Some solutions for finitely conducting viscous MHD plane flows

Generalized fundamental solutions for unsteady viscous flows.

A number of closed-form fundamental solutions for generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two parts corresponding to a longitudinal wave and a transversal wave. As examples of application, the hydrodynamic forces acting on a sphere and on a circular cylinder...

Plane Wave Reflection and Refraction Involving a Finitely Conducting Medium

In this work the structure of the electromagnetic field in a lossy conducting medium is studied in detail. The meaning of the complex angle of refraction is explained in terms of real parameters involved in this problem. The concepts are illustrated with a wave refracting from air into pure water at a frequency of 95 GHz and an incidence angle of 60 . The approach is similar to that used to der...

Agglomeration Multigrid Solutions of Laminar Viscous Flows

The paper describes the implementation details and validation results for an agglomeration multigrid procedure developed in the context of hybrid, unstructured grid solutions of aerodynamic flows. The procedure is applied to the solution of 2-D, laminar viscous flows of aerospace interest. The governing equations are discretized with an unstructured grid finite volume method which is capable of...

Numerical Methods for Viscous Incompressible Flows: Some Recent Advances

Instability of Some Ideal Plane Flows

We prove the instability of large classes of steady states of the two-dimensional Euler equation. For an odd shear flow, beginning with the Rayleigh equation, we define a family of operators depending on some positive parameter. Then we use infinite determinants to keep track of the signs of the eigenvalues of these operators. The existence of purely growing modes follows from a continuation ar...