Development and validation of a multi-timescale reduced-order model for high-speed simulations of solid–fluid systems

The discrete element method coupled with computational fluid dynamics (DEM-CFD) method has been extensively employed as the standard numerical approach to scientifically elucidate complex solid–fluid systems. However, the excessive computational cost of DEM-CFD simulations is one of the essential problems to clarify the dominant phenomena efficiently. Recently, the data-driven reduced-order models (ROMs) have been developed to accelerate computational efficiency. Nevertheless, ROMs have critical problems such as the decision of time step for each physical variables since the dynamics of distinct physical variables feature different timescales. Indeed, this fact is true without exception of the ROM-based DEM-CFD method. To resolve this inherent problem of ROM, a novel multi-timescale ROM (MT-ROM) is proposed for the DEM-CFD simulation, employing an error-estimation-based algorithm to optimize the timescale for each variable individually, enabling high-speed and high-accuracy simulations with the optimally required snapshots. Validated in two typical solid–liquid and gas–solid flow systems, namely a bead mill and a fluidized bed, MT-ROM achieves extremely high acceleration over the traditional DEM-CFD method while preserving adequate fidelity for a wide range of physical variables. The criterion for reliable MT-ROM simulations is also established for physical variables in DEM-CFD simulations. The proposed MT-ROM effectively leverages the advantages of data-driven modeling through a common error estimation approach. Ultimately, our proposed MT-ROM makes it feasible to clarify the complex phenomena for solid–fluid mixture systems efficiently and scientifically.