Discontinuous particles method on gas dynamic examples

The paper is devoted to the study of the features of the discontinuous particle method. The algorithmic fundamentals of the particle method are described in detail. The possibility of using limiters was investigated. The results of calculations for the Hopf, Burgers, shallow water and gas dynamics equations, including nonlinear acoustics, are presented. Numerical solutions are compared with some exact ones. Tests show that the method is well 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. Namely, if for the problem of the structure of the front of the shock wave instead of the Navier–Stokes equations to take the equations of stochastic gas dynamics, then the need for limiters disappears.