A novel liquid–gas–solid computational fluid dynamics-discrete element method-volume of fluid coupling method with compressible fluid phases.

This article presents a novel three-phase coupling method integrating computational fluid dynamics (CFD), discrete element method (DEM), and volume of fluid (VOF) techniques, explicitly accounting for the compressibility of both liquid and gas phases via a unified equation of state. The method rigorously derives the α transport and continuity equations incorporating compressibility effects and employs a fractional step solution strategy based on the MULES algorithm. Validation against benchmark cases—including particle sedimentation from gas to liquid, dam break, and particle block water entry—demonstrates the model's accuracy and mass conservation capabilities. Application to unsaturated soil loading reveals that significant water level rise occurs only after deep soil disturbance, with pore pressure and particle-fluid velocity responses varying spatially and influenced by liquid compressibility coefficients. The study highlights the method's potential for improved simulation of multiphase flows in geotechnical and engineering contexts, recommending future enhancements through more advanced equations of state and broader application scenarios.