ADVECTION-DIFFUSION AS AN ASYMPTOTIC LIMIT FOR TRANSPORT IN ANISOTROPIC MEDIA

In describing particle transport in anisotropic media, the total cross section depends upon the particle direction, and the scattering kerne l depends separately upon the incident and exiting directions rather t han simply upon the scattering angle. In this paper we demonstrate tha t an advection-diffusion equation is an asymptotic limit for one parti cular class of such one-speed transport equations describing particle transport in anisotropic media. This class is that considered earlier in this journal by Cassell and Williams (1992). In addition to obtaini ng the time-dependent advection-diffusion equation in full three-dimen sional generality, we derive the asymptotically consistent initial and boundary conditions to be applied to this equation.