On a stability of discontinuous particle method for transfer equation

Nonlinear transfer of mass, momentum and energy is the main pecularity of gas dynamics. A «discontinuous» particle method is proposed for its efficient numerical modeling. The method is discribed in details in application to linear and nonlinear transfer processes. Necessary and sufficient monotonicity and stability condition of discontinuous particle method for regularized Hopf equation is obtained. At a simplest example of discontinuous solution, the method advantages, which include a discontinuty widening over only one particle, self adaptation of space resolution to solution pecularities, are shown.