3-D FDTD Computation of Electromagnetic Fields Associated With Lightning Strikes to a Tower Climbed on a Trapezoidal Mountain

Abstract

In this paper, we are interested in the study of electromagnetic (EM) field waveforms generated by a lightning strike to a tower located on a trapezoidal mountain. The latter has a height of 500 m and a steepness angle of slope of 45°. The EM field components are calculated at six points and in three directions from the tower. Among these six points, four of them are placed on a flat ground and located at close distances from the mountain bottom while the other two points are located on the mountain at close distances from the tower. Also, because of the three-dimensional (3-D) geometry of the problem being treated, the computation is performed in three dimensions by using the finite-difference time-domain (FDTD) method. In this computation, the lightning channel is represented by the transmission line model extended to include a tall strike object. To evaluate the influence of the presence of mountain on the EM field waveforms, a comparison between the results obtained in the presence and absence of the mountain has been done. On the other hand, the ground conductivity effect on the EM field components has been also studied. At the end of this study, we show that the trapezoidal mountain shadowing effect causes a reduction of the vertical electric field calculated on a flat ground at close distances from the mountain bottom, while the field is enhanced on the top of the mountain. The same conclusion is drawn for the azimuthal magnetic field. Furthermore, the initial peaks of the vertical electric field and the azimuthal magnetic field, above the ground, have been attenuated because of the finite conductivity of ground. The horizontal electric fields above the ground are characterized by oscillations due to the presence of tower and mountain. The underground horizontal electric field and azimuthal magnetic field have the same waveforms as those obtained above the ground but with smaller magnitudes. Thus, the underground vertical electric is initially bipolar and then essentially zero. Finally, the 3-D-FDTD developed program was validated (see the Appendix).