Reduced order models for the incompressible <scp>Navier‐Stokes</scp> equations on collocated grids using a ‘discretize‐then‐project’ approach

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on fully (space and time) discrete full (FOM) formulation. This ‘discretize-then-project’ approach requires no pressure stabilization technique (even though the term present in ROM) nor boundary control (to impose conditions at ROM level). These are two main advantages compared to existing approaches. The FOM obtained finite volume discretization of Navier-Stokes equations collocated grid, with forward Euler time discretization. Two variants method, inconsistent consistent flux have been investigated. latter leads divergence-free velocity fields, also level, whereas fields only approximately former method. For both methods, accurate results test cases different types conditions: lid-driven cavity an open-cavity (with inlet outlet). having slightly more but expensive solve speedup ratio computation times highest open case