Pressure separation––a technique for improving the velocity error in finite element discretisations of the Navier–Stokes equations

Abstract

This paper presents a technique to improve the velocity error in finite element solutions of the steady state Navier–Stokes equations. This technique is called pressure separation. It relies upon subtracting the gradient of an appropriate approximation of the pressure on both sides of the Navier–Stokes equations. With this, the finite element error estimate can be improved in the case of higher Reynolds numbers. For practical reasons, the pressure separation can be applied above all for finite element discretisations of the Navier–Stokes equations with piecewise constant pressure. This paper presents a computational study of five ways to compute an appropriate approximation of the pressure. These ways are assessed on two- and three-dimensional examples. They are compared with respect to the error reduction in the discrete velocity and the computational overhead.