POD-Based reduced-order models with deforming grids

Abstract

Proper orthogonal decomposition based reduced order modeling (POD/ROM) is examined with deforming grids. POD/ROM is a technique that operates in an index-space for computations, not typically accounting for grid dynamics. Two model problems are presented to demonstrate the method of accounting for the effects of grid deformation on POD/ROM. The analytical solution of flow about an oscillating cylinder and potential flow over an oscillating panel. The accuracy and robustness of POD/ROM on deforming grids are compared to that of rigid grid POD/ROM. Deforming grid POD/ROMs are found to require more modes than rigid grid POD/ROMs for similar accuracy levels. In addition, for deforming grids, POD/ROMs are less accurate when the grid deformation is significantly altered from the deformations seen in the POD/ROM development. To address these issues, a new technique is developed that compares the relative grid motion between the POD/ROM creation and execution. The technique determines the current relative grid deformation and selects the best POD/ROM from those available.