Three Dimensional Numerical Simulation of Stepped Leadee by means of Fractal Model

采用基于分形数学概念改进的Leader Progression模型，对近地表台阶状先导进行了三维数值模拟。本文用有限差分法求解三维泊松方程，模拟了起始于云层下部、通常向地面人工建筑物行进的阶梯状先导，研究了理论上的阶梯状先导过程。闪电通道的曲折和分叉是闪电通道的典型特征，本文在数值模拟的基础上，通过计算静止图像闪电通道的分形维数来研究闪电通道的特征。平均估计的分形维数约为1.2，估计的分形维数被用来评估数值模拟结果。通过本研究，完整地建立了分形阶跃先导模型。

Three-dimensional numerical simulations of a stepped leader near the ground surface are carried out by using the Leader Progression Model which is improved by using the novel mathematical concept, Fractal. The finite difference method is applied to the three dimensional Poisson's equation and the stepped leaders, which are initiated at the lower part of the cloud and usually are proceeding toward the artificial constructions on the ground, are simulated to study the theoretical stepped leader progression. The zig-zags and branches of channels, which are believed to be the representative characters of lightning channel, can be simulated in this study.Besides the numerical simulations, lightning channel's features are examined by estimating the Fractal dimensions of lightning channels of still pictures. The average estimated Fractal dimensions is about 1.2, and the estimated Fractal dimension is used to evaluate the numerically simulated results. Through this study the Fractal stepped leader model is completely established.