Radial Waves Based Dispersion Analysis of the Body-of-Revolution FDTD Method

Detailed numerical dispersion analysis for the body-of-revolution finite-difference time-domain method is presented. Critical analysis is based on the proper cylindrically radial wave functions, which result in a usable numerical dispersion relation for all space, including the near vicinity of the axis of rotation. The corresponding stability criterion is also derived. The focus of dispersion analysis presented here is on numerical accuracy and stability limits within close proximity to the axis of rotation as they change with the rotational mode order. Simulation experiments are included to verify the accuracy of derived dispersion and stability formulas. An important result obtained is the confirmation and accurate prediction of relatively dense grids when modeling increasing rotational mode orders. Furthermore, the precise formulas derived here are critical to future precision implementations of auxiliary modeling tools, such as controlled source injection and absorbing boundary conditions.