We develop an on-the-fly reduced-order model (ROM) integrated with a flow simulation, gradually replacing a corresponding full-order model (FOM) of a physics solver. Unlike offline methods requiring a separate FOM-only simulation prior to model reduction, our approach constructs a ROM dynamically during the simulation, replacing the FOM when deemed credible. Dynamic mode decomposition (DMD) is employed for online ROM construction, with a single snapshot vector used for rank-1 updates in each iteration. Demonstrated on a flow over a cylinder with Re = 100, our hybrid FOM/ROM simulation is verified in terms of the Strouhal number, resulting in a 4.4 times speedup compared to the FOM solver.

翻译：我们开发了一种与流场模拟集成的在线降阶模型(ROM)，能够逐步替换物理求解器中对应的全阶模型(FOM)。与需要先在纯FOM模拟中进行模型降阶的离线方法不同，我们的方法在模拟过程中动态构建ROM，并在其可靠性得到验证后替代FOM。采用动态模态分解(DMD)进行在线ROM构建，每次迭代使用单个快照向量实现秩1更新。通过在雷诺数Re=100的圆柱绕流问题上的验证，混合FOM/ROM模拟的斯特劳哈尔数得到确认，相比FOM求解器实现了4.4倍的加速比。