隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

Implicit-explicit Integration Factor Discontinuous Galerkin Method for 2D Radiation Diffusion Equations

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.

A numerical method is developed for two-dimensional nonequilibrium radiation diffusion equations. Discontinuous Galerkin method is applied in spatial diseretization in which numerical flux is constructed with weighted flux averages. Implicit-explicit integration factor method for time discretization is applied to nonlinear ordinary differential equations which is obtained with discontinuous Galerkin method. Radiation diffusion equations with multiple materials are solved on unstructured grids in numerical tests. It demonstrates that the method is effective for high nonlinear and tightly coupled radiation diffusion equations.