Modelling of lossy curved surfaces in the 3-D frequency-domain finite-difference methods

摘要

A conformal first-order or Leontovic surface-impedance boundary condition (SIBC) for the modelling of fully three-dimensional (3-D) lossy curved surfaces in a Cartesian grid is presented for the frequency-domain finite-difference (FD) methods. The impedance boundary condition is applied to auxiliary tangential electric and magnetic field components defined at the curved surface. The auxiliary components are subsequently eliminated from the formulation resulting in a modification of the local permeability value at boundary cells, allowing the curved 3-D surface to be described in terms of Cartesian grid components. The proposed formulation can be applied to model skin-effect loss in time-harmonic driven problems. In addition, the impedance matrix can be used as a post-processor for the eigenmode solver to calculate the wall loss. The validity of the proposed model is evaluated by investigating the quality factors of cylindrical and spherical cavity resonators. The results are compared with analytic solutions and numerical reference data calculated with the commercial software package CST Microwave Studio™ (MWS). The convergence rate of the results is shown to be of second-order for smooth curved metal surfaces. The overall accuracy of the approach is comparable to that of CST MWS™.