Commun. Comput. Phys., 14 (2013), pp. 1287-1303.


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

Rongpei Zhang 1*, Xijun Yu 2, Jiang Zhu 3, Abimael F. D. Loula 3, Xia Cui 2

1 School of Sciences, Liaoning ShiHua University, Fushun 113001, China.
2 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China.
3 Laboratorio Nacional de Computacao Cientifica, MCTI, Avenida Getulio Vargas 333, 25651-075 Petropolis, RJ, Brazil.

Received 19 June 2012; Accepted (in revised version) 1 March 2013
Available online 13 June 2013
doi:10.4208/cicp.190612.010313a

Abstract

Weighted 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.

AMS subject classifications: 35R05, 35Q79, 65M60, 80A20

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Key words: Discontinuous Galerkin, weighted interior penalty, semi-implicit integration factor, non-equilibrium radiation diffusion.

*Corresponding author.
Email: rpzhang@lncc.br (R. Zhang), yuxj@iapcm.ac.cn (X. Yu), jiang@lncc.br (J. Zhu), aloc@lncc.br (A. Loula), cui_xia@iapcm.ac.cn (X. Cui)
 

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