Reconstruction of Gappy Unsteady Flow Fields using Improved Reduced Order POD Model based on Temporal Decomposition Procedure

In this paper, the proper orthogonal decomposition method has been used for gappy data reconstruction of the unsteady incompressible viscous flow and calculation of related forces (such as aerodynamics coefficients). The present approach is based on combination of POD method and solution of an optimization problem to get a reduced order model. This model reconstructs missed data or incomplete snapshots with relevant accuracy and fast speed. Two kinds of model have used in this manner. In the first approach, a simple iterative approach is used to reconstruct of the relative missed or incomplete basis functions of snapshots ensemble. The Second method, which is proposed recently by the author, used a time advancing and domain decomposition method along time direction, for reconstruction of incomplete ensemble members with high missing percentage. Essential trait of this method is about application of step by step reconstruction of primary ensemble to reduce number of unknown variables and obtaining an accurate model to recover the missed data. The outcome results of two approaches have compared with direct simulation CFD data which are shown appropriate ability and good agreement