  We compare three iterative pressure correction schemes for solving the
Navier-Stokes equations with a focus on exactly divergence free solution with
higher order discontinuous Galerkin discretisations. The investigated schemes
are the incremental pressure correction scheme on the standard differential
form (IPCS-D), the same scheme on algebraic form (IPCS-A), and the
semi-implicit method for pressure linked equations (SIMPLE). We show
algebraically and through numerical examples that the IPCS-A and SIMPLE schemes
are exactly mass conserving due to the algebraic pressure correction, while the
IPCS-D scheme cannot be exactly divergence free due to the stabilisation terms
required in the pressure Poisson equation. The SIMPLE scheme requires a
significantly higher number of pressure correction iterations to obtain
converged results than the IPCS-A scheme, so for efficient and mass conserving
simulation the IPCS-A method is the best option among the three evaluated
schemes.
