PRESSURE BOUNDARY-CONDITIONS FOR A SEGREGATED APPROACH TO SOLVING INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

It has been well accepted that Dirichlet and Neumann boundary conditio ns for the pressure Poisson equation give the same solution. The purpo se of this article is to reveal that the above statement is computatio nally acceptable but is not theoretically correct. Analytic proof as w ell as computational evidences are presented through examples in suppo rt of our observation. In this work we address that the mixed finite-e lement formulation for solving incompressible Navier-Stokes equations in primitive variables is equivalent to the formulation that involves solving the pressure Poisson equation, subject to Neumann boundary con ditions, iteratively with the momentum equations provided the velocity field is classified as having divergence-free and conservative proper ties.