Moving least-squares corrections for smoothed particle hydrodynamics

First-order moving least-squares are typically used in conjunction with smoothed particle hydrodynamics in the form of post-processing filters for density fields, to smooth out noise that develops in most applications of smoothed particle hydrodynamics. We show how an approach based on higher-order moving least-squares can be used to correct some of the main limitations in gradient and second-order derivative computation in classic smoothed particle hydrodynamics formulations. With a small increase in computational cost, we manage to achieve smooth density distributions without the need for post-processing and with higher accuracy in the computation of the viscous term of the Navier–Stokes equations, thereby reducing the formation of spurious shockwaves or other streaming effects in the evolution of fluid flow. Numerical tests on a classic two-dimensional dam-break problem confirm the improvement of the new approach.

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

[2]  Ivo F. Sbalzarini,et al.  Discretization correction of general integral PSE Operators for particle methods , 2010, J. Comput. Phys..

[3]  Robert A. Dalrymple,et al.  SPH on GPU with CUDA , 2010 .

[4]  J. Kuhnert,et al.  Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations , 2003 .

[5]  Ted Belytschko,et al.  A unified stability analysis of meshless particle methods , 2000 .

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

[7]  Giovanni Russo,et al.  SPH MODELING OF LAVA FLOWS WITH GPU IMPLEMENTATION , 2010 .

[8]  Guirong Liu,et al.  Investigations into water mitigation using a meshless particle method , 2002 .

[9]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[10]  Eugenio Rustico,et al.  Numerical simulation of lava flow using a GPU SPH model , 2011 .

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

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

[13]  Jean-Paul Vila,et al.  Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws , 2008, SIAM J. Numer. Anal..

[14]  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.

[15]  Marc Alexa,et al.  Point based animation of elastic, plastic and melting objects , 2004, SCA '04.

[16]  Robert A. Dalrymple,et al.  Levee Breaching with GPU-SPHysics Code , 2009 .

[17]  Joe J. Monaghan,et al.  SPH particle boundary forces for arbitrary boundaries , 2009, Comput. Phys. Commun..

[18]  Robert A. Dalrymple,et al.  Modeling Water Waves in the Surf Zone with GPU-SPHysics , 2009 .

[19]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[20]  P. Cleary,et al.  Conduction Modelling Using Smoothed Particle Hydrodynamics , 1999 .

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

[22]  G. Golub,et al.  Eigenvalue computation in the 20th century , 2000 .

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

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

[25]  Ted Belytschko,et al.  ON THE COMPLETENESS OF MESHFREE PARTICLE METHODS , 1998 .

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

[27]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[28]  Gary A. Dilts,et al.  Moving least‐squares particle hydrodynamics II: conservation and boundaries , 2000 .

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