对流扩散方程GLxF格式数值解振荡的可控性

The Controllability of Oscillations in Numerical Solutions of GLxF Scheme for Convective-diffusion Equation

关键词:  对流扩散方程  GLxF格式  振荡  可控性  Fourier分析

Key words:  convective-diffusion equation  GLxF scheme  oscillations  controllability  Fourier analysis

摘要:

提出对流扩散方程u_t+au_x=εu_xx,a∈R,ε>0的广义Lax-Friedrichs格式(GLxF),并给出GLxF格式的稳定与收敛条件.然后通过数值仿真说明GLxF格式数值解存在振荡,并根据仿真结果提出振荡可控的3个猜测.最后用Fourier分析方法证明了GLxF格式数值解振荡的可控性.

Abstract:

GLxF scheme of convective-diffusion equation u_t+au_x=εu_xx, a∈R, ε>0, is proposed, and its stability and convergence conditions is presented.Then the behavior of numerical solution of GLxF scheme is simulated.The results show that there are oscitlations, of which three guesses of controllability are proposed.Finally, Fourier analysis is used to prove that the oscillations of numerical solution are controllable.