Simulation of air invasion in immersed granular beds with an unresolved FEM–DEM model

This paper is devoted to an unresolved model for the simulation of air invasion in immersed granular flows without interface reconstruction between the liquid and the gas. Experiments of air invading a granular bed immersed in ethanol were achieved in a Hele-Shaw cell to observe the gas invasion paths and to calibrate the numerical multiscale model. The grains movements are computed at a fine scale using the non-smooth contact dynamics method, a time-stepping method considering impenetrable grains. The fluid flow is modelled by equations averaged using the volume fraction of fluid and computed at a coarse scale with the finite element method. A phase indicator function is used to dissociate the gas and the liquid constituting the fluid and to compute the density and viscosity of the fluid at each position. It is moved using a convection equation at each time step. The fluid, solid and phase indicator function computations are validated on simple cases before being used to reproduce experiments of air invasion in immersed granular flows. The experiments are supported by simulations in two dimensions to refine the study and the understanding of the invasion dynamics at short times.