Resolution of Maxwell’s Equations in Atmospheric Electromagnetic Phenomena

This paper focuses on the numerical resolution of Maxwell’s equations applied to atmospheric electromagnetic phenomena, particularly lightning discharges. Lightning generates intense transient electromagnetic fields that interact with the ground and nearby structures, posing challenges for accurate modeling and protection design. To analyze these interactions, the two-dimensional Finite-Difference Time-Domain (2D-FDTD) method is employed to solve Maxwell’s equations in the time domain with high spatial and temporal resolution.

This study considers a realistic configuration involving a 168 m tall object interconnected with the lightning channel and a clayey soil characterized by moderate electrical conductivity (σ = 0.0025 S/m) and high permittivity. The simulation framework enables the investigation of the spatiotemporal evolution of the electric and magnetic fields both above and below the ground, capturing the complex coupling between the lightning channel, the tall structure, and the soil.

Results demonstrate that the soil’s electrical properties significantly affect the electromagnetic field amplitudes and waveform shapes, particularly below ground in the near-field region. Variations in conductivity and permittivity alter the current distribution and the attenuation of electromagnetic waves. This work highlights the importance of accurate numerical modeling of soil characteristics in the computational analysis of atmospheric electromagnetic phenomena and contributes to improving the reliability of lightning protection and grounding system design.