Nonintrusive Model Order Reduction Theory in a Fixed Size Domain with Particle in Fluid Flow Application

High-fidelity numerical simulation of particle-in-fluid systems is critical for engineering applications such as proppant transport in hydraulic fracturing, cuttings transport in drilling, and fluidization processes, but its practical use is often limited by the high computational cost of Eulerian–Lagrangian (CFD (Computational Fluid Dynamics)–DEM (Discrete Element Method)) methods. Although reduced-physics approaches such as Eulerian–Eulerian models offer faster solutions, they typically sacrifice accuracy by oversimplifying particle dynamics. This work introduces a new nonintrusive Reduced Order Modeling (ROM) strategy that integrates Proper Orthogonal Decomposition (POD) with a previously developed nonintrusive model-order reduction framework to achieve substantial computational acceleration while preserving the fidelity of CFD–DEM simulations. Snapshot-based POD is used to extract dominant flow and particle-motion modes from high-resolution simulations, enabling projection operators that reduce the system dimension by two to three orders of magnitude without modifying the underlying solver. Nonintrusive serial and parallel bridges are constructed to link system states along and across trajectories in input space, allowing nonlinear behavior to be retained while enabling rapid prediction. Additional speed-ups are achieved by projecting these bridges into reduced space, resulting in a ROM–ROM framework. The method is validated using a particle–fluid gas blower model with 3,151 particles and a 12,604-dimensional state space. Snapshot data from four simulations are used to construct reduced bases for particle position and velocity, with 30 POD modes preserving approximately 80–85% of system energy. Predictions for a new operating condition show excellent agreement between the ROM–ROM model, nonintrusive full-space predictions, and the full CFD–DEM solution. Performance analysis demonstrates that the ROM–ROM approach is approximately 3×10⁵ times faster than the full CFD–DEM simulation and about 40 times faster than the nonintrusive full-space method. These results confirm that combining POD with nonintrusive trajectory-based reduction provides an efficient and accurate framework for accelerating multiphase particle-transport simulations, with even greater potential gains for larger systems. This study represents the first POD-enabled nonintrusive ROM applied to particle-in-fluid systems with a fixed particle count, enabling fast surrogate models suitable for real-time simulation, optimization, and uncertainty analysis in complex engineering workflows.