Space-time adaptive model order reduction utilizing local low-dimensionality of flow field

The cost of unsteady flow simulations, such as large eddy simulations, has been increasing because of the large number of mesh cells and the use of high-order numerical schemes. In contrast, recent data-driven reduced-order models (ROMs) predict a flow field quickly; however, their application is often limited to relatively simple flow problems. In this study, we investigate space-time adaptive model order reduction for unsteady flow simulation, where full-order Navier-Stokes equations and a proper orthogonal decomposition (POD)-based reduced-order model are adaptively switched in a block-by-block manner on a multi-block Cartesian mesh. The full-order model (FOM) is switched to the ROM when POD modes effectively represent the unsteady flow field in each block. Owing to the local low-dimensionality of a flow field, the degree of freedom of fluid flow in each block can be smaller than that of the entire flow field; hence, the flow field is effectively represented by a small number of POD modes. First, the hybrid FOM/ROM approach is tested with a low-Reynolds-number flow around a circular cylinder, where the reduction in computational time and the accuracy of the simulated flow field are evaluated. We then consider a flow around a circular cylinder with a Reynolds number of 1000, where the flow field is reduced except for the highly unsteady wake. The potential computational advantage of this method is demonstrated by load balancing on a distributed memory computer. In addition, we utilize bred vector dimensions to quantify the degree of freedom of the flow field in each block, which is closely related to whether ROMs effectively reduce the flow field.