The Lattice Boltzmann equation Method (LBM) is an alternative approach to the classical Navier-Stokes solvers for fluid flow and works on an equidistant grid of cells, called lattice cells, which interact only with their direct neighbours (He & Luo, 1997). The fluid domain is divided into a rectangular grid or lattice, with the same spacing ‘h’ in both the x- and the y-directions, as shown in the figure. Multiple Relaxation Time (MRT) with Large-Eddy Simulations is used to model turbulent behaviour at high Reynolds number.

The Lattice Boltzmann discretization and D2Q9 scheme: (a) a standard LB lattice; (b) D2Q9 model

Lattice Boltzmann approach can accommodate large grain sizes and the interaction between the fluid and the moving grains can be modelled through relatively simple fluid – grain interface treatments. Further, employing the Discrete Element Method (DEM) to account for the grain – grain interaction naturally leads to a combined LB – DEM procedure (Kumar, Soga, & Delenne, 2012). The Eulerian nature of the LBM formulation, together with the common explicit time step scheme of both LBM and DEM makes this coupling strategy an efficient numerical procedure for the simulation of grain – fluid systems.

Main features

  • 2D Coupled LBM-DEM
  • D2Q9 with Multiple Relaxation Time
  • Large Eddy Simulations for turbulence modelling


  • The 2D version of the LBM-DEM code is now available at GitHub

  • The docker image of the LBM code is available at DockerHub



Krishna Kumar

Assistant Professor, UT Austin

Reihaneh Hosseini

PhD candidate, UT Austin

Qiuyu Wang

PhD candidate, UT Austin


Multiphase lattice Boltzmann modeling of cyclic water retention behavior in unsaturated sand based on X-ray Computed Tomography

Wang, Q., Milatz, M., Hosseini, R., Kumar, K;

The water retention curve (WRC) defines the relationship between matric suction and saturation and is a key function for determining the hydro-mechanical behavior of unsaturated soils. We investigate possible microscopic origins of the water retention behavior of granular soils using both Computed Tomography (CT) experiment and multiphase lattice Boltzmann Method (LBM). We conduct a CT experiment on Hamburg sand to obtain its WRC and then run LBM simulations based on the CT grain skeleton. The multiphase LBM simulations capture the hysteresis and pore-scale behaviors of WRC observed in the CT experiment. Using LBM, we observe that the spatial distribution and morphology of gas clusters varies between drainage and imbibition paths and is the underlying source of the hysteresis. During drainage, gas clusters congregate at the grain surface; the local suction increases when gas clusters enter through small pore openings and decreases when gas clusters enter through large pore openings. Whereas, during imbibition, gas clusters disperse in the liquid; the local suction decreases uniformly. Large pores empty first during drainage and small pores fill first during imbibition. The pore-based WRC shows that an increase in pore size causes a decrease in suction during drainage and imbibition, and an increase in hysteresis.

Investigating the source of hysteresis in the Soil-Water Characteristic Curve using the multiphase lattice Boltzmann method

Hosseini, R., Kumar, K., Delenne, J.Y.;

The soil-water characteristic curve (SWCC) is the most fundamental relationship in unsaturated soil mechanics, relating the amount of water in the soil to the corresponding matric suction. From experimental evidence, it is known that SWCC exhibits hysteresis (i.e. wetting/drying path dependence). Various factors have been proposed as contributors to SWCC hysteresis, including air entrapment, contact angle hysteresis, ink-bottle effect, and change of soil fabric due to swelling and shrinkage, however, the significance of their contribution is debated. From our pore-scale numerical simulations, using the multiphase lattice Boltzmann method, we see that even when controlling for all these factors SWCC hysteresis still occurs, indicating that there is some underlying source that is not accounted for in these factors. We find this underlying source by comparing the liquid/gas phase distributions for simulated wetting and drying experiments of 2D and 3D granular packings. We see that during wetting (i.e. pore filling) many liquid bridges expand simultaneously and join together to fill the pores from the smallest to the largest, allowing menisci with larger radii of curvature (lower matric suction). Whereas, during drying (i.e. pore emptying), only the limited existing gas clusters can expand, which become constrained by the size of the pore openings surrounding them and result in menisci with smaller radii of curvature (higher matric suction).

Effect Of Slope Angle On The Runout Evolution of Granular Column Collapse for Varying Initial Volumes

Wang, Q., Hosseini, R., Kumar, K.;
Proceedings of the 20th International Conference on Soil Mechanics and Geotechnical Engineering, Sydney 2021

In nature, submarine slope failures usually carry thousands of cubic-meters of sediments across extremely long distances and cause tsunamis and damages to offshore structures. This paper uses the granular column collapse experiment to investigate the effect of slope angle on the runout behavior of submarine granular landslides for different initial volumes. A two-dimensional coupled lattice Boltzman and discrete element method (LBM-DEM) approach is adopted for numerically modeling the granular column collapse. Columns with four different slope angles and six different volumes are modelled under both dry and submerged conditions. The effects of hydrodynamic interactions, including the generation of excess pore pressures, hydroplaning, and drag forces and formation of turbulent vortices, are used to explain the difference in the runout behavior of the submerged columns compared to the dry columns. The results show that at any given slope angle, there is a threshold volume above which the submerged columns have a larger final runout compared to their dry counterpart, and this threshold volume decreases with slope angle.

Effect of Initial Volume on the Run-Out Behavior of Submerged Granular Columns

Wang, Q., Hosseini, R., Kumar, K.;
GeoCongress 2021, Dallas, USA

Submarine landslides transport thousands of cubic meters of sediment across continental shelves even at slopes as low as 1° and can cause significant casualty and damage to infrastructure. The run-out mechanism in a submarine landslide is affected by factors such as the initial packing density, permeability, slope angle, and initial volume. While past studies have focused on the influence of density, permeability, and slope angle on the granular column collapse, the impact of volume on the run-out characteristics has not been investigated. This study aims to understand how the initial volume affects the run-out using a two-dimensional coupled lattice Boltzman and discrete element (LBM-DEM) method. The coupled LBM-DEM approach allows simulating fluid flow at the pore-scale resolution to understand the grain-scale mechanisms driving the complex continuum-scale response in the granular column collapse. For submerged granular column collapse, the run-out mechanism is heavily influenced by the interaction between the grains and the surrounding fluid. The development of negative pore pressures during shearing and hydrodynamic drag forces inhibit the flow. On the other hand, entrainment of water resulting in hydroplaning enhances the flow. With an increase in volume, the interaction between the grains and the surrounding fluid varies, causing changes in the run-out behavior. For smaller volumes, the forces inhibiting the underwater flow predominates, resulting in shorter run-outs than their dry counterparts. At large volumes, hydroplaning results in larger run-out than the dry cases, despite the inhibiting effects of drag forces and negative pore pressures.

Investigating the effect of porosity on the soil water retention curve using the multiphase Lattice Boltzmann Method

Hosseini, R., Kumar, K., Delenne, J.Y.;
Powders and Grains 2021, Buenos Aires, Argentina

The soil water retention curve (SWRC) is the most commonly used relationship in the study of unsaturated soil. In this paper, the effect of porosity on the SWRC is investigated by numerically modeling unsaturated soil using the Shan-Chen multiphase Lattice Boltzmann Method. The shape of simulated SWRCs are compared against that predicted by the van Genuchten model, demonstrating a good fit except at low degrees of saturation. The simulated SWRCs show an increase in the air-entry value as porosity decreases.