The application of boundary value techniques in the solution of the Navier-Stokes equation

An investigation of the numerical boundary value techniques for a two-dimensional steady state, viscous, incompressible flow in a rectangular cavity is presented. Solutions for the two-dimensional Navier-Stokes equations are found in the case of a plate moving over the top of the fluid-filled cavity. Four boundary equations are defined and an elliptic parabolic partial differential equation system is obtained. Consideration is given to successive line over-relaxation models in the Re range 100-500,000. An iterative solution procedure is demonstrated for the finite difference equations. The number of iterations necessary to reach an accuracy of 1/1000 for each Re is found to decrease with the boundary value technique.