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| 间断有限元方法求解一维非平衡辐射扩散方程 | |
| 引用本文： | 张荣培,蔚喜军,崔霞,冯涛.间断有限元方法求解一维非平衡辐射扩散方程[J].计算物理,2012,29(5):641-646. |
| 作者姓名： | 张荣培 蔚喜军 崔霞 冯涛 |
| 作者单位： | 1. 辽宁石油化工大学理学院,抚顺113001;中国工程物理研究院研究生部,北京100088 2. 北京应用物理与计算数学研究所计算物理实验室,北京,100088 3. 中国工程物理研究院研究生部,北京,100088 |
| 摘 要： | 研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形. |
| 关 键 词： | 非平衡辐射扩散方程 间断有限元 间断系数 |
Discontinuous Finite Element Method for 1D Non-equilibrium Radiation Diffusion Equations |
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| ZHANG Rongpei , YU Xijun , CUI Xia , FENG Tao.Discontinuous Finite Element Method for 1D Non-equilibrium Radiation Diffusion Equations[J].Chinese Journal of Computational Physics,2012,29(5):641-646. | |
| Authors: | ZHANG Rongpei YU Xijun CUI Xia FENG Tao |
| Institution: | 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.Graduate School,China Academy of Engineering Physics,Beijing 100088,China) |
| Abstract: | We discuss numerical simulation of one-dimensional non-equilibrium radiation diffusion equations.A weighted numerical flux between adjacent grid cells is obtained by solving heat conduction equation with discontinuous coefficient.With this numerical flux of diffusive generalized Riemann problem(dGRP),a discontinuous finite element method is proposed for radiation diffusion equations.A backward Euler time discretization is applied for semi-discrete form and a Picard iteration is used to solve nonlinear system of equations.Numerical results demonstrate that the method has a capability of capturing strong gradients and can be accommodated to discontinuous diffusion coefficient. |
| Keywords: | non-equilibrium radiation diffusion equation discontinuous finite element method discontinuous coefficient |
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