Hybrid Newmark-Conformal FDTD Method for Multiphysics Modeling of Short Spark Gaps With Curved Metallic Surfaces

Abstract

A new semi-implicit conformal finite-difference time-domain (FDTD) method is proposed for accurately modeling a short spark gap between metallic objects with curved surfaces. This new scheme is formulated on the basis of hybridizing the Newmark-Beta method and the simplified conformal scheme without cell enlargement. No dependency of mesh step in the direction of a spark channel is included in the stability condition of this scheme and its maximum stable time step is unaffected by the existence of effectively small meshes near curved perfectly conducting surfaces. The proposed semi-implicit conformal scheme has the same form as the one in the staircase approximation. This feature makes it simpler to couple with nonlinear spark resistance models. The proposed scheme is applied to two typical spark-gap systems with curved surfaces in air: spheres and a spheroid-ground structure. Its accuracy is demonstrated in comparison with the typical explicit and implicit conformal FDTDs, and also the semi-implicit staircase FDTD. It is also shown that the scheme is stable and second-order convergent even with a larger time step than the Courant-Friedrichs-Lewy stability limit. The proposed method is validated in comparison with the existing experimental data.