A New Asymptotic Diffusion Theory

The variational formalism is used to derive from the monoenergetic Boltzmann equation a diffusion theory with the asymptotic transport diffusion coefficient. By considering an interface between two media as the limiting case of a medium with continuously varying properties, the boundary conditions are found to be continuity of current and a specified discontinuity in the scalar flux. The variational formalism gives the linear extrapolation distance for a pure scatterer accurate to within one-half percent. Numerical comparisons with classical (P-1) diffusion theory for a cell calculation indicate that the variational diffusion theory is significantly more accurate; the accuracy appears to be comparable with that of the P-3 method.