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A novel reduced order model (ROM) for incompressible flows is developed byperforming a Galerkin projection based on a fully (space and time) discretefull order model (FOM) formulation. This 'discretize-then-project' approachrequires no pressure stabilization technique (even though the pressure term ispresent in the ROM) nor a boundary control technique (to impose the boundaryconditions at the ROM level). These are two main advantages compared toexisting approaches. The fully discrete FOM is obtained by a finite volumediscretization of the incompressible Navier-Stokes equations on a collocatedgrid, with a forward Euler time discretization. Two variants of the timediscretization method, the inconsistent and consistent flux method, have beeninvestigated. The latter leads to divergence-free velocity fields, also on theROM level, whereas the velocity fields are only approximately divergence-freein the former method. For both methods, accurate results have been obtained fortest cases with different types of boundary conditions: a lid-driven cavity andan open-cavity (with an inlet and outlet). The ROM obtained with the consistentflux method, having divergence-free velocity fields, is slightly more accuratebut also slightly more expensive to solve compared to the inconsistent fluxmethod. The speedup ratio of the ROM and FOM computation times is the highestfor the open cavity test case with the inconsistent flux method.

Reduced order models for the incompressible Navier-Stokes equations on collocated grids using a 'discretize-then-project' approach