Discretisation and solution of quasi-diffusion equations

Abstract

We show how the Quasi-diffusion method performs on radiative transfer problems in slab geometry and XY geometry for steady state, one-energy-group problems. We explain first how we derive for slab geometry, the discretization we use for the transport sweep. Then we show how we derive Gol'din's finite-volume and a Mixed Finite Element discretization for the low-order problem. Then we explain how we derive the transport discretization and Gol'din's finite-volume discretization of the low-order problem for XY geometry. The discretization of the low-order problem leads to a large sparse linear non-symmetric system of equations. We then explain about the iterative methods that we use to solve efficiently this set of discrete equations. Finally, we discuss accuracy and efficiency of this discretized Quasi-diffusion method for various kinds of problems. Those problems include typical radiative transfer problems containing optically-thick, highly-scattering regions as well as boundary layers.