On pressure compatibility condition in numerical simulation of incompressible viscous flows using primitive variable formulation

Abstract

The numerical simulation of incompressible viscous flows using primitive variable formulation requires that the pressure be obtained by solving the pressure Poisson equation (PPE). It is mentioned in the literature on incompressible flows [1,2] that when all the pressure boundary conditions are of Neumann type, then the pressure compatibility condition (PCC) has to be satisfied for guaranteeing the existence of solution. The main aim of this paper is to show that the PCC is not an important issue as has been claimed in the literature [1–3]. On the other hand, it will be shown that the crucial issue, in numerical simulation of incompressible viscous flows, is to ensure solenoidality of the velocity field accurately. We will further show that the accuracy of solenoidality depends on the choice of pressure boundary conditions. The demonstration is based on the computation for 2-D lid-driven cavity problem for Re=100 on 129² uniform grid.