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Summary: ESAIM: M2AN 42 (2008) 887901 ESAIM: Mathematical Modelling and Numerical Analysis
DOI: 10.1051/m2an:2008026 www.esaim-m2an.org
THE CHANGE IN ELECTRIC POTENTIAL DUE TO LIGHTNING
William W. Hager1
and Beyza Caliskan Aslan2
Abstract. The change in the electric potential due to lightning is evaluated. The potential along
the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise
harmonic eigenfunction which is constant along the lightning channel. The change in the potential
outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms
of the pre-flash potential and the post-flash potential along the lightning channel. The expression
for the lightning induced electric potential change is derived both for the continuous equations, and
for a spatially discretized formulation of the continuous equations. The results for the continuous
equations are based on the properties of the eigenvalues and eigenfunctions of the following generalized
eigenproblem: Find u H1
0 (), u = 0, and R such that u, v L = u, v for all
v H1
0 (), where Rn
is a bounded domain (a box containing the thunderstorm), L is a subdomain
(the lightning channel), and ·, · is the inner product u, v =
u · v dx.
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