New physics-based preconditioning of implicit methods for non-equilibrium radiation diffusion

2003 ◽  
Vol 190 (1) ◽  
pp. 42-51 ◽  
Author(s):  
V.A. Mousseau ◽  
D.A. Knoll
Keyword(s):  
New Physics ◽  
Implicit Methods ◽  
Radiation Diffusion ◽  
Equilibrium Radiation ◽  
Non Equilibrium

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

2011 ◽  
Vol 10 (4) ◽  
pp. 844-866 ◽  
Author(s):  
Jingyan Yue ◽  
Guangwei Yuan
Keyword(s):  
Iterative Method ◽  
Time Integration ◽  
Step Size ◽  
Time Step ◽  
Radiation Diffusion ◽  
Reaction Diffusion Systems ◽  
Time Step Size ◽  
Step Control ◽  
Equilibrium Radiation ◽  
Non Equilibrium

AbstractFor 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.

Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

2013 ◽  
Vol 14 (5) ◽  
pp. 1287-1303 ◽  
Author(s):  
Rongpei Zhang ◽  
Xijun Yu ◽  
Jiang Zhu ◽  
Abimael F. D. Loula ◽  
Xia Cui
Keyword(s):  
Diffusion Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Implicit Integration ◽  
Interior Penalty ◽  
Radiation Diffusion ◽  
Factor Method ◽  
Equilibrium Radiation ◽  
Non Equilibrium

AbstractWeighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh. There are three weights including the arithmetic, the harmonic, and the geometric weight in the weighted discontinuous Galerkin scheme. For the time discretization, we treat the nonlinear diffusion coefficients explicitly, and apply the semi-implicit integration factor method to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization. The semi-implicit integration factor method can not only avoid severe timestep limits, but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method. Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.

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