Fractional dynamics and nonlinear mixing in multi-phase porous flow: A hybrid SPH–machine learning framework

This study investigates the dynamics of multi-phase porous flow using a hybrid numerical and machine learning approach. The incompressible smoothed particle hydrodynamics (ISPH) method is employed to simulate fluid-porous interactions. The research examines the effects of density ratios (ρX,ρY), porosity (εX,εY), resistance parameters (α,β), and fractional time-order parameters (αfrac) on wavefront propagation, energy dissipation, and mixing efficiency. Results show that high-density contrasts (ρX=1.6) generate forceful wavefronts and enhanced mixing due to increased gravitational forces and momentum, while lower density ratios (ρX=1.0) result in slower, laminar-like flows. Porosity (ε) governs flow resistance and permeability, with high porosity facilitating rapid wave propagation and low porosity restricting fluid transport, creating localized energy dissipation. Resistance parameters (α,β) significantly impact flow behavior, with higher values increasing drag and suppressing wavefront dynamics, while lower values promote faster propagation and efficient fluid redistribution. The fractional time-order parameter introduces memory effects, tuning temporal diffusion and influencing wavefront progression. The XGBoost model successfully predicts nonlinear wavefront dynamics, achieving low mean squared error (MSE) and deviation rates across diverse parameter variations. This study offers critical insights for optimizing systems involving density-driven flows, porous structures, and fractional-order dynamics. Applications range from environmental fluid mechanics and coastal defense to industrial mixing and groundwater remediation. Future research could extend these findings to three-dimensional domains and integrate advanced machine learning techniques for enhanced predictive capabilities.