Finite difference method

Abstract: The characteristic impedance and the attenuation of transmission lines supporting TEM modes can be computed by using finite difference methods for solving the Laplace equation for the domain defined by the inner and the outer conductor. The difference equations can be solved by machine computation and the impedance and the attenuation is obtained by integrating the field gradients and the squares of field gradients over both boundaries. The case of a shielded strip transmission line is treated as a numerical example. A computation time of approximately 0.015 hour on the IBM 7094 is required for achieving an accuracy of 0.5 percent for the impedance and 2 percent for the attenuation. The finite difference method is also used for lines which are partially filled with dielectric material and it is concluded that low attenuations are obtained by placing the dielectric material in such a way that high field regions are avoided.

Abstract: This paper presents incompressible laminar boundary-layer results on both the leeside and windside of a prolate spheroid. The results are obtained by an implicit finite difference method of the Crank–Nicolson type. Particular attention has been given to the determination of separation and of embedded streamwise vortices. No restriction on the angle of attack or the thickness ratio is imposed, nor are there invoked any of the common assumptions such as similarity, conical flow and others. The results suggest an embedded vortex region existing between the regular boundary-layer region and the separated region. At higher angle of attack, the vortex region becomes so thick that it itself may be more appropriately called ‘separated’ also. The latter possibility leads to questions of applicability for existing theories on three-dimensional separation.