A meshless approach for solution of Burgers' equation

被引:28
作者
Hashemian, Alireza [1 ]
Shodja, Hossein M. [1 ]
机构
[1] Sharif Univ Technol, Ctr Excellence Struct & Earthquake Engn, Dept Civil Engn, Tehran, Iran
关键词
Burgers' equation; gradient reproducing kernel particle method; steep gradient; meshless;
D O I
10.1016/j.cam.2007.08.014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities. comparison with the results obtained using other numerical schemes in the literature further attests the desirable features of the presented methodology. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:226 / 239
页数:14
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