华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (5): 10-16,5.

• 应用数学,统计学 • 上一篇    下一篇

磁流耦合问题中边界层解法的探索

侯磊1,2,韩月红1,李金龙1   

  1. 1.上海大学数学系,上海200444;2.上海高校计算科学,E-研究院上海交通大学研究所,上海200030
  • 收稿日期:2008-06-12 修回日期:2008-07-05 出版日期:2008-09-25 发布日期:2008-09-25
  • 通讯作者: 侯磊

Exploration of boundary layer solutions in magnetic-current coupling problems (Chinese)

HOU Lei1,2,HAN Yue-hong1,LI Jin-long1
  

  1. 1.Department of Mathematics,Shanghai University,Shanghai 200444,China; 2.Computational Sciences E-institute of Shanghai Universities at SJTU,Shanghai 200030,China
  • Received:2008-06-12 Revised:2008-07-05 Online:2008-09-25 Published:2008-09-25
  • Contact: HOU Lei

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摘要： 由磁场和受重力影响的流场扰动耦合而成的磁流体动力学方程(MHD)是一个非常复杂的非线性系统.而由MHD得到边界层里的二阶微分方程是一个复数形式线性方程. 求解过程中要求边界层内部解与外部解相匹配. 中心差分结合二阶R-K格式和中心差分结合四阶R-K格式两种方法提高了分析的速度, 保证算法的精度.结果表明了算法的有效性和合理性. 同时着重分析了重力参数G和匹配值KI对特征函数h的影响.

关键词: MHD方程, 特征函数, 边界层, MHD方程, 特征函数, 边界层

Abstract: The MHD equations are complicated non-linear systems.This paper obtained equations which are linear in the complex space from MHD.The procedure of solving the equations needs the matching of the "external" solution and the "internal" solution.Central difference with the second R-K and central difference with the fourth order R-K not only improve the speed of analysis,but also assure the algorithm’s precision.The results are effective and robust.The paper analyzed the effects of the parameters Gand KI on the eigen-functionh of differential equations.

Key words: eigen-function, boundary-layer, MHD, eigen-function, boundary-layer

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