Computational fluid dynamics (CFD) simulation is a computational tool for exploring flow applications in science and technology. Of central importance in many flow scenarios is the accurate modelling of the boundary layer phenomenon. This is particularly true in the aerospace industry, where it is central to the prediction of drag. Modern CFD codes as applied to modelling aerodynamic flows have to be fast and efficient in order to model complex realistic geometries. When considering viscous flows, the boundary layer typically requires the largest part of computational resources. To simulate boundary layer flow with most current CFD codes, requires extremely fine mesh spacing normal to the wall and is consequently computationally very expensive. Boundary layer modelling approaches offer considerable computational cost savings. One boundary layer method which proved to be very accurate is the two-integral method of Drela (1985). Coupling the boundary layer solution to inviscid external flow, however, is a challenge due to the Goldstein singularity, which occurs as separation is approached. This research proposed to develop a new method to couple Drela‟s two-integral equations to a generic outer flow solver in an iterative fashion. The study introduced an auxiliary equation, which was solved along with the displacement thickness to overcome the Goldstein singularity without the need to solve the entire flow domain simultaneously. In this work, the incompressible Navier-Stokes equations were used for the outer flow. In the majority of previous studies, the boundary layer thickness was simulated using a wall transpiration boundary condition at the interface between viscous and inviscid flows. This boundary condition was inherently non-physical since it added extra mass into the system to simulate the effects of the boundary layer. Here, this drawback was circumvented by the use of a mesh movement algorithm to shift the surface of the body outward without regridding the entire mesh. This replaced the transpiration boundary condition. The results obtained show that accurate modelling is possible for laminar incompressible flow. The predicted solutions obtained compare well with similarity solutions in the case of flat and inclined plates, and with the results of a NACA0012 airfoil produced by the validated XFOIL code (Drela and Youngren, 2001). Copyright / Dissertation (MEng)--University of Pretoria, 2012. / Mechanical and Aeronautical Engineering / unrestricted