Calibration of Reduced Order POD Model of Unsteady Incompressible Laminar Flow Using Pressure Representation as a Function of Velocity Field Modes

In this study, the proper orthogonal decomposition has been used to develop a reduced order model of the unsteady incompressible flows. After projection of governing equations along high level energy modes, a low-dimensional dynamical system is constructed. Usually, this model is developed using velocity field modes therefore pressure term representation in momentum equation will have an important role for stability and accuracy of outcome reduced order model. Two approaches are available for pressure term deputation, the first is based on elimination of pressure term due to homogenous condition on control volume boundaries and the second used appropriately method for pressure term representation in momentum equation. The method, which is used in this research, is based on using pressure snapshots and velocity field modal coefficients for calculation pressure field modes. The obtained results from proposed model have been compared with related DNS results. Because the instability behavior of reduced order model is not only related to pressure term modeling therefore response of low-dimensional dynamical system is not exactly verified with DNS data. But the outcome results from proposed model have higher accuracy than classic reduced order models.