A co-located incompressible Navier–Stokes solver with exact mass, momentum and kinetic energy conservation in the inviscid limit

Abstract

The incompressible Navier-Stokes equations conserve mass, momentum, and kinetic energy in the inviscid limit. Therefore, numerical methods should attempt to mimic these conservation properties as well. There exists many well-established methods with exact conservation properties based on staggered grids, but existing methods based on co-located grids introduce numerical dissipation in order to yield smooth pressure fields. In the present work, a novel method that utilizes null space vectors to yield a smooth pressure field is presented. The method exactly preserves mass, momentum, and kinetic energy on co-located grids.