TABLE OF CONTENTS / Summary and Motivation / Evolution Equations / Interpolation / Alternative Interpolations / Weight Functions / SPAM Continuity Equation with ? u / Spatial Derivatives ( ? ?, ? P , ? Q) / SPAM Equation of Motion and Energy Equation / Rezoning, Effect of Particle Size / Ideal Gas Isomorphism / Alternative Spatial Derivatives ( ? u , ? T) / Artificial Viscosity /
/ 8 Figures /
Example Problems :
[ Adiabatic Atmosphere, Isothermal Atmosphere ]
The notion of "smooth particles" allows us to solve continuum problems by following the motion of representative particles. In this approach, just as in the finite-element and finite-difference methods, the partial differential field equations of continuum mechanics become a finite set of ordinary differential equations, here for the evolution of particles' positions and energies. SPAM (Smooth Particle Applied Mechanics) encompasses a set of techniques each with a corresponding computer algorithm which are specially useful in simulating complex mechanical deformations of fluids and solids. Smooth particles are not "tracer" particles, or the particles used in "particle-in-cell" methods. Although their mechanics resembles point-particle mechanics, SPAM particles are also not the usual mass points. Instead the SPAM particles can best be thought of as moving clumps or distributions of material, characterized by stresses, strains, heat fluxes, temperature and velocity gradients, and internal energies, as well as by the usual coordinates and velocities of ordinary particle mechanics.
In this Chapter we describe the smooth-particle...
