  Projection-based reduced order models rely on offline-online model
decomposition, where the data-based energetic spatial basis is used in the
expensive offline stage to obtain equations of reduced states that evolve in
time during the inexpensive online stage. The online stage requires a solution
method for the dynamic evolution of the coupled system of pressure and velocity
states for incompressible fluid flows. The first contribution of this article
is to demonstrate the applicability of the incremental pressure correction
scheme for the dynamic evolution of pressure and velocity states. The evolution
of a large number of these reduced states in the online stage can be expensive.
In contrast, the accuracy significantly decreases if only a few reduced states
are considered while not accounting for the interactions between unresolved and
resolved states. The second contribution of this article is to compare three
closure model forms based on global, modal and tensor artificial viscosity
approximation to account for these interactions. The unknown model parameters
are determined using two calibration techniques: least squares minimization of
error in energy approximation and closure term approximation. This article
demonstrates that an appropriate selection of solution methods and data-driven
artificial viscosity closure models is essential for consistently accurate
dynamics forecasting of incompressible fluid flows.
