Finite Difference Analysis of Plane Couette Flow using MATLAB

Abstract

Internal flow is a flow for which the fluid is confined by a surface. Hence, the boundary layer is unable to develop without eventually being constrained. An internal flow is constrained by the bounding walls, and the viscous effects will grow and meet and permeate the entire flow. Some examples of internal flows are: flow between two parallel horizontal plates, Couette flow, plane Poiseuille flow, flow through pipes, etc. In the present study, a plane Couette flow has been analyzed by a classical method (exact solution of Navier-Stokes equation) as well as by an approximate method using central difference scheme (numerical solution of Navier-Stokes equation). The flow domain has been divided into various nodes and the velocities are obtained at different nodes for various time intervals. The stability condition for the convergence of solution has been determined and further the convergence of solution has been obtained using a MATLAB program for Couette flow using Crank-Nicolson scheme.