Commutation error in reduced order modeling of fluid flows (Q2305543)

Reduced-order modeling (ROM) is an efficient method for numerical simulations of fluid flows, by reducing the state space dimension. However, it could be inaccurate when the ROM dimension is too low to capture the relevant flow features. Luckily, this can be remedied by ROM spatial filters. This paper studies the commutation error (CE) of ROM with two types of ROM spatial filters (the ROM differential filter and the ROM projection filter) and finds out that CE has a significant effect on the ROM development for low Reynolds numbers, but not so much for higher Reynolds numbers.