A NEWTON-RAPHSON APPROACH FOR NONLINEAR DIFFUSION-EQUATIONS IN RADIATION HYDRODYNAMICS

Numerical solutions of radiative transfer problems via a flux-limited diffusion equation coupled with the material energy balance equation are in general characterized by a standard explicit treatment of all the nonlinearities. An increase in accuracy has been recently obtained by analyzing the rate of convergence of a fully implicit treatment. In this paper a complete Newton-Raphson linearization algorithm at each time step is investigated. Numerical results are presented for radiation penetration into a cold slab driven by a constant incident surface intensity.