Commun. Comput. Phys., 10 (2011), pp. 844-866.


Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem

Jingyan Yue 1, Guangwei Yuan 1*

1 National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China.

Received 31 January 2010; Accepted (in revised version) 16 October 2010
Available online 13 June 2011
doi:10.4208/cicp.310110.161010a

Abstract

For a new nonlinear iterative method named as Picard-Newton (P-N) iterative method for the solution of the time-dependent reaction-diffusion systems, which arise in non-equilibrium radiation diffusion applications, two time step control methods are investigated and a study of temporal accuracy of a first order time integration is presented. The non-equilibrium radiation diffusion problems with flux limiter are considered, which appends pesky complexity and nonlinearity to the diffusion coefficient. Numerical results are presented to demonstrate that compared with Picard method, for a desired accuracy, significant increase in solution efficiency can be obtained by Picard-Newton method with the suitable time step size selection.

AMS subject classifications: 65M06, 65M08, 65M12

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Key words: Non-equilibrium radiation diffusion, Picard, Picard-Newton based on linearization-discretization, nonlinear iterative method, time step control.

*Corresponding author.
Email: yue_jingyan@iapcm.ac.cn (J. Yue), yuan_guangwei@iapcm.ac.cn (G. Yuan)
 

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