一种高效的霍尔电场数值模拟方法  

AN EFFICIENT NUMERICAL SIMULATION METHOD FOR HALL ELECTRIC FIELD

作　　者：李恒 金科[1,3,4] 寇勇 李凯 王斌 叶柳青[1,3,4] Li Heng;Jin Ke;Kou Yong;Li Kai;Wang Bin;Ye Liuqing(School of Aerospace Science and Technology,Xidian University,Xi’an 710126,China;Guangzhou Institute of Technology,Xidian University,Guangzhou 510555,China;Shaanxi Key Laboratory of Space Extreme Detection,Xi’an 710126,China;Research Center for Applied Mechanics,Xidian University,Xi'an 710126,China)

机构地区：[1]西安电子科技大学空间科学与技术学院,西安710126 [2]西安电子科技大学广州研究院,广州510555 [3]陕西省空间超限探测重点实验室,西安710126 [4]西安电子科技大学应用力学研究中心,西安710126

出　　处：《力学学报》2025年第1期79-88,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(12202331);广东省基础与应用基础研究基金(2021A1515110002);陕西省自然科学基础研究计划(2022JQ-028);中央高校基本科研业务费(XJS211304)资助项目。

摘　　要：针对高超声速飞行器电磁调控分析中霍尔电场高效数值模拟方法的需求,以磁流体动力学基本原理为基础,构造了双曲形式的霍尔电场控制方程.基于自行开发的计算流体力学数值求解框架,在非结构混合网格上通过格心有限体积方法建立了新的霍尔电场数值模拟方法.迎风分裂格式基于Rusanov格式,时间推进基于LU-SGS隐式算法.以立方体区域泊松方程算例和分段电极流动通道霍尔电势算例为例对文章数值方法的准确性、收敛特性以及计算效率进行了考核和验证.数值模拟结果表明,当前数值方法计算结果与传统方法相同,且具有良好的收敛特性,对于立方体区域泊松方程算例,当前方法所需墙上时间为传统方法的28.76%,而对于分段电极流动通道霍尔电势算例,当前方法所需墙上时间仅为传统方法的0.61%.文章提出的新的霍尔电场数值模拟方法具有较高的计算效率.Based on the fundamental principles of magnetohydrodynamics,a hyperbolic Hall electric field governing equation is constructed to meet the need of an efficient numerical simulation method for the electromagnetic control analysis of hypersonic vehicles.A new numerical simulation method of Hall electric field on unstructured hybrid grids is established by using the cell-centered finite volume method with in-house CFD numerical solution framework.The Rusanov scheme is used as upwind splitting scheme,and time marching is based on LU-SGS implicit algorithm.The accuracy,convergence characteristics and computational efficiency of the numerical method are evaluated and verified by the two case,and that is Poisson’s equation on cube region and the Hall electric field on segmented electrode flow channel.The numerical simulation shows that the results of the present numerical method are the same as those of the traditional method,and has good convergence characteristics.For the case Poisson’s equation on cube region,the wall time required by the present method is 28.76%of that of the traditional method,while for the Hall electric field on segmented electrode flow channel,the wall time required by the present method is only 0.61%of that of the traditional method.The new numerical simulation method of Hall electric field proposed in this paper has high computational efficiency.

关 键 词：计算流体力学 磁流体动力学 霍尔效应 泊松方程 数值模拟 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程] V411.3[理学—流体力学] O361.3[理学—力学]