The infuence of numerical diffusion on the solution of the radiative transfer equations

Abstract : We investigate the explicit numerical solution strategies of multi-dimensional radiative transfer equations which are commonly used, e.g., to determine the radiation emerging from astrophysical objects surrounded by absorbing and scattering matter. For explicit grid solvers, we identify numerical di usion as a severe source of error in ÿrst-order discretization schemes, underestimated in former work about radiative transfer. Using the simple example of a beam propagating through vacuum, we illustrate the in uence of the di usion on the solution and discuss various techniques to reduce it. In view of the large required storage for implicit solvers, we propose to use second-order explicit grid techniques to solve 3D radiative transfer problems. ?