An Improvement of a Thin Wire Representation for FDTD Electromagnetic and Surge Calculations

Abstract

In this paper, we have shown that FDTD calculations for a conductor system having a radius smaller than 0.15Δs or larger than 0.65Δs (Δs is the lateral side length of cells employed), represented using arbitrary-radius-wire representation techniques proposed by Noda and Yokoyama, and Railton et al., with a time increment determined from the upper limit of Courant's stability condition, result in numerical instability. The reason for this numerical instability is that the speed of waves propagating outward in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light, and therefore, Courant's condition is not satisfied there. Furthermore, we have improved the arbitrary-radius-wire representation proposed by Noda and Yokoyama. In representing a wire whose radius is smaller than the equivalent radius (r0 =0.230Δs) using the improved technique, the permeability for calculating the axial magnetic field components closest to the wire and for calculating the circulating magnetic field components closest to and half cell away from the tip of the wire is modified in addition to the permeability and the permittivity for calculating the circulating magnetic field components and the radial electric field components, closest to the wire, respectively. In representing a wire whose radius is larger than r0 using the technique, the permittivity for calculating the axial electric field components closest to the wire is modified in addition to the permittivity and the permeability for calculating the radial electric field components and the circulating magnetic field components, respectively. The improved technique is effective in representing a wire whose radius ranges from 0.0001Δs to 0.9Δs.