  We develop an on-the-fly reduced-order model (ROM) integrated with a flow
simulation, gradually replacing a corresponding full-order model (FOM) of a
physics solver. Unlike offline methods requiring a separate FOM-only simulation
prior to model reduction, our approach constructs a ROM dynamically during the
simulation, replacing the FOM when deemed credible. Dynamic mode decomposition
(DMD) is employed for online ROM construction, with a single snapshot vector
used for rank-1 updates in each iteration. Demonstrated on a flow over a
cylinder with Re = 100, our hybrid FOM/ROM simulation is verified in terms of
the Strouhal number, resulting in a 4.4 times speedup compared to the FOM
solver.
