Calibrated reduced-order POD-Galerkin system for fluid flow modelling

To improve the behaviour of reduced-order proper orthogonal decomposition (POD)-Galerkin systems, two numerical methods are proposed. These methods determine free parameters in the POD-Galerkin system from flow simulations via a minimization problem. They give rise to linear systems and their computational costs are reasonable. Both methods are assessed for two flow configurations: a two-dimensional flow around a square-cylinder for a Reynolds number of 100 and a three-dimensional flow past a backward-facing step for a Reynolds number of 7432 based on the step height and the streamwise velocity at the middle of the inlet. For both configurations, the methods are effective since accurate calibrated reduced-order POD-Galerkin systems are obtained.