A novel hybrid SPH-DEM scheme with spatiotemporal porosity evolution for cross-scale particulate flows

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Cross-scale particulate flows are widespread in natural and engineering systems and are commonly modeled using SPH-DEM coupling methods. Fully resolved SPH-DEM coupling requires the SPH resolution tens of times smaller than the finest particles, leading to prohibitive computational cost, whereas locally averaged schemes cannot accurately capture near-surface flow and hydrodynamic loads on coarse particles. This study proposes a three-dimensional hybrid SPH-DEM framework that assigns resolved, semi-resolved, or unresolved coupling particle-wise according to the ratio of SPH resolution to DEM particle size. For the semi-resolved and unresolved regimes, a porosity-aware SPH discretization is proposed, this formulation accounts for apparent-density evolution, and evaluates pressure acceleration using intrinsic density. To further support engineering scale simulations, a CUDA-based GPU parallel framework is also implemented. Single-particle settling, hydrostatic, and particle-group water-entry tests verify the accuracy and stability of the constituent schemes and improved formulation. The improved formulation reduces hydrostatic pressure-fluctuation measures by 89.4–91.1 % and lowers the best mean particle-velocity error in the water-entry test from 21.58 % to 5.61 %. Cross-scale tests involving a coarse particle impacting a fine-particle bed and dam-break flow over a sloping bed show improved near-particle flow, bed deformation, and seepage predictions relative to a single locally averaged scheme. For the reference dam-break case, the hybrid model uses 240,350 SPH particles, whereas the examined fully resolved configurations require 5.88–39.04 million. The framework therefore provides an accurate and computationally practical approach for three-dimensional cross-scale particulate flow simulation.