Time-Dependent Numerical Method with Boundary-Conforming Curvilinear Coordinates Applied to Wave Interactions with Prototypical Antennas

Abstract

A new unstaggered finite-difference time-dependent technique to accurately model scattring from prototypical 2D antenna structures is devised. The unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries. Generalized curvilinear coordinates are generated such that physical boundaries correspond to coordinate lines. A numerical procedure to generate almost orthogonal, boundary-conforming, fine grids over these bounded regions is developed. Once the governing equations are written in terms of the new curvilinear coordinates, a time-dependent numerical method is applied to obtain time harmonic steady-state solutions to these problems. The electric field wave amplitude as well as the wave pattern inside the waveguide and the scattered field from the prototypical antennas are obtained. Accuracy and computational cost are compared when almost orthogonal and nonorthogonal grids are in use. An optical theorem for a flanged waveguide antenna with perfect electrical conductor walls is derived. It is verified that the approximate solutions obtained by application of the time-dependent numerical method with boundary-conforming, curvilinear coordinates satisfy the optical theorem.