The main purpose of this project is to show the implementation of finite difference method for unidirectional fluid flow of velocity pressure formulation. To find the numerical solution of fluids for unidirectional flow confined between tw o parallel walls, we can use explicit and implicit finite difference methods. The solution is uniform, desirable and independent of the size of the time step in the case of implicit finite difference method than explicit method. We also implement finite difference method in the case of two layer flow in a channel by considering the continuity of velocity, continuity of shear stress and normal stress at the interface. The velocity profile shows non uniformity when the numerical diffusion number, which is the minimum of the numerical diffusive number of the lower layer and the upper layer, is greater than 0.5.

A project submitted to the department of Mathematics Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics