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 kernel depends separately upon the incident and exiting directions rather than simply upon the scattering angle. In this paper we demonstrate that an advection-diffusion equation is an asymptotic limit for one particular 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 obtaining the time-dependent advection-diffusion equation in full three-dimensional generality, we derive the asymptotically consistent initial and boundary conditions to be applied to this equation