ASYMPTOTICALLY CONSISTENT REFLECTION BOUNDARY-CONDITIONS FOR DIFFUSION-THEORY

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.