Comparison and applications of solid weighting functions for fluid-particle modeling using the lattice Boltzmann-discrete element coupling method

• A comparison of the solid weighting functions for moving solid boundaries is presented. • The viscosity-dependence and convergence of the solid weighting functions are analysed. • The settlement of a particle pack is investigated and the settling velocity has a non-monotonic variation with the solid volume fraction. • A parametric study on the sub-grid technique is demonstrated. This paper presents a comparative study of the solid weighting functions within the text of the partially saturated method, which is an effective fluid-solid boundary condition in the lattice Boltzmann-discrete element coupling method (LBM-DEM). In its original form, the solid weighting function is τ dependent. Past studies have shown that the computational drag is viscosity-dependent when using the τ -dependent solid weighting function to solve fluid-particle interactions. To address this issue, two modified solid weighting functions, namely, the higher-order function and the solid-coverage function, are proposed. Nevertheless, the literature lacks a comparison of these functions, especially for viscosity dependence. In this study, the solid weighting functions are implemented and tested through two benchmark multiphase configurations, i.e., a sphere settling between two parallel plates and the ‘drafting, kissing and tumbling’ of two settling spheres. The computational accuracy, viscosity dependence and convergence of the two modified functions are validated and compared against the original τ -dependent function. The LBM-DEM-MPSM formulation is then applied to study the settling behavior of a particle pack with varying solid fractions in a narrow fracture, which highlights the potential of employing the LBM-DEM-MPSM approach to a broader range of fluid-particle systems.