Smooth Particle methods

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Smooth Particle Applied Mechanics (SPAM) and Smoothed Particle Hydrodynamics (SPH) are numerical methods for solving the equations of continuum mechanics (the continuity equation, the equation of motion, and the energy equation) with particles. This approach was originated by independently by Lucy [1] and by Gingold and Monaghan [2] in 1977 for astrophysical applications, and has since been applied to many challenging problems in fluid and solid mechanics. The main advantage of smooth-particle methods is that the partial differential equations (continuity, motion, energy) are replaced by ordinary differential equations (like molecular dynamics) describing the motion of particles. The particles can be of any size, from the microscopic to the astrophysical, and can obey any chosen constitutive equation. The main disadvantages are the difficulties in treating sharp surfaces or interfaces with discrete particles and in avoiding the instabilities that can result for materials under tension.

Some works have been able to link this technique and DPD, thus creating the "SDPD method" [3]. Other approach is to establish the volume of a particle as the volume of its Voronoi_cell.


  1. L. B. Lucy "A numerical approach to the testing of the fission hypothesis", Astronomical Journal 82 pp. 1013-1024 (1977)
  2. R. A. Gingold and J. J. Monaghan "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society 181 pp. 375–389 (1977)
  3. Pep Español and Mariano Revenga "Smoothed dissipative particle dynamics", Physical Review E 67 p. 026705 (2003)

Related reading

  • William Graham Hoover "Smooth Particle Applied Mechanics -The State of the Art", Advanced Series in Nonlinear Dynamics 25 World Scientific Publishing (2006) ISBN 978-981-270-002-5