Benchmark cases for a multi-component Lattice–Boltzmann method in hydrostatic conditions

Hydrostatic properties of partially saturated granular materials at the pore scale are evaluated by the lattice Boltzmann method (LBM) using Palabos implementation of the multi-component multiphase Shan-Chen model. Benchmark cases are presented to quantify the discretization errors and the sensitivity to geometrical and physical properties. This work offers practical guidelines to design LBM simulations of multiphase problems in porous media. Namely, a solid walls retraction procedure is proposed to reduce discretization errors significantly, leading to quadratic convergence. On this basis the equilibrium shapes of pendular bridges simulated numerically are in good agreement with the Young-Laplace equation. Likewise, entry capillary pressure and meniscus profiles in tubes of various cross-sectional shapes are in agreement with analytical predictions. The main points of this article are summarized as: • Benchmark cases for a multi-component Lattice-Boltzmann method are illustrated to be a guideline to calibrate the method in hydrostatic conditions. • A wall retraction procedure is introduced to minimize discretization errors.