PRESSURE BOUNDARY CONDITIONS FOR A SEGREGATED APPROACH TO SOLVING INCOMPRESSIBLE NAVIER-STOKES EQUATIONS - Sheu, Tony W. H.; Wang, Morten M. T.; Tsai, S. F. (Numerical heat transfer. Part B, Fundamentals, 1998)
It has been well accepted that Diricklet and Neumann boundary conditions for Ike pressure Poisson equation give the same solution. The purpose of this article is to reveal that the above statement is computationally acceptable but is not theoretically correct. Analytic proof as well as computational evidences are presented through examples in support of our observation. In this work we address that the mixed finite-element 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 conditions, Uerativety with the momentum equations provided the velocity field is classified as having divergence-free and conservative properties.