On development of continuous time Monte Carlo methods for problems of Boltzmann equation with external forces

We consider Continuous time Monte Carlo (CTMC) methods [Khisamutidinov, A. I. (1988) Simulation statistical modeling of the kinetic equation of rarefied gases. Dokl. Akad. Nauk SSSR 302:75-79], based on some special Markov jump processes, and inhomogeneous smoothed Boltzmann equation with external forces. In the first place, the corresponding changes are brought into definitions of these methods to correct their applications to the problems with external forces. Secondly, we revise and refine a generalized fictitious collisions technique and a rejection one for simulation of scatterings. Third, a non-stationary problem on plane Poiseuille flow is solved by employing one of the modified methods.