Numerical solution of general boundary layer problems by the method of differential quadrature

Abstract

Accurate numerical solutions to some boundary layer equations are presented for boundary layer flows of incompressible Newtonian fluid over a semi-infinite plate. The differential quadrature method (DQM) is first used to reduce the governing nonlinear differential equations to a set of nonlinear algebraic equations. The Newton-Raphson method is then employed to solve the resulting system of nonlinear algebraic equations. The proposed formulation is applied here to solve some boundary layer problems including Blasius,Sakiadis, Falkner-Skan, magnetohydrodynamic (MHD) Falkner-Skan, Jeffery-Hamel, unsteady two-dimensional and three-dimensional MHD flows. A simple scheme is also presented for solving Blasius boundary layer equation. In this techniques, Blasius boundary value problem is first converted to a pair of nonlinear initial-value problems and then solved by a step-by-step DQM. The accuracy and efficiency of the proposed formulations are demonstrated by comparing the calculated results with those of other numerical and semi-analytical methods. Accurate numerical solutions are achieved using both formulations via a small number of grid points for all the cases considered