Pressure boundary conditions for a segregated approach to solving incompressible Navier-Stokes equations

摘要

It has been well accepted that Dirichlet and Neumann boundary conditions for the 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, iteratively with the momentum equations provided the velocity field is classified as having divergence-free and conservative properties. [References: 14]