数值求解对流扩散方程的特征有限分析方法

本文在详细分析了对流扩散过程物理特性的基础上,按对流扩散过程的物理要求应用特征方法处理对流项、以能充分描述扩散效应的有限分析方法处理扩散项,建立了一种合乎对流扩散物理要求的、无条件L_∞稳定的、数值模拟对流扩散物理现象的特征有限分析方法;并就非线性情况证明了特征有限分析方法的收敛性、给出了解的误差估计。最后的数值实验表明它能很好地模拟对流扩散过程,数值粘性小,精度高,稳定性好,并且没有伪振荡现象发生。

THE CHARACTERISTIC FINITE ANALYTIC METHOD FOR THE NUMERICAL SOLUTION OF CONVECTIVE DIFFUSION EQUATION

A characteristic finite analytic method is proposed to obtain the numeri cal solution of convective diffusion eguation. The scheme formed is unconditionally L_∞ stable and in accordance with the convective diffusion phenomenon in physics.In this paper the existence and uniqueness of the scheme is proved and the error estimate of the numerical solution for the linear and non-linear equation is given. The numevical experiment shows that the present method has the ability to simulate the convective diffusion equation with high order accuracy, Irttle numerical dissipation, perfect stability and without any parasitic osillation.