Simulations of Unsteady Compressible Fluid Motion by an Interactive Cored Particle Method

Abstract

A grid-free particle method is presented for the simulations of unsteady compressible fluid motion. The movements of the particles are determined by a system of ordinary differential equations which in turn is derived from the one-dimensional equations for compressible fluids, i.e., the linear wave equation, the Burgers equation, and the equation for a compressible fluid with and without a diffusion term. Our method successfully simulates the generation of the shock and expansion waves and the interaction of linear waves and that of nonlinear waves. Our numerical study also shows that the Gaussian-cored particles create “soliton” when it is used to simulate the inviscid Burgers equation.