带速度项电磁场控制方程的无网格解法  

Meshfree method for electromagnetic field governing equations with velocity term

作　　者：阳恩会[1] 王石刚[1] 王新洪[1] 莫锦秋[1] 曹家勇[1] 

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《电机与控制学报》2010年第1期1-6,共6页Electric Machines and Control

基　　金：国家自然科学基金(50875169)

摘　　要：提出采用无网格法求解带速度项的电磁场控制方程,并结合有限元中的流线迎风稳定化方法对由速度项引起的无网格法解中的数值振荡进行抑制。避免了采用迎风有限元法求解带速度项的电磁场控制方程时所带来的网格畸变以及人工稳定项中二阶导数项被忽略的问题。针对1D及由A-φ-A矢量模型所描述的带速度项的电磁场控制方程,讨论其无网格法流线迎风方案,并建立稳定化的离散数值模型。数值结果表明:尽管无网格方法中流线迎风的稳定因子不再是优化的,但其对由速度项引起的电磁场控制方程无网格解中数值振荡的抑制效果是显著的,流线迎风无网格法能有效地求解带速度项的电磁场控制方程。In order to avoid the grid distortion when the FEM is used to compute electromagnetic field equations with velocity term and the loss of accuracy which is induced by the omission of the second-order derivative in artificial diffusion term, the meshfree method coupling streamline upwinding approach is proposed for these equations. Based on the investigation of stabilization factor in the meshfree method, a vector form of streamline upwinding was implemented for these equations. The numerical model of stream- line upwinding meshfree method for electromagnetic field equations with velocity term which were formulated by the magnetic vector potential and the scalar potential was deduced. Different equations were used to verify the effect of streamline upwinding meshfree method. The non-physical oscillation contained in the meshfree method solution of electromagnetic field equations with velocity term can be suppressed effectively by streamline upwinding.

关 键 词：电磁场方程 速度项 无网格法 流线迎风 数值振荡 

分 类 号：TM153[电气工程—电工理论与新技术] O241.82[理学—计算数学]