Monte Carlo functional expansion calculation of free molecular flows

Abstract:

A Monte Carlo technique for Knudsen flow, light transmission in tubes, the flow of cold neutrons, phonon transmission, heat transfer calculations and other problems involving free streaming in cylindrical enclosures is described. The coefficients of a functional expansion of the view factors are estimated by Monte Carlo, are then perturbed in a least squares minimum sense to satisfy some consistency conditions, and finally are used to calculate the collision density on the boundary and the transmission of the enclosure. Without importance sampling or other variance reduction techniques, the calculational work required for a given accuracy is reduced by a factor frequently near 10 when compared to a simple calculation in which particles are followed from entrance to exit.