A grey transport acceleration method for time-dependent radiative transfer problems

Abstract

A new iterative method for solving the time-dependent multifrequency radiative transfer equations is described. The method is applicable to semi-implicit time discretizations that generate a linear steady-state multifrequency transport problem with pseudo-scattering within each time step. The standard “lambda” iteration method is shown to often converge slowly for such problems, and the new grey transport acceleration (GTA) method; based on accelerating the lambda method by employing a grey, or frequency-independent transport equation, is developed. The GTA method is shown, theoretically by an iterative Fourier analysis, and experimentally by numerical calculations, to converge significantly faster than the lambda method. In addition, the GTA method is conceptually simple to implement for general differencing schemes, on either Eulerian or Lagrangian meshes.