Smooth Particle methods

Smooth Particle Applied Mechanics [SPAM] and Smooth 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 Lucy and Monaghan 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 microscopic to astophysical, and can obey any chosen constitutive equation. The main disadvantages (or research opportunities!) are the difficulties in treating sharp surfaces or interfaces with discrete particles and in avoiding the instabilities that can result for materials under tension, For a recent text see Wm. G. Hoover's "Smooth Particle Applied Mechanics -- The State of the Art" (World Scientific, Singapore, 2006).