Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem (Communications in Computational Physics, 2011)
For a new nonlinear iterative method named as Picard-Newton (P-N) iterativemethod for the solution of the time-dependent reaction-diffusion systems, whicharise in non-equilibrium radiation diffusion applications, two time step control methodsare investigated and a study of temporal accuracy of a first order time integrationis presented. The non-equilibrium radiation diffusion problems with flux limiter areconsidered, which appends pesky complexity and nonlinearity to the diffusion coefficient. Numerical results are presented to demonstrate that compared with Picardmethod, for a desired accuracy, significant increase in solution efficiency can be obtainedby Picard-Newton method with the suitable time step size selection.