Research on Fast Calculation Method of Lightning Distribution in Mountainous Area Based on Conformal Mapping

The study of lightning distribution is crucial for implementing differentiated lightning protection measures, with lightning channel simulation serving as the foundation for such research. Particularly in mountainous areas, lightning protection presents unique challenges due to complex terrain. However, current numerical calculation methods for simulating lightning channels in mountainous regions suffer from lengthy computation times that fail to meet the requirements of lightning distribution research. Additionally, existing lightning channel models are overly simplified, necessitating the exploration of faster and more accurate simulation methods. To address these limitations, this paper proposes a rapid calculation approach utilizing conformal mapping to project the mountainous electric field onto flat terrain, resulting in accelerated computation speeds. The accuracy of the electric field calculation is verified using COMSOL. Furthermore, a Cooray distribution-based lightning channel model is employed to represent the spatial characteristics of mountainous regions. Combining fractal theory, the study simulates lightning channels within mountainous terrains and efficiently calculates the lightning distribution in typical mountainous topographies. The results demonstrate a significant reduction in lightning strike time to 10 s when employing the Cooray distribution-based lightning channel model, which exhibits paths and distribution closer to actual observations compared to uniformly distributed lightning channels. The findings of this study provide valuable insights for future differentiated lightning protection in mountainous areas.