Physics-informed dynamic mode decomposition for reconstruction and prediction of dense particulate pipe flows

Dynamic mode decomposition (DMD) effectively captures the growth and frequency characteristics of individual modes, enabling the construction of reduced-order models for flow evolution, thereby facilitating the prediction of fluid dynamic behavior. However, DMD's predictive accuracy is inherently constrained by its inability to inherently incorporate physical principles. Therefore, for dense particulate pipe flows with complex flow mechanisms, we introduce a physics-informed dynamic mode decomposition (PIDMD) approach, which augments the purely data-driven DMD framework by incorporating the conservation of mass as a constraint. This ensures that the extracted dynamic modes adhere to known physical principles. Initially, we apply the DMD to reconstruct and predict the velocity field, comparing the results against benchmark computational fluid dynamics-discrete element method (CFD-DEM) simulations. Findings indicate that while DMD can reconstruct the flow field simulated by CFD-DEM and provide predictions of future flow states, its predictive accuracy gradually deteriorates over time. Next, we utilize both PIDMD and DMD to reconstruct and predict particle volume fraction, evaluating both models based on CFD-DEM outcomes. The results indicate that both PIDMD and DMD can predict particle aggregation toward the center, but PIDMD provides more accurate predictions regarding the size of particle aggregations and their distribution near the tube wall. Furthermore, the average prediction error for particle volume fraction using PIDMD is 6.54%, which is lower than the error of 13.49% obtained by DMD. Both qualitative and quantitative comparisons highlight the superior predictive capability of PIDMD. The methodology developed in this study provides valuable insights for high-precision predictions of particulate flows.