ABSTRACT
This chapter examines the finite difference representation of the two-dimensional Navier–Stokes equations for incompressible and laminar flow of a constant property fluid, including the energy conservation as well as the boundary layer equations. For simple geometries and flow conditions, similarity solutions are possible for the problems of velocity and temperature distribution in boundary layers; but a numerical method of solution is necessary when dealing with the complicated situations. For computational purposes, the advantage of parabolic boundary layer equations is the fact that the behavior of flow at any location is influenced only by the conditions on the upstream side of that location. The chapter considers a laminar two-dimensional incompressible flow field for a constant property fluid, without considering the boundary layer simplifications. For two-dimensional cases, the most successful numerical technique for solving such a system is based on the vorticity-stream function formulation.
