Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.