UWR-FDTD矿井电磁波数值分析方法  

Numerical analysis method of the electromagnetic fields in coal mine roadway using UWR-FDTD

作　　者：张高敏 刘毅[1] 彭铭 ZHANG Gaomin;LIU Yi;PENG Ming(School of Mechanical Electric&Information Engineering,China University of Mining&Technology-Beijing,Beijing 100083,China)

机构地区：[1]中国矿业大学(北京)机电与信息工程学院,北京100083

出　　处：《煤炭学报》2022年第11期4157-4166,共10页Journal of China Coal Society

基　　金：国家重点研发计划资助项目(2016YFC0801800)。

摘　　要：为减小FDTD(Finite-Difference Time-Domain)对计算机内存空间与算力的需求,提高FDTD求解矿井电磁波的计算效率,根据矿井巷道断面小、轴向长的特点,提出了单位窗口循环使用时域有限差分方法(Unit Window Recycling, UWR-FDTD)。该方法沿巷道轴向把待研究的巷道平均划分多个虚拟窗口,虚拟窗口的断面面积与巷道断面面积相同,为一个同虚拟窗口大小相同的单位窗口分配内存空间,所有虚拟窗口循环使用单位窗口的内存空间,执行传统FDTD迭代过程。激励源设在第1个虚拟窗口,根据1个单位窗口电磁波传播时间,确定每个虚拟窗口的迭代次数,按照时间步存储单位窗口内最后一个Yee网格的电磁场分量,作为下一个虚拟窗口的子激励源。每个虚拟窗口在单位窗口内迭代完成后,均存储完成时刻单位窗口的电磁场分量,用于合成整个巷道内的电磁场数值。结果表明:同传统FDTD方法相比,UWR-FDTD方法在一维二维三维计算空间均可减少内存使用量,划分虚拟窗口数目越多,仿真时所需的内存空间越小,在三维空间内提高的计算效率更加显著;在无耗介质、有耗介质计算空间,分别用时谐源和脉冲源作为激励源,在一维二维三维空间内用UWR-FDTD计算出合成电场的周期和幅值,与传统FDTD计算结果一致。UWR-FDTD矿井电磁波仿真时间与巷道断面面积、巷道长度和电磁波频率有关;划分虚拟窗口的长度为待研究巷道长度的1/10~1/6时,计算用时最短,计算效率最高。In order to reduce the requirements of the finite-difference time-domain(FDTD) on computer memory space and computing power, and improve the calculation efficiency of the FDTD in solving mine electromagnetic waves, a unit window recycling finite-difference time-domain method(UWR-FDTD) is proposed according to the characteristics of small in sectional area and long in axial direction of mine roadway. In this method, the roadway to be studied is divided into several virtual windows along the axis of the mine roadway. The sectional area of the virtual window is the same as that of the roadway. A unit window with the same size as the virtual window is allocated with memory space. All virtual windows recycle the memory space of the unit window and execute the conventional FDTD iteration process. The excitation source is set in the first virtual window. The iteration times of each virtual window are determined according to the time of electromagnetic wave propagation in the unit window. The electromagnetic field component of the last Yee grid in the unit window is stored as the sub-excitation source of the next virtual window according to the time step. Each virtual window stores the electromagnetic field component of the unit window at the completion time after the iteration in the unit window, which is used to synthesize the electromagnetic field in the whole mine roadway. The results show that compared with the conventional FDTD, the UWR-FDTD method can reduce the memory consumption in one-dimensional, two-dimensional and three-dimensional finite space. The more the number of virtual windows, the smaller the memory space needed for simulation. The computational efficiency is improved more significantly in three-dimensional space. In the finite space of lossless medium and lossy medium, the period and amplitude of the synthetic electric field computed by the UWR-FDTD in one-dimensional, two-dimensional and three-dimensional space are consistent with those calculated by the conventional FDTD, whether the time harmonic

关 键 词：矿井电磁波 矿井无线传输 时域有限差分 单位窗口循环使用 虚拟窗口 内存空间 

分 类 号：TD655[矿业工程—矿山机电]