求解Burgers方程的两层隐式紧致差分格式  

TWO-LEVEL IMPLICIT COMPACT DIFFERENCE SCHEME FOR THE BURGERS EQUATION

作　　者：杨晓佳 魏剑英 葛永斌 

机构地区：[1]宁夏大学数学统计学院,银川750021

出　　处：《高等学校计算数学学报》2017年第4期340-354,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(11361045;11772165);宁夏高等学校科学技术研究项目(NGY201502

摘　　要：Burgers方程是流体力学中扩散波最简单的非线性模型方程，它出现在许多物理问题当中，包括气体动力学问题、交通流问题和流体力学问题等．同时Burgers方程也可以作为流体动力学Navier—Stokes方程的简化模型方程．近年来，求解一维Burgers方程的计算方法受到科研工作者的广泛关注，有关的文献报道已有很多，如文献[1-5]．Based on the fourth-order compact difference scheme of the spatial derivative and the error remainder correction method of the temporal derivative, a new two-level implicit compact finite difference scheme is proposed for solving the one-and two-dimen^ional Burgers equation. The local truncation error of the scheme is O（τ-2 ＋ τh2 ＋ h4）, i.e., the scheme is the fourth order accuracy in the space when τ - O（h2） and is second order accuracy in the time. Then, numerical experiments are conducted to verify the accuracy and the reliability of the present scheme.

关 键 词：BURGERS方程 紧致差分格式 求解 STOKES方程 动力学问题 隐式 模型方程 流体力学 

分 类 号：O241.82[理学—计算数学]