On lift and drag decomposition coefficients in a model reduction framework using pressure-mode decomposition (PMD) analysis

Proper orthogonal decomposition (POD) has been extensively used for developing reduced-order models (ROM) in fluid mechanics. In most of the research, velocity POD modes are employed for analysis while there is less focus on using pressure POD modes. In fact, pressure POD modes can be beneficial to gain physical insight to the aerodynamic forces acting on a structure. In this study, we simulate the flow past a circular cylinder and compute the velocity and pressure POD modes from the data ensemble. We then perform the novel process of pressure mode decomposition (PMD). We consider the localized pressure POD modes on the cylinder surface, integrate each mode on the cylinder surface, and decompose them into normal and streamwise components, namely lift (LDC) and drag (DDC) decomposition coefficients, respectively. The LDC and DDC are scalar quantities and are independent of spatial coordinates. These coefficients provide insight to the contribution of each mode in the development of aerodynamic forces. The lift and drag coefficients are expanded in a Galerkin fashion using the decomposition coefficients. The temporal coefficients are computed through a mapping function based on a quadratic stochastic estimator. The main contribution and strength of our research is the PMD analysis and to develop an efficient ROM for aerodynamic forces which shows promising results for circular and elliptic cylinders.