Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method

The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique. The study explores the properties of the finite difference method and discusses its efficacy in solving the boundary layer flow problem. Additionally, we discuss an inverse problem related to the Falkner-Skan equation, aiming to obtain precise values for the second derivative's initial value. This inverse problem is successfully resolved using an appropriate initial value procedure. The results obtained from the finite difference method and the inverse problem resolution is compared with those from cubic spline interpolation, proposed by Alavi and Aminikhan. By doing so, the reliability and accuracy of present approach is demonstrated. Overall, this study contributes to a better understanding of boundary layer flow and presents a viable numerical technique for tackling similar fluid dynamics problems. The findings shed light on the significance of choosing appropriate numerical methods for solving complex systems of equations in fluid mechanics.