Non-orthogonal Grids Research Articles

Diffraction of electromagnetic waves at the seam of two-dimensionally periodic waveguide arrays and dielectric rods

The diffraction of electromagnetic waves at the seam of two-dimensionally periodic arrays of semiinfinite circular waveguides, connected in the plane of the seam by an ideally conducting flange and dielectric rods placed at the nodes of a nonorthogonal grid is investigated in rigorous electrodynamic formulation by the method of projection matching of the fields. A system of algebraic equations is obtained for computing the elements of the scattering matrix of the seam of the arrays. The convergence of the solution and the accuracy of computation of the reflection coefficient of the fundamental waveguide mode are investigated numerically as functions of the diameters of the waveguides and the rods, the period of the array, and the dielectric constants of the rod and the medium within the waveguides.

Computer Analysis of Three-Dimensional Turbulent Flows around Ships' Hulls

This paper describes a general solution method for three-dimensional, steady, turbulent flows around long, smoothly-shaped bodies, of arbitrary and varying cross-sectional shape. The particular example considered here concerns the flow around the hull of a ship, but the method can equally well be applied to other, similarly shaped bodies such as an aircraft fuselage, or a submarine. Moreover, the basic non-orthogonal grid method described can also be applied to internal flows in irregular shaped passages, or to the prediction of flows around bodies in ducts. The mathematical model consists of the partial differential equations for continuity and three components of momentum, along with a two-equation model of turbulence, and proper modelling of the ship's hull. The solution method utilizes a non-orthogonal coordinate system in the plane normal to the axis of the body, which has one coordinate surface coinciding with the hull surface. This coordinate system is flexible and is easily modified to enable the calculation procedure to handle bulbous ships' hulls, which are of great importance in modern ship design. The differential equations involved are solved numerically after provision of the proper boundary and initial conditions. The solution procedure is a unique one, called ‘partially-parabolic’, as first used by Pratap and Spalding (1). Solutions are presented for flow around ships' hulls, which demonstrate the physical realism of the achieved results and the potential of the present method.