Artificial boundary method for two-dimensional Burgers' equation
Artificial boundary method for two-dimensional Burgers' equation
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DOI：
10.1016/j.camwa.2007.11.047
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发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Xiaonan Wu;Jiwei Zhang
中科院分区：
文献类型：
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作者：
Xiaonan Wu;Jiwei Zhang
研究了无界区域上二维Burgers方程的数值解。通过引入圆形人工边界，研究了人工边界包围的圆盘上的初边值问题。基于Cole-Hopf变换和Fourier级数展开，得到了人工边界上的精确边界条件和一系列近似边界条件。然后将原问题转化为有界域上的等价问题。此外，还得到了约化问题的稳定性。最后，将有限差分法应用于约化问题，并通过数值算例验证了该方法的可行性和有效性。
The numerical solution of the two-dimensional Burgers equation in unbounded domains is considered. By introducing a circular artificial boundary, we consider the initial-boundary problem on the disc enclosed by the artificial boundary. Based on the Cole–Hopf transformation and Fourier series expansion, we obtain the exact boundary condition and a series of approximating boundary conditions on the artificial boundary. Then the original problem is reduced to an equivalent problem on the bounded domain. Furthermore, the stability of the reduced problem is obtained. Finally, the finite difference method is applied to the reduced problem, and some numerical examples are given to demonstrate the feasibility and effectiveness of the approach.