Wj. Rider, FILTERING NON-SOLENOIDAL MODES IN NUMERICAL-SOLUTIONS OF INCOMPRESSIBLE FLOWS, International journal for numerical methods in fluids, 28(5), 1998, pp. 789-814
Solving the incompressible Navier-Stokes equations requires special ca
re if the velocity field is not discretely divergence-free. Approximat
e projection methods and many pressure Poisson equation methods fall i
nto this category. The approximate projection operator does not dampen
high frequency modes that represent a local decoupling of the velocit
y held. For robust behavior, filtering is necessary. This is especiall
y true in two instances that were studied: long-term integrations and
large density jumps. Projection-based filters and velocity-based filte
rs are derived and discussed. A cell-centered velocity filter, in conj
unction with a vertex-projection filter, was found to be the most effe
ctive in the widest range of cases. (C) 1998 John Wiley & Sons, Ltd.