间断有限元方法求解一维非平衡辐射扩散方程  

Discontinuous Finite Element Method for 1D Non-equilibrium Radiation Diffusion Equations

作　　者：张荣培[1,2] 蔚喜军[3] 崔霞[3] 冯涛[2] 

机构地区：[1]辽宁石油化工大学理学院,抚顺113001 [2]中国工程物理研究院研究生部,北京100088 [3]北京应用物理与计算数学研究所计算物理实验室,北京100088

出　　处：《计算物理》2012年第5期641-646,共6页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11171038,11261035)资助项目

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.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.

关 键 词：非平衡辐射扩散方程 间断有限元 间断系数 

分 类 号：O241.82[理学—计算数学]