Discontinuous Particle Method on Gas Dynamic Examples

Abstract

The paper is devoted to studying the features of the discontinuous particle method. The algorithmic fundamentals of the particle method are described in detail. The possibility of using limiters is investigated. The results of the calculations for the Hopf, Burgers, shallow water, and gas dynamics’ equations, including nonlinear acoustics, are presented. The numerical solutions are compared with some exact ones. The tests show that the method is suited for problems with discontinuities. It is shown that in order to obtain a more accurate numerical solution, it is necessary to refine the initial mathematical models. In other words, for the problem of the structure of the front of the shock wave if we take the equations of stochastic gas dynamics instead of the Navier-Stokes equations, then the need for limiters disappears.