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

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 road⁃ way 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 win⁃ dow 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⁃dimen⁃ sional， two⁃dimensional and three⁃dimensional space are consistent with those calculated by the conventional FDTD， whether the time harmonic source or the pulse source is used as the excitation source. The simulation time of the UWR - FDTD is related to the sectional area and length of the roadway and the electromagnetic wave frequency. When the length of the virtual window is 1 / 10 to 1 / 6 of the length of the roadway to be studied， the time is the shortest and the computation efficiency is the highest.