The evolution and discharge of electric fields within a thunderstorm
An analysis of the present three-dimensional thunderstorm electrical model and its finite-difference approximations indicates unconditional stability for the discretization that results from the approximation of the spatial derivatives by a box-schemelike method and of the temporal derivative by either a backward-difference or Crank-Nicholson scheme. Lightning propagation is treated through numerical techniques based on the inverse-matrix modification formula and Cholesky updates. The model is applied to a storm observed at the Kennedy Space Center in 1978, and numerical comparisons are conducted between the model and the theoretical results obtained by Wilson (1920) and Holzer and Saxon (1952).
Hager, William W.↗