A hybrid reduced-order model combing deep learning for unsteady flow

Reduced-order models such as dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) have been extensively utilized to model unsteady flow. Although the major flow patterns can be captured by DMD and POD, due to the linear assumption, the modeling accuracy is low for complex and strongly nonlinear flow structures such as shock wave and vortex. To improve the accuracy and robustness of predicting unsteady flow, this work proposes a novel modeling method based on a hybrid reduced-order model. Since the flow can be regarded as a fusion of the main flow and the residual flow from a modeling perspective, the hybrid reduced-order model is constructed by DMD and POD, which are, respectively, used to obtain different flow properties. First, DMD is applied in describing the main flow, which contains the dominant modes determining most properties of the flow. Then, POD combining the long short-term memory is conceived to model the residual flow that the DMD cannot capture, to further enhance the modeling accuracy. The proposed method is validated by modeling two unsteady flows, which are the flow past a two-dimensional circular cylinder at Reynolds number 100 and the forced oscillation of an airfoil at transonic speed. The results indicate that the proposed method with proper modeling efficiency gains better accuracy and robustness than the existing methods. In particular, this approach has better forecasting accuracy of shock wave and vortex.