Calibration the Effects of Non-Divergence Free and High Level Energy Modes in POD Reduced Order Model of Incompressible Flows Using Adjoint Continuity Equation

In this paper the POD method has been used for development of a reduced order model of the unsteady incompressible flow fields. After projection of the governing equations along POD modes, a low-dimensional dynamical system is achieved. Due to variations in energy level of POD modes and large differencing in modes’ energy, the outcome dynamical system can be converted to a reduced order model with a few amount of error. The standard low-dimensional models, due to some reasons, do not predict time variations of flow field accurately. One of these reasons is due to non-divergence free modes. Accuracy of dynamical system has been improved by using combined form of continuity and linear momentum equations which has been proposed by the author. The obtained reduced order model can predict time variations of flow field with fast computational speed and relatively good accuracy. The results from this low-dimensional model have been compared with direct numerical simulation data and shown good accuracy and salient simplicity in computations.