Table 6-1: Breakdown time comparison for different values of w
breakdown time breakdown time
w value with the ambient conductivity with the reduced conductivity
(without cloud) (with cloud)
w = 1 00 64.7500 s
w = 4 15.5625 s 13.6875 s
w = 16 1.1850 s 1.75000 s
V/m which is less than the breakdown threshold 250,000 V/m, as t tends to
infinity. Therefore, the breakdown never happens when w = 1.
In a thundercloud, the conductivity is less than the ambient conductivity that
appears in Equation (6.1). Next, we consider the effect of reducing conductivity in
order to simulate a cloud. More precisely, the ambient conductivity is multiplied
by the factor 0.05 as described in [7]. The results are shown in the third column of
Table 6-1. Again, the breakdown time decreases dramatically as w increases. This
pattern is consistent with the previous computed breakdown times for the ambient
conductivity.
As can be seen in Table 6-1, reducing in conductivity to simulate a cloud leads
to the occurrence of breakdown when w = 1, while with the ambient conductivity,
charge is conducted into the surrounding atmosphere faster enough to prevent the
electric field from reaching the breakdown threshold. In the remaining experiments,
the conductivity is given by Equation (6.1) times 0.05 (to simulate a cloud).
6.2 Experiment 2
A finer mesh in our model is expected to obtain more accurate results.
However, such refinement is not only time consuming, but also increasing memory
usage. In order to maintain the accuracy of our results efficiently, a graded mesh
is considered. We place a large percentage of grid points near the charge centers
along the z- direction where the potential changes rapidly. The grid along the