Picard-Newton Iterative Method for Multimaterial Nonequilibrium Radiation Diffusion Problem on Distorted Quadrilateral Meshes

A new nonlinear iterative method for nonlinear parabolic equation is developed and applied to a multimaterial nonequilibrium radiation diffusion problem on distorted meshes. The new iterative method is named by Picard-Newton method (PN for short). Solution process of the method is as follows. First, by linearizing the time-discretized nonlinear partial differential equation(PDE), we can get an iterative sequence of linear PDE. Then, we design the spatial discretization of the linear PDE, and educe a system of linear algebraic equations. Finally, solve the linear problem by Krylov-subspace methods. The main part of the method is consistent with Picard iterative method, and we can get P-N schemes by adding Newton correction terms to Picard scheme. The efficiencies of Picard method and Picard-Newton method are compared and the good performance of P-N method is demonstrated.