  In this paper we consider discontinuous Galerkin (DG) methods for the
incompressible Navier-Stokes equations in the framework of projection methods.
In particular we employ symmetric interior penalty DG methods within the
second-order rotational incremental pressure correction scheme. The major focus
of the paper is threefold: i) We propose a modified upwind scheme based on the
Vijayasundaram numerical flux that has favourable properties in the context of
DG. ii) We present a novel postprocessing technique in the Helmholtz projection
step based on $H(\text{div})$ reconstruction of the pressure correction that is
computed locally, is a projection in the discrete setting and ensures that the
projected velocity satisfies the discrete continuity equation exactly. As a
consequence it also provides local mass conservation of the projected velocity.
iii) Numerical results demonstrate the properties of the scheme for different
polynomial degrees applied to two-dimensional problems with known solution as
well as large-scale three-dimensional problems. In particular we address
second-order convergence in time of the splitting scheme as well as its
long-time stability.
