Coupled phase-field lattice Boltzmann method and discrete element method for gas–liquid–solid multiphase flows

A methodology combining the lattice Boltzmann method (LBM) and discrete element method (DEM) is proposed to simulate gas–liquid–solid multiphase flows and interphase interactions. Specifically, the phase-field LBM is employed to simulate the fluid flow, incorporating the virtual density boundary method. This method effectively enables the realization of wetting phenomena with relatively small spurious velocities, in comparison with the pseudopotential LBM. The DEM is utilized to simulate the motion of multiple solid particles. As for the interaction between fluid and solid, leveraging the features of LBM, the calculation of fluid forces acting on solids can be achieved by going through all fluid nodes surrounding the solid walls, enabling a straightforward and efficient calculation process. The numerical stability and accuracy of the hybrid LBM-DEM are demonstrated via benchmark cases. It is then applied successfully to simulate the upward migration of leaked gas bubbles through a deformable porous medium composed of solid particles.