Fdtd電磁界・サージ解析のための細線導体模攎法の改善

摘要

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 (r_0 = 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 r_0 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 0.0001 Δs to 0.9Δs.%近年，Maxwellの方程式の電界および磁界に関する2つのrn回転の式を時間，空間に対して差分化して解くFDTD（finiterndifftrence time domain）法が電力系統のサージ解析に盛rnんに適用されている。一般に，FDTD法を用いた解析では，rn解析対象の導体系を含む直方体の空間をセルと呼ばれる直rn方体の微小要素に分割し，各セルに対して媒質定数（導電rn率，誘電率および透磁率）を設定することによって，導体rn系やそれを囲む空間を模擬する。