基于无网格局部Petrov-Galerkin(MLPG)法求解任意磁场方向下的定常MHD流动  

Meshless Local Petrov-Galerkin Method for Fully Developed Magnetohydrodynamic Flow

作　　者：蔡星会[1] 孙新利[1] 朱满林[1] 苏光辉[2] 秋穗正[2] 

机构地区：[1]第二炮兵工程学院,陕西西安710025 [2]西安交通大学,陕西西安710043

出　　处：《力学季刊》2011年第1期35-42,共8页Chinese Quarterly of Mechanics

摘　　要：磁流体流动在现代工业和科研中有着广泛的应用,但磁流体的流动受到磁场的影响,与一般流体区别较大,需要对其进行深入的研究。磁流体的流动受到流体力学流动方程和麦克斯韦方程的共同影响,其精确解在有限条件下才能得到,因此对磁流体的流动进行数值模拟具有重要的意义。本文采用移动最小二乘法计算形函数,利用无网格局部Petrov-Galerkin(MLPG)法得到控制方程的离散形式,在管壁为任意电导率及任意方向外加磁场的条件下,对方形直管道中定常流动的磁流体进行了数值计算。MLPG法的计算是基于节点的,不需要任何网格或单元,是一种真正的无网格方法。计算结果与Scheriff精确解进行了比较,表明该方法适用于中等以下哈特曼数的磁流体流动计算。The magneto-hydrodynamic（MHD） flow is broad applied in modern industry and research.MHD flow is quite different from the common flow due to the influence from the external magnetic field.The problem of MHD flow is rather complex since it involves both the hydrodynamic flow and Maxwell equations.The exact solutions can be achieved only in some simple cases.Therefore,it is of great importance to do the numerical simulation of MHD flow.A meshless local Petrov-Galerkin（MLPG） method was given to obtain the numerical solution of coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic flow through a straight duct of rectangular section with arbitrary wall conductivity and orientation of applied magnetic field.Local weak forms were developed by using weighted residual method locally from the governing equation of fully MHD flow.The implementation procedure of MLPG method is node based,and it doesn＇t need any ＂mesh＂ or ＂element＂.Computations have been carried out for different Hartmann numbers,wall conductivities and orientations of applied magnetic field.

关 键 词：MHD流动 无网格法 局部Petrov-Galerkin法 

分 类 号：O361.3[理学—流体力学]