Toward a Hybrid Vortex Simulation Approach with Mode Decomposition

Turbulence contains vortices with a broad range of spatial and temporal scales, which leads to expensive simulations when resolving all features in these flows. Accordingly, data-driven methods that model system dynamics from existing data have recently been of great interest to researchers. This study proposes a hybrid vortex simulation approach that combines classic vortex methods with proper orthogonal decomposition (POD) or Koopman mode decomposition (KMD). We seek a data-driven model that balances efficiency and accuracy. To automate the selection of the model parameter values, we record total circulation, enstrophy, and angular impulse and solve their theoretical evolution equations. We first test the robustness of selecting each of the above three flow quantities to assess the accuracy of the approach. We then verify that POD/KMD eigenvalues recover the correct time scales of the flow systems. Finally, we analyze the model performance by simulating the merger of uniform, patch-like co-rotating vortex pairs under different Reynolds numbers. This approach has the potential to be beneficial for solving flows with fine features in large domains.