一维非定常对流扩散方程的高阶组合紧致迎风格式  

A HIGHT-ORDER COMBINED COMPACT UPWIND DIFFERENCE SCHEME FOR SOLVING 1D UNSTEADY CONVECTION-DIFFUSION EQUATION

作　　者：赵秉新[1,2] 

机构地区：[1]复旦大学力学与工程科学系,上海200433 [2]宁夏大学数学计算机学院,银川750021

出　　处：《数值计算与计算机应用》2012年第2期138-148,共11页Journal on Numerical Methods and Computer Applications

基　　金：宁夏自然科学基金资助项目(NZ0938)

摘　　要：通过将对流项采用四五阶组合迎风紧致格式离散,扩散项采用四阶对称紧致格式离散之后,对得到的半离散格式在时间方向采用四阶龙格库塔方法求解,从而得到了一种求解非定常对流扩散方程问题的高精度组合紧致有限差分格式,其收敛阶为O(h^4+τ~4).经Fourier精度分析和数值验证,证实了格式的良好性能.三个数值算例包括线性常系数问题,矩形波问题和非线性问题,数值结果表明:该格式具有很高的分辨率,且适用于对高雷诺数问题的数值模拟.A fourth-order combined compact upwind （CCU） finite difference scheme was proposed for solving 1D unsteady convection-diffusion equation. Convection terms were discretized by combined fourth-order and fifth-order compact upwind schemes. Viscous terms were dis- cretized by fourth-order compact symmetric finite difference scheme. After that, the semi- discretized equation was solved by fourth-order Runge-Kutta formula in time. The truncation error of the CCU scheme is O（h4＋τ4） . Its excellent properties are proved by Fourier anal- yses and three numerical examples, which include linear and nonlinear convection-diffusion equations and rectangular wave problem. The results show that the CCU scheme is capable of capturing the minute physical changes for its high resolution, and is applicable to high Reynolds number problems.

关 键 词：高精度 有限差分 非线性 对流扩散方程 

分 类 号：O241.82[理学—计算数学]