An Artificial Boundary Method for Burgers’ Equation inthe Unbounded Domain
An Artificial Boundary Method for Burgers’ Equation inthe Unbounded Domain
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DOI：
10.3970/cmes.2014.100.445
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发表时间：
2014-08
影响因子：
2.4
通讯作者：
Q. Zheng;Lei Fan;Xuezheng Li
中科院分区：
文献类型：
--
作者：
Q. Zheng;Lei Fan;Xuezheng Li
本文利用人工边界条件构造了无界区域上一维Burgers方程的一种数值方法。通过Hopf-Cole变换将原问题转化为无界区域上的热传导方程，利用两个人工积分边界条件将后者转化为一个有界计算区域上的等价问题，对后者利用降阶方法建立了一个带离散人工边界条件的有限差分方法，从而得到Burgers方程的数值解。证明了该方法在计算域上解Burgers方程时是唯一可解的、无条件稳定的、空间上2阶收敛、时间上3/2阶收敛。
In this paper, we construct a numerical method for one-dimensional Burgers’ equation in the unbounded domain by using artificial boundary conditions. The original problem is converted by Hopf-Cole transformation to the heat equation in the unbounded domain, the latter is reduced to an equivalent problem in a bounded computational domain by using two artificial integral boundary conditions, a finite difference method with discrete artificial boundary conditions is established by using the method of reduction of order for the last problem, and thereupon the numerical solution of Burgers’ equation is obtained. This artificial boundary method is proved and verified to be uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time for solving Burgers’ equation on the computational domain.