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

Abstract

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.

Future challenges on focused fluid migration in sedimentary basins: Insight from field data, laboratory experiments and numerical simulations

“…4b, C) for an initially homogeneous granular layer. The current work focuses on modelling an interface between two layers -a challenge accessible to this method, which has recently been developed to capture the interface between two non-miscible fluids during their migration [118].…”

Numerical analysis of the drag on a rigid body in an immersed granular flow

“…where v is the volume-averaged fluid velocity, ρ f its density, η its dynamic viscosity, d the deformation rate tensor, p the pressure, I the identity tensor, f the fluid-grain interaction force, and g the acceleration due to gravity. These equations are solved with a PSPG-SUPG stabilised P1-P1 Finite Element Method that is corrected for incompressibility with a LSIC term [17]. The currently used volume-averaging process requires the elements to be larger than the grains, but progress has been made that may suppress this constrain [15].…”

“…For the sake of computational convenience, the fluid and the granular solvers are explicitly coupled. A predictor corrector scheme, detailed in [17], is used to improve the overall stability. However, with such an explicit coupling, the interaction force is still unstable.…”

Numerical investigation of the density sorting of grains using water jigging

“…In the following simulations, a perfectly inelastic collision law is considered without restitution coefficient. More details about the model and its validation are presented in [26,27].…”

“…where the notation < •, • > is used for the L 2 -inner product on the domain Ω while S p and S u hold for the stabilization terms needed to use equal order interpolation functions. More information about the numerical implementation of the model are described in [27]. The right-hand terms A, B, E, G are the boundary terms obtained from the integration by part of the gradient and divergence terms for which the notation •, • Γ is used to specify the L 2 -inner product on the boundary Γ = Γ l ∪ Γ b ∪ Γ t .…”