Description of Reynolds number dependence by a reduced-order model based on stepped proper orthogonal decomposition

Abstract

This paper presents a reduced-order model (ROM) based on proper orthogonal decomposition (POD) for a dataset containing flow around a cylinder at various Reynolds numbers to represent the Reynolds number dependence. Even when the dataset contains the numerous flow fields with different Reynolds numbers, the ROM using the POD modes cannot accurately predict the flow field. To address this problem, a novel ROM framework is proposed that does not lack accuracy when using datasets containing enough flow fields. Our ROM obtains a set of POD modes from a single Reynolds number flow field in the dataset. To predict the flow field by the ROM, we select only two of these sets of POD modes with Reynolds numbers close to the predicted conditions and perform POD for those modes in the second stage. Our ROM accurately describes the Reynolds number dependence and is significantly faster than the conventional methods, even accounting for the computational time to perform a second stage POD.