Asymptotic-Preserving \& Well-Balanced schemes for radiative transfer and the Rosseland approximation

We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow theWell-Balanced approach's canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type Dt <= O(Dx^2) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.