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


Department of Mechanical Engineering, K. N. Toosi University, P. O. Box 19395-1999, Tehran, Iran


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