Solution of Electromagnetic and Velocity Fields for an Electrohydrodynamic Fluid Dynamical System

Abstract

We studied the temporal evolution of the electromagnetic and velocity fields in an incompressible conducting fluid by means of computer simulations from the Navier Stokes and Maxwell’s equations. We then derived the set of coupled partial differential equations for the stream function vector field and the electromagnetic field. These equations are first order difference equations in time and fetch simplicity in discretization. The spatial partial derivatives get converted into partial difference equations. The fluid system of equations is thus approximated by a nonlinear state variable system. This system makes use of the Kronecker Tensor product. The final system has taken account of anisotropic permittivity. The conductivity and magnetic permeability of the fluid are assumed to be homogeneous and isotropic. Present work in this paper describes characterization of magneto hydrodynamic anisotropic medium due to permittivity. Also an efficient and modified novel numerical solution using Tensor product has been proposed. This numerical technique seems to be potentially much faster and provide compatibility in matrices operation. Application of our characterization technique shall be very useful in tuning of permittivity in Liquid crystal polymer, Plasma and Dielectric lens antennas for obtaining wide bandwidth, resonance frequency reconfigure ability and better beam control.