Gc. Pomraning et Bd. Ganapol, ASYMPTOTICALLY CONSISTENT REFLECTION BOUNDARY-CONDITIONS FOR DIFFUSION-THEORY, Annals of nuclear energy, 22(12), 1995, pp. 787-817
It is well known that the classic diffusion equation is an asymptotic
limit of the one-speed linear transport equation. In this paper, we ca
rry out the analysis required to obtain an asymptotically consistent b
oundary condition for this diffusion equation in the case of partial s
urface reflection. The specification of this boundary condition requir
es the transport theory solution to a purely scattering halfspace prob
lem. A variational treatment is used to obtain explicit results for th
is halfspace problem in the general case. In the special case of purel
y diffuse reflection, simple considerations give exact halfspace resul
ts, and a more involved exact halfspace analysis is presented in the c
ase of specular reflection. These exact results are used to assess the
accuracy of the variational treatment.