Department of Mathematics

University of Houston

Abstract

The gray approximation for thermal non-equilibrium radiation
diffusion problems yields a time dependent non-linear system
of equations coupling the radiation energy and the material
temperature. A flux-limiting term is added to the diffusion
coefficient for the radiation energy. Implicit time stepping
schemes lead to the solution of non-linear systems of equations.

A Newton-Krylov-method is employed in the solution of arising
non-linear problems. For GMRES iterations, we study
preconditioners based on multigrids methods. The first
approach is to apply a geometric multigrid method directly
to the coupled linearized problems. Another approach is to
construct an operator splitting which treats the transport
phenomenon and the equilibration coupling in separate substeps.
A similar approach was proposed by Mousseau, Knoll and Rider,
2000.

We demonstrate the effectiveness of the proposed approaches
by solving one-dimensional and two-dimensional model problems.