Classical kinetic theory simulations using smoothed particle hydrodynamics

The technique of smoothed particle hydrodynamics (SPH) is used to simulate a variety of three-dimensional systems comprised of elastic spheres contained in a box with perfectly reflecting walls. Particle interactions are determined solely by the conservative SPH body forces, from which the potential energy function is derived. This function is followed to monitor the conservation of the total energy as various initial nonequilibrium velocity distributions are quickly randomized by particle collisions. The resulting equilibrium speed and velocity distributions are found to agree with those predicted by kinetic theory. The algorithm conserves the total energy to within 0.02%. The pressure exerted on the box walls and the mean free path between collisions are comparable with those expected for a system of rigid particles. The problem of two isolated systems that are allowed to mix after an impenetrable partition is removed is also simulated with acceptable results. Finally, the equilibrium spatial distribution of the particles is considered and a semiemperical relationship derived for this multiply anticorrelated distribution. © 1996 The American Physical Society.