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We propose a novel artificial compression, reduced order model (AC-ROM) for the numerical simulation of viscous incompressible fluid flows. The new AC-ROM provides approximations not only for velocity, but also for pressure, which is needed to calculate forces on bodies in the flow and to connect the simulation parameters with pressure data. The new AC-ROM does not require that the velocity-pressure ROM spaces satisfy the inf-sup (Ladyzhenskaya-Babuska-Brezzi) condition and its basis functions are constructed from data that are not required to be weaklydivergence free. We prove error estimates for the reduced basis discretization of the AC-ROM. We also investigate numerically the new AC-ROM in the simulation of a two-dimensional flow between offset cylinders.

Grad-div stabilization, adding a term −γ grad div u, has proven to be a useful tool in the simulation of incompressible flows. Such a term requires a choice of the coeffiecient γ and studies have begun appearing with various suggestions for its value. We give an analysis herein that provides a

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