A family of flux-limited diffusion theories

We present a family of diffusion approximations to the equation of radiative transfer, parameterized functionally by a function χ(ω, R). Here ω is the effective (treating emission as scattering) single scatter albedo, and R is roughly speaking the magnitude of the dimensionless spatial gradient of the energy density. For any member of this family, i.e., for any function χ, this diffusion theory is flux-limited, properly predicts a single asymptotic mode in a sourcefree homogeneous medium, and gives the correct weak gradient limit. If the choice χ ≡ 1 is made, this family reduces to the flux-limited diffusion theory proposed earlier by Levermore and Pomraning. We suggest a function χ that depends only upon the single variable ω. Simple test problems indicate that this choice leads to improved accuracy over both classic and the earlier flux-limited diffusion theory. This choice also allows the radiative flux and energy density gradient to have independent directions, and this may result in increased accuracy in multidimensional problems.