算子分裂法求解对流–扩散–反应方程

An Operator Splitting Scheme for Advection-Diffusion-Reaction Equation

采用一阶精度的Lie分裂求解对流–扩散–反应方程,在每个时间步内,对于要求解的两个方程,关于时间分别采用特征线和欧拉方法进行离散,空间采用P2元进行离散.这两个方程,一个沿着特征线为常微分方程,另一个为典型的抛物型方程.同时导出了适合分裂方程的中间边界条件,分析了其分裂误差.数值结果表明,所提方法能够有效的求解对流–扩散–反应方程.

The convection-diffusion-reaction equation is solved by virtue of the first order Lie splitting in this paper.At each time step,an ODE along characteristic and an parabolic equation need to be resolved after the methods of the characteristic and Euler discrete with respect to time.Intermediate boundary condition and splitting error are further conducted.The numerical result shows that the proposed method can be used to solve the convection-diffusion-reaction equation effectively.