Comparison of the three main multifluid extensions of the lattice Boltzmann method used for modeling unsaturated soils

The complex behavior of unsaturated soils is closely linked to the distribution of the two fluids, water and air, within their pore space. Pore-scale modeling of the fluid distribution can therefore be beneficial for advancing unsaturated soil mechanics. The Lattice Boltzmann Method (LBM) is a popular choice for such modeling, due to its simplicity and computational efficiency. Several extensions of the single-phase LBM have been proposed to model multifluid systems; however, there is no clear consensus on which formulation is most suitable for simulations of unsaturated soils. The objective of this study is to compare the three multifluid approaches commonly used in the field: multiphase Shan–Chen (MPSC), multi-component Shan–Chen (MCSC), and He–Chen–Zhang (HCZ). All three approaches are implemented within an in-house LBM code and are carefully calibrated to ensure consistent interfacial properties. The methods are then applied to simulate drainage and imbibition in a two-dimensional granular packing. Their performance is evaluated in terms of their ability to reproduce pore-scale fluid distributions as well as their computational efficiency. A simple physical model is additionally used to provide qualitative verification of the simulated fluid configurations. The results indicate that, for the capillarity-dominated, quasi-static simulations examined in this study, the MPSC approach provides the most favorable balance between accuracy and computational efficiency.