对流扩散方程GLxF格式解的局部振荡  

Local Oscillations in Solutions of Glxf Scheme for Convective-Diffusion Equation

作　　者：杨继昌[1,2] 沈柳平[1] 

机构地区：[1]柳州师范高等专科学校数计系,广西柳州545004 [2]首都师范大学数学科学学院,北京100037

出　　处：《数学的实践与认识》2013年第18期210-222,共13页Mathematics in Practice and Theory

基　　金：973项目"流体力学与材料科学中的偏微分方程"(2006CB805902)

摘　　要：提出了对流扩散方程ut+aux=εuxx,a∈R,ε>0的GLxF格式,给出GLxF格式的稳定与收敛条件,并讨论了该格式与其它常用格式的关系.然后在稳定及收敛条件下,通过特殊的初始数据离散化数值图例说明了GLxF格式解的局部振荡,提出振荡可控的三个猜测.最后着重用傅里叶分析和修正方程分析两种方法研究了GLxF格式解的数值耗散和相对相位误差,指明由于高频波型的数值耗散无法抑制相位误差,从而使数值解产生振荡,并论证振荡与数值耗散、相对相位误差、数值衰减的相互关系,从理论上阐明了振荡的可控性.In this paper, we propose a GLxF schenie for a convective-diffusion equation ut＋aux=εuxx,α∈R,ε〉0, and discuss the stability, convergence and its relation with other commonly used schemes. For the discretization of some special initial data under stable conditions, local oscillations in numerical solutions are observed. Three strategies are presented about how to control those oscillations via some numerical examples. Finally, main focus is paid on investigating oscillations by the discrete Fourier analysis and the modified equation analysis, respectively. Pointing out that the numerical disspation of high frequency modes can＇t suppress phase error.So that bring about oscillations in numerical solutions.And demonstrating the interrelation among oscillations, numerical dissipations, numerical damping and relative phase errors.

关 键 词：对流扩散方程 GLxF格式 振荡 傅里叶分析 修正方程分析 

分 类 号：O241.82[理学—计算数学]