Extension Ability of Reduced Order Model of the Unsteady Incompressible Flows Using Combination ...

In this article, a new low-dimensional modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along POD modes, a dynamical system is obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. To improve the response of the dynamical system a calibration method based on a least square optimization process, was used. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least square procedure is a combination of POD method with solution of an optimization problem and the obtained model can predict accurate time variations of flow field with high speed. For the long time periods, the calibration term is computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has been proposed by the authors recently. The results obtained from the calibrated low-dimensional model show close agreements to the benchmark DNS data and proving high accuracy of our model.