On the Stability of the Discontinuous Particle Method for the Transfer Equation

Abstract

The nonlinear transfer of mass, momentum, and energy is the main peculiarity of gas dynamics. A discontinuous particle method is proposed for its efficient numerical modeling. The method is described in detail in application to linear and nonlinear transfer processes. The necessary and sufficient monotonicity and stability condition of the discontinuous particle method for the regularized Hopf equation is obtained. On the simplest example of a discontinuous solution, the method’s advantages, which include the discontinuity widening over only one particle and the selfadaptation of the space resolution to the solution’s peculiarities, are shown.