Numerical solutions for the incompressible Navier-Stokes equations in primitive variables using a non-staggered grid, II

Abstract

In Part I of this study, a method was developed for the solution of the pressure Poisson equation, with Neumann boundary conditions, on a non-staggered grid. This method was used to determine the pressure when given the velocity field from a stream function-vorticity solution. In Part II, the pressure equation is solved iteratively with the momentum (Navier-Stokes) equations on a non-staggered grid. In this case, the solution of the pressure equation not only provides the pressure, but also serves to indirectly satisfy the continuity equation. This primitive variables formulation has a major advantage over the stream function-vorticity method in its applicability for three-dimensional flow. Numerical results are obtained and compared with the stream function-vorticity results for the driven cavity of Part I.