Online Model Order Reduction for Flow Simulations problems using Dynamic Mode Decomposition

Resumo

In this study, a reduced-order model (ROM) was directly coupled with a physical solver to predict system evolution and progressively replace the full-order model (FOM) solutions. Dynamic Mode Decomposition (DMD), implemented via the PyDMD library, was employed to perform the ROM predictions. The flow around a 2D cylinder with Reynolds number Re = 100 was chosen as the case study. The FOM solver uses the FEniCSx platform. The quality of the online DMD model approximation was evaluated using the residual norm generated exclusively by the DMD prediction, ensuring that velocity and pressure predictions remained within an acceptable tolerance. Additionally, the Frobenius norm was employed to monitor the accuracy of the velocity and pressure matrix predictions, assessing DMD’s non-intrusive capability to capture and reproduce the system’s dynamics. Experiments were conducted varying the number of dynamic modes required to achieve the desired accuracy. Using DMD as an alterative to the nonlinear solver reduced the computational time for the numerical simulations up to 20% with little to no loss in the solution quality.