On the implicit immersed boundary method in coupled discrete element and lattice Boltzmann method

Abstract

The coupled discrete element method and lattice Boltzmann method (DEMLBM) has increasingly drawn attention of researchers in geomechanics due to its mesoscopic nature since 2000. Immersed boundary method (IBM) and immersed moving boundary (IMB) are two popular schemes for coupling fluid particle in DEMLBM. This work aims at coupling DEM and LBM using the latest IBM algorithm and investigating its accuracy, computational efficiency, and applicability. Two benchmark tests, interstitial fluid flow in an ideal packing and single particle sedimentation in viscous fluid, are carried out to demonstrate the accuracy of IBM through semi-empirical Ergun equation, finite element method (FEM), and IMB. Then, simulations of particle migration with relatively large velocity in Poiseuille flow are utilized to address limitations of IBM in DEMLBM modeling. In addition, advantages and deficiencies of IBM are discussed and compared with IMB. It is found that the accuracy of IBM can be only guaranteed when sufficient boundary points are used and it is not suitable for geomechanical problems involving large fluid or particle velocity.discrete element method, fluid-solid interaction, immersed boundary method, immersed moving boundary, lattice Boltzmann method | INTRODUCTIONThe fluid-solid interaction (FSI) is frequently encountered in geotechnical engineering. Its complexity stems from the interaction between pore fluid and grains which consist of geomaterials like soil and rock. Liquefaction, soil erosion, and sand production are typical geomechanical problems which involve strong pore fluid-particle coupling. However, microscopic investigations for such kind of problems in laboratory experiments are extremely hard due to the limitation of current techniques. As an alternative, the numerical method, like the discrete element method (DEM) 1 or bonded particle method (BPM), 2 has been proved to be useful for modeling geomaterials at the grain level. Since the 1980s, there have been several fluid approaches proposed for solving pore fluid flow and its coupling with solid particles in the framework of DEM.Hakuno and Tarumi 3 first combined DEM and Darcy fluid flow (DFF) to analyze liquefaction of saturated sands under seismic excitation. In this method, the excess pore water pressure was taken into account by tracing /journal/nag the change of individual pore volumes formed by neighboring particles and the dissipation of excess pore water pressure was accomplished by two permeability coefficients for water moving through pores. However, only the tendency of gradually increased excess pore water pressure was captured and the fully liquefaction condition was not observed. In order to avoid the complicated individual pore volume calculation, an alternative method was proposed to consider the generation of excess pore water pressure at cell level rather than at pore level. 4 Applications of DEM-DFF in undrained behaviors of saturated sands and upward seepage were performed by Shafipour and Soroush 5 and Goodarzi et al. 6 However, this co...

Particulate Modeling of Sand Production Using Coupled DEM-LBM

“…Practically, a fluid flow with Ma ≤ 0.1 is assumed to be incompressible [59]. The computational Mach number in LBM models can be calculated as [60,61]:…”

Instability and treatments of the coupled discrete element and lattice Boltzmann method by the immersed moving boundary scheme

“…However, hydrodynamic forces were seldom given in the literature. Our recent work 27 reported that some IBM schemes are capable of obtaining smooth profiles of particle position and velocity but unexpected oscillation of computed hydrodynamic forces can be found.…”

“…Instead of a fixed iteration number in the fixed multidirect forcing IBM, a flexible subiteration for the velocity correction is terminated when the convergence limit is satisfied. However, oscillation of hydrodynamic forces can be found in this flexible implicit IBM, especially in flows with large Reynolds number 27 …”

“…However, oscillation of hydrodynamic forces can be found in this flexible implicit IBM, especially in flows with large Reynolds number. 27 To eliminate the obvious oscillation of hydrodynamic forces observed in the modified half-way bounce-back method, an immersed moving boundary (IMB), 28 also called the partially saturated method, was proposed. In this method, a weighting function associated with a nodal solid area was introduced to smoothly represent the boundary profile of a solid particle.…”

Effect of gas content in macropores on hydraulic fracturing in rocks using a fully coupled DEM/CFD approach

“…Hu et al 13 applied FVM (OpenFOAM) for investigating both the kinetics of fines' removal and the micromechanisms of suffusioninduced deformation of soils. Intensive research works have also been carried out by applying LBM in coupling with DEM [14][15][16][17][18] To model a seepage-induced fine particle migration through the skeleton formed of coarse particles, Cheng et al 19 proposed a semi-resolved CFD-DEM model, wherein a resolved fictitious domain method was used to resolve the fluid flow around coarse particles and an unresolved method based on a locally averaging theory was adopted to describe interactions between fine particles and fluid flow. To study the complicated impacts of debris flow on flexible barriers, Li and Jidong 20 proposed a discrete-based approach to couple CFD with DEM, wherein they solved the continuity equation and the locally averaged Navier-Stokes equation in a discretized fluid domain.…”