Preconditioning of the Navier-Stokes equations with multiple constraints

Abstract

The Navier-Stokes equations represent a mathematical model of incompressible fluid flow. To obtain a unique solution, these need to be supplemented by a physically relevant set of boundary conditions (BCs). These BCs, such as natural outflow, no-slip, no-penetration, can be easily imposed within the finite element setting in the case of straight boundaries that are aligned with the Cartesian axes. When more general domains are considered, as in many realistic industrial applications, one practical way of imposing BCs is with Lagrange multipliers. This procedure leads to an augmented linear system at the discrete level. In this paper we discuss efficient preconditioning of such systems. © 2013 AIP Publishing LLC.