Principle of the Random Walk Method for Radiative Transfer Equations and Application. Pt. 2: Application to Fleck's Monte-Carlo Method

摘要

In this paper we shall use the Random Walk procedure to accelerate the tracking of the particles which have a large number of collision events. This method is based on the approximation of Fleck's transport equation by a diffusion equation using the multiple scale technique. The chapter is organized as follows: In Sec. I we derive the transfer equation satisfied by a Monte-Carlo particle and the corresponding diffusion equation, the explicit solution of which is known in a sphere. We calculate the probability of escaping from the sphere and the probability of remaining inside at the end of the time step in Sec. 2. We study some criteria for the validity of this approximation in Sec. 3, using Monte-Carlo calculations in the sphere. Numerical results are given in Sec. 4. (ERA citation 11:042227)