Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration

We present a solution method for fully implicit radiation diffusion problems discretized on meshes having millions of spatial zones. This solution method makes use of high order in time integration techniques, inexact Newton–Krylov nonlinear solvers, and multigrid preconditioners. We explore the advantages and disadvantages of high order time integration methods for the fully implicit formulation on both two- and three-dimensional problems with tabulated opacities and highly nonlinear fusion source terms.