一维无界域上Burgers方程的局部人工边界条件

摘要

针对无界域上的一维Burgers方程，首先运用Cole-Hopf函数变换，将非线性Burgers方程变换成线性的热传导方程；再通过P a dé逼近得到局部的人工边界条件；最后，对得到的非线性初边值问题进行有限差分离散。数值实验表明，提出的人工边界条件是恰当的，并且是有效的。%With respect to one-dimensional Burgers equation in unbounded domain, the nonlinear Burgers equation is firstly transformed into a linear heat equation by the Cole-Hopf function transformation, and then the artificial boundary conditions are obtained through Padé approximation, finally a finite difference discretization is applied for the obtained initial-boundary value problem. The numerical experiment shows that the proposed artificial boundary conditions are appropriate and effective.