An optimal projection method for the reduced-order modeling of incompressible flows

A new method to build reduced order models (ROMs) for incompressible flows is addressed in this paper. Proper orthogonal decompositions (PODs) are used to efficiently represent both the fluid velocity and pressure fields with a small number of spatial modes. A minimum-residual projection is then developed for building the reduced models in which the velocity and pressure temporal coefficients are fully coupled. Comparisons of numerical calculations based on the proposed approach with results arising from the classical Galerkin projection are exposed on three fluid flows: a transient ventilated cavity, a periodic lid-driven cavity and a transient mixed convection flow. It is shown that both stability and accuracy of the ROMs are strongly enhance when the minimum-residual projection is used.