Volume 10, Issue 4
Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-equilibrium Radiation Diffusion Problem

Jingyan Yue & Guangwei Yuan

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

Published online: 2011-10

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  • 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 coef- ficient. 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.

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@Article{CiCP-10-844, author = {Jingyan Yue and Guangwei Yuan}, title = {Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-equilibrium Radiation Diffusion Problem}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {4}, pages = {844--866}, 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 coef- ficient. 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.310110.161010a}, url = {http://global-sci.org/intro/article_detail/cicp/7464.html} }
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