Application of Proper Orthogonal Decomposition to Variable in Computational Space for Reduced Order Modeling

A reduced order model (ROM) has been widely used as a new approach in computational fluid dynamics (CFD). The ROM estimates a flow field roughly and quickly while the conventional CFD approach obtains the flow field with high accuracy. One of the advantages of CFD is the ability to modify the shape of an object and perform calculations. This enables the optimization of object shape, aiming to increase the lift force and reduce the drag force. However, in conventional CFD, it is necessary to perform a vast number of computations for flow fields around each specific shape. To reduce computational time, one approach is to develop an ROM using a limited number of flow fields under representative conditions. The developed ROM can estimate the flow field with unknown shapes quickly. There are various methods for the development of ROM. An ROM based on the proper orthogonal decomposition (POD) has been studied. The POD is a method to construct a reduced-order space that best represents the snapshots. However, The POD cannot decompose snapshots of flow fields including various computational grids. Therefore, at present, POD-based ROM cannot be utilized in shape optimization. To utilize shape optimization, we propose a POD method that performs decomposition with respect to the velocity in the generalized coordinate system rather than in the Cartesian coordinate system. To be based on the proposed POD, an ROM for flow fields around an object with different shapes is developed.