Calibrated Low-dimensional POD Dynamical Model for Simulation of Unsteady Incompressible Flows

In this paper, reduced order proper orthogonal decomposition method has been used for simulation of unsteady incompressible flow fields. After projection of the governing equations along POD modes, a low-dimensional dynamical system is achieved. Normally, standard low-dimensional models, due to some reasons, do not predict time variations of flow field accurately. Accuracy of dynamical system has been improved by using a linear calibration term. The presented method is based on combination of POD and an optimization problem, which is solved using least square approach. The obtained reduced order model can predict time variations of flow field with relatively fast computational speed and good accuracy. This method is based on a local minimization technique proposed by these authors. The results have been compared with direct numerical simulation (DNS) data and shows good accuracy and simplicity of the computations.