Design of a novel computational procedure for solving electrohydrodynamic flow equation

Abstract

The aim of the present study is to describe and demonstrate a new computational procedure based on nonuniform mesh compact finite difference method to approximate the solution of a nonlinear singular boundary value problem which describes the electrohydrodynamic flow (EHF) of a fluid in a circular cylindrical conduit. The EHF problem under consideration is highly nonlinear and the nonlinearity confronted in the problem is in the form of a rational function and has a singularity at the point $x=0$. To construct a non-uniform grid, we use a grading function. This function generates a finer mesh near the singular point. The efficiency and applicability of the new method are demonstrated by applying it to the EHF equation for small and large values of two relevant parameters, namely the strength of nonlinearity $\alpha$ and the electric Hartmann number $\tilde{H}$. The velocity field of EHF flow of a fluid in radial direction is computed. It is shown that the proposed new scheme produces a fourth-order numerical approximation to the solution of the considered EHF problem and the velocity field is clearly influenced by the parameters $\tilde{H}$ and $\alpha$. The computed results are compared with some published numerical results.