Modification of the large-particle method to solve shock waves and rarefaction waves propagation

In this article, we present a modification of the large-particle method. We perform a numerical analysis of various modifications of the large-particle method applied to problems of wave dynamics (gas dynamics). We solve the problems on calculation of the decay of an arbitrary discontinuity, as well as the problems on propagation of stationary shock waves with reflection from a solid wall. Calculations show that the solution obtained by the modified large-particle method best coincides with the analytical solution to the shock wave reflection problem from a solid wall. The numerical analysis shows that this modification allows to carry out stable flow calculations with large parameter gradients. A significant advantage of this modification is the fact that the considered problems can be solved without introducing the \textquotedblleft artificial" viscosity into the laws of conservation, and with large Courant numbers.