Application of 3D Smoothed Particle Hydrodynamics to a shock tube flow: Effects and control of particle distribution

The effects of the initial particle distribution in Smoothed Particle Hydrodynamics (SPH) are explored for standard and non-standard formulations. A Sod shock tube calculation is performed in three dimensions as a means of evaluating the effects of regular, non-aligned, and randomized initial distributions of particles. Results from the classical formulation of SPH are compared to similar trials using a formulation that has been corrected for linear consistency, as well as a method that employs an adaptive particle distribution. When the initial particle distribution is not aligned with the direction of the shock wave, or if particles are not uniformly spaced, the classical formulation of SPH yields significant error. The integrity of the solution is restored by corrected methods, which show similar results regardless of initial distribution. The three-dimensional shock calculations are further improved with adaptive particle insertion and removal during the course of the simulation.