Wavelet Preconditioners of Electrohydrodynamic flow problem

Abstract

In \u00a0this \u00a0paper \u00a0wavelet \u00a0preconditioned \u00a0method \u00a0is \u00a0used \u00a0for \u00a0the \u00a0solution \u00a0of \u00a0Electrohydrodynamic flow problem. A finite difference method is used for the solution of Electrohydrodynamic flow equation. The method comprise the nonlinear Newton iteration on the outer loop and a linear iteration on the inside loop where \u00a0wavelet \u00a0based \u00a0preconditioned \u00a0GMRES \u00a0(Generalized \u00a0Minimum \u00a0Residual) \u00a0method \u00a0is \u00a0used. \u00a0In \u00a0the scheme \u00a0the \u00a0Jacobian vector product \u00a0is \u00a0approximated \u00a0accurately with \u00a0much \u00a0ease (without forming \u00a0Jacobian explicitly \u00a0and \u00a0requiring \u00a0no \u00a0extra \u00a0storage). \u00a0It \u00a0overcomes \u00a0the \u00a0limitations \u00a0of \u00a0conventional \u00a0schemes \u00a0for \u00a0the numerical solution of Electrohydrodynamic flow problem, for computing fluid velocity, covering wide range of Hartmann electric number (Ha) parameter with constant of practical interest. To confirm and validate the solutions obtained, by the present method, are compared with those obtained by GMRES method.