In this paper, two Galerkin projection based reduced basis approaches are investigated for the reduced-order modeling of parameterized incompressible Navier-Stokes equations for laminar transient flows. The first approach solves only the reduced momentum equation with additional, physics-based approximations for the dynamics of the pressure field. On the other hand, the second approach solves both the reduced momentum and continuity equations. The reduced bases for the velocity and pressure fields are generated using the method of snapshots combined with Proper Orthogonal Decomposition (POD) for data compression. To remedy the stability issues of the two-equation model, the reduced basis of the velocity is enriched with supremizer functions. Both reduced-order modeling approaches have been implemented in GeN-Foam, an OpenFOAM-based multi-physics solver. A numerical example is presented using a two-dimensional axisymmetric model of the Molten Salt Fast Reactor (MSFR) and the dynamic viscosity as the uncertain parameter.
The results indicate that the one-equation model is slightly more accurate in terms of velocity, while the two-equation model, built with the same amount of modes for the velocity, is far more accurate in terms of pressure. The speed-up factors for the reduced-order models are 3060 for the one-equation model and 2410 for the two-equation model.