基于Hopf-Cole变换的二维Burgers方程的新数值解法

A New Numerical Method Based on Hopf-cole Transformation for Two Dimensional Burgers Equation

讨论了二维Burgers方程初边值问题的数值解法.新的方法是基于二维Hopf-Cole变换,将Bur-gers方程的初边值问题相应的变为热传导方程的初边值问题,用修正局部Crank-Nicolson法进行求解,得到了较好的结果,然后再进行逆变换得出原Burgers方程的解.同时也给出了稳定性、相容性及收敛性的理论证明.数值实验结果表明了该方法的正确性和格式的有效性。

In this paper,we discuss a numerical method of two dimensional Burgers equation for the initial- boundary value problem. Based on the two-dimensional Hopf-Cole transformation, the new method transforms in- itial-boundary value problem of Burgers equation to initial-boundary value problem of heat equation by using Hopf-Cole transformation. We use Modified Local Crank-Nicolson Method for heat equation, and obtain a better solution for Burgers equation in inverse transform method. And we give a corresponding theoretical proof for sta- bility, consistence and convergence. The numerical experiment shows the theoretical accuracy and computational effectiveness of proposed method.