On the numerical solution of the incompressible Navier-Stokes equations in primitive variables using grid generation techniques (Q2455823)

Summary: A new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables is presented, using grid generation techniques. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation is implied at each grid point in the solution of pressure equation, while the SOR method is used for the Neumann problem for pressure. Results obtained for the model problem of driven flow in a square cavity demonstrate that the method yields accurate solutions. The results of the numerical computations in a driven cavity, which are presented for the history of the residues at several Reynolds numbers \(\text{Re}=100,1000,4000\) and 5000 all the computed results are obtained without any artificial dissipation. This feature of the present procedure demonstrates its excellent convergence and stability characteristics. Numerically results obtained for the steady state static pressure in the driven cavity are presented for the first time at \(\text{Re}=4000\) and 5000 using non-staggered grid.