Efficient solution of multi-dimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization

Many algorithms for the second-order time evolution of the coupled radiation diffusion and material conduction equations have been published. Most of them are cumbersome to implement and much slower computationally than their first-order equivalent algorithms. This paper presents a simpler approach that is both computationally efficient and easy to implement. Second-order behavior can be achieved even when the iteration at each time step is incompletely converged. The test problem uses multiple materials and nonlinear heat capacities. Unexpectedly, details in the discretization of the gradient in the flux limiter significantly affect the spatial and temporal convergence of the solution.