Adaptive particle refinement and derefinement applied to the smoothed particle hydrodynamics method

SPH simulations are usually performed with a uniform particle distribution. New techniques have been recently proposed to enable the use of spatially varying particle distributions, which encouraged the development of automatic adaptivity and particle refinement/derefinement algorithms. All these efforts resulted in very interesting and promising procedures leading to more efficient and faster SPH simulations. In this article, a family of particle refinement techniques is reviewed and a new derefinement technique is proposed and validated through several test cases involving both free-surface and viscous flows. Besides, this new procedure allows higher resolutions in the regions requiring increased accuracy. Moreover, several levels of refinement can be used with this new technique, as often encountered in adaptive mesh refinement techniques in mesh-based methods.

[1]  Joseph John Monaghan,et al.  SPH and Riemann Solvers , 1997 .

[2]  P. Raviart,et al.  A particle method for first-order symmetric systems , 1987 .

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

[4]  C. Pastor,et al.  Smooth particle hydrodynamics: importance of correction terms in adaptive resolution algorithms , 2003 .

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

[6]  Benedict D. Rogers,et al.  Development of SPH variable resolution using dynamic particle coalescing and splitting , 2012 .

[7]  Richard P. Nelson,et al.  Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics , 1994 .

[8]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[9]  Matteo Antuono,et al.  Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Salvatore Marrone,et al.  Free-surface flows solved by means of SPH schemes with numerical diffusive terms , 2010, Comput. Phys. Commun..

[11]  J. Owen,et al.  Adaptive Smoothed Particle Hydrodynamics: Methodology. II. , 1995, astro-ph/9512078.

[12]  Dirk Roose,et al.  Dynamic particle refinement in SPH: application to free surface flow and non-cohesive soil simulations , 2013 .

[13]  V. Springel,et al.  Cosmological smoothed particle hydrodynamics simulations: the entropy equation , 2001, astro-ph/0111016.

[14]  David Le Touzé,et al.  Validation of a conservative variable-resolution SPH scheme including ∇h terms , 2011 .

[15]  Salvatore Marrone,et al.  Numerical diffusive terms in weakly-compressible SPH schemes , 2012, Comput. Phys. Commun..

[16]  J. Monaghan,et al.  Kernel estimates as a basis for general particle methods in hydrodynamics , 1982 .

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

[18]  Matthieu De Leffe.  Modélisation d'écoulements visqueux par méthode SPH en vue d'application à l'hydrodynamique navale , 2011 .

[19]  B. Buchner.  Green water on ship-type offshore structures , 2002 .

[20]  Hitoshi Gotoh,et al.  Enhancement of stability and accuracy of the moving particle semi-implicit method , 2011, J. Comput. Phys..

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

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

[23]  Benedict D. Rogers,et al.  Accurate particle splitting for smoothed particle hydrodynamics in shallow water with shock capturing , 2012 .

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

[25]  Bachir Benmoussa.  Analyse numerique de methodes particulaires regularisees de type sph pour les lois de conservation , 1998 .

[26]  A. Colagrossi,et al.  Nonlinear water wave interaction with floating bodies in SPH , 2013 .

[27]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

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

[29]  L. Hernquist,et al.  Some cautionary remarks about smoothed particle hydrodynamics , 1993 .

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

[31]  Jean-Luc Lacome.  Analyse de la methode particulaire sph applications a la detonique , 1998 .

[32]  Andrea Colagrossi,et al.  A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH , 2009, Comput. Phys. Commun..

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

[34]  Salvatore Marrone,et al.  Multi-purpose interfaces for coupling SPH with other solvers , 2013 .

[35]  Benedict D. Rogers,et al.  Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass , 2012 .

[36]  Stephan Rosswog,et al.  Astrophysical smooth particle hydrodynamics , 2009, 0903.5075.

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

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

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

[40]  Raushania Gaifullina,et al.  The Use of Histochrome in the Complex Treatment of the Patients with Acute Coronary Syndrome with ST Segment Depression Diagnosed on ECG , 2014 .

[41]  Bertrand Alessandrini,et al.  An improved SPH method: Towards higher order convergence , 2007, J. Comput. Phys..

[42]  Guillaume Oger,et al.  Numerical predictions of ship flooding scenarios using SPH , 2010 .