Application of time-domain finite-volume method to some radiation problems in two and three dimensions

This paper reports that Maxwell's curl equations in the time domain are cast into a conservation form and discretized using a finite-volume procedure which has been very successful in solving hyperbolic differential equations of fluid dynamics. The Lax-Wendroff explicit scheme is then used to solve the discretized Maxwell's equations, resulting in second-order accuracy with respect to both time and space. Unlike some other time-domain schemes, this one does not require an interlaced mesh for electric and magnetic fields. The computational domain comprising the antenna or array of antennas and the surrounding space are divided into a number of zones each of which is independently mapped into a local system of body-fitted coordinates, allowing for nonmatching grid lines at the interfaces. A first-order, nonreflecting boundary condition is used at the outer boundary of the computational domain. The electric and magnetic fields tangential to a conveniently chosen contour very close to the radiator are stored and used in the post-processing stage to obtain the near-and far-field quantities of interest such as input impedance, mutual coupling, and radiation pattern. Fast Fourier transforms are used to obtain the frequency domain information of radiation due to both time harmonic and pulse sources. Radiation pattern and input impedance of some typical parallel-plate waveguides and mutual coupling for arrays of parallel-plate waveguides are computed and, whenever possible, compared with closed form exact or approximate solutions. Also, radiation patterns for a two-dimensional horn and a rectangular waveguide are presented