  A method for post-processing the velocity after a pressure projection is
developed that helps to maintain stability in an under-resolved, inviscid,
discontinuous element-based simulation for use in environmental fluid mechanics
process studies. The post-processing method is needed because of spurious
divergence growth at element interfaces due to the discontinuous nature of the
discretization used. This spurious divergence eventually leads to a numerical
instability. Previous work has shown that a discontinuous element-local
projection onto the space of divergence-free basis functions is capable of
stabilizing the projection method, but the discontinuity inherent in this
technique may lead to instability in under-resolved simulations. By enforcing
inter-element discontinuity and requiring a divergence-free result in the weak
sense only, a new post-processing technique is developed that simultaneously
improves smoothness and reduces divergence in the pressure-projected velocity
field at the same time. When compared against a non-post-processed velocity
field, the post-processed velocity field remains stable far longer and exhibits
better smoothness and conservation properties.
