求解一维对流扩散反应方程的高阶紧致格式  

A High-order Compact Difference Scheme for Solving 1D Convection-Diffusion-Reaction Equation

作　　者：赵秉新[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《重庆理工大学学报（自然科学）》2012年第7期100-104,共5页Journal of Chongqing University of Technology：Natural Science

基　　金：宁夏自然科学基金资助项目(NZ0938);2011宁夏高校科研基金资助项目

摘　　要：通过指数变换将原方程变换为对流扩散方程,对变换后方程中的对流项和扩散项分别采用高阶迎风紧致格式和对称紧致格式进行离散,在时间上采用四阶龙格库塔方法进行推进,从而得到了一种具有O(h4+τ4)阶收敛精度求解非定常对流扩散反应问题的紧致格式。通过数值算例并与已有格式的结果进行对比,验证了格式具有良好性能。A fourth-order compact upwind finite difference scheme was proposed for solving 1 D unsteady convection-diffusion-reaction equation. By using an exponential function, the convection-diffu-sion-reaction equation was rewritten in the form of the convection-diffusion equation. Convection terms and diffusion terms were discretized by fourth-order compact upwind schemes and fourth-order compact symmetric schemes, respectively. Then, the spatial semi-discretized equation was solved by fourth-order Runge-Kutta formula in time. The truncation error of the present scheme is O（h^4＋τ^4）.Its excellent properties are proved by numerical examples in comparison with literature results.

关 键 词：高精度 对流扩散反应方程 有限差分方法 非定常 

分 类 号：O241.82[理学—计算数学]