Numerical solution for a 3D rectangular waveguide using the Finite Volume Control method

In this paper, a modified Finite Volume Control (FVC) method is introduced and used to solve for the fields in a 3D rectangular waveguide. The FVC method finds its main applications in Computational Fluid Dynamics (CFD) problems and has been rarely used in Computational Electromagnetics (CEM). The 3D rectangular waveguide under consideration is coupled through its apertures to two infinite conducting planes. The aperture\´s shape and size are the same as the waveguide cross-sections. The main complexity arises in the discretization of the aperture boundary equations. In fact, those equations do not exhibit any of the classic forms of boundary equations recognized in the FVC method. Therefore, a "surface control" approach over the two apertures was introduced where each aperture is divided into control areas of dimensions equal to the control volumes of the initial problem. The computed fields inside the waveguide are given and compared to the full wave simulation results.