Analysis of some modifications of the large-particle method to model wave dynamics problems

We perform a numerical analysis of various modifications of the large-particle method applied to problems of wave dynamics (gas dynamics). We use modifications of the large-particle method to solve the problems on calculation of the decay of an arbitrary discontinuity, propagation of shock waves and propagation of rarefaction waves. Calculations of the propagation of stationary shock waves show that all considered modifications of the large-particle method allow to calculate correctly a pressure behind the shock wave, despite the fact that a width of the shock transition zone and a profile of the shock wave pressure in the zone depend on the modification of the large-particle method. During solving the problem on the decay of an arbitrary discontinuity, we show that the solution obtained by modified large-particle method with recalculation of pressure at the Euler stage best coincides with the analytical solution to the problem, both in the region of the shock wave and in the rarefaction wave region. A significant advantage of this modification is the fact that the considered problems can be solved without introducing the "artificial" viscosity into the laws of conservation.