An Artificial Compression Reduced Order Model
For computational fluid dynamics practitioners, this method simplifies ROM construction by removing the inf-sup condition, but the improvement is incremental as it adapts existing artificial compression techniques to reduced order modeling.
The paper introduces an artificial compression reduced order model (AC-ROM) for viscous incompressible flows that provides both velocity and pressure approximations without requiring inf-sup stable ROM spaces or weakly-divergence-free data. Numerical tests on 2D flow between offset cylinders demonstrate its effectiveness.
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 weakly-divergence 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.