ha H. Bui,et al.  Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model , 2008 .

[11]  G. Oger,et al.  Two-dimensional SPH simulations of wedge water entries , 2006, J. Comput. Phys..

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

[13]  Javier Bonet,et al.  Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems , 2007 .

[14]  Zdzislaw Meglicki,et al.  3D structure of truncated accretion discs in close binaries , 1993 .

[15]  Jonathan Feldman,et al.  Dynamic refinement and boundary contact forces in smoothed particle hydrodynamics with applications in fluid flow problems. , 2006 .

[16]  I. A. Bonnell,et al.  Modelling accretion in protobinary systems , 1995 .

[17]  M. Lastiwka,et al.  Adaptive particle distribution for smoothed particle hydrodynamics , 2005 .

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