NUMERICAL-SOLUTION OF THE NAVIER-STOKES EQUATIONS USING A PROJECTION METHOD

The paper presents some new developments in the projection method for solving the Navier-Stokes equations. At the first step of the proposed approach a provisional velocity field is computed from the momentum equation without a pressure gradient. Then the pressure is determined as a solution of the Neumann problem for the Poisson equation, and finally the velocity field is corrected. The main improvement of the method consists in an application of the method of lines and the method of spline functions, which simplify the first and the second steps of the algorithm to an initial problem for a system of ordinary differential equations. A test example of the driven cavity problem is reported.