Integral conditions for the pressure in the computation of incompressible viscous flows

Abstract

The problem of finding the correct conditions for the pressure in the time discretized Navier-Stokes equations when the incompressibility constraint is replaced by a Poisson equation for the pressure is critically examined. It is shown that the pressure conditions required in a nonfractional-step scheme to formulate the problem as a system of split second-order equations are of an integral character and similar to the previously discovered integral conditions for the vorticity. The novel integral conditions for the pressure are used to derive a finite element method which is very similar to that developed by Glowinski and Pironneau and is the finite element counterpart of the influence matrix method of Kleiser and Schumann.