Gc. Pomraning et Ak. Prinja, ADVECTION-DIFFUSION AS AN ASYMPTOTIC LIMIT FOR TRANSPORT IN ANISOTROPIC MEDIA, Annals of nuclear energy, 22(3-4), 1995, pp. 159-180
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.