Analysis of two partially-saturated-cell methods for lattice Boltzmann simulation of granular suspension rheology

The lattice Boltzmann method (LBM) has been widely used to simulate fluid--solid flows with various approaches to couple the two phases. We study the partially-saturated-cell (PSC) approach proposed by Nobel and Torcznski [A lattice-Boltzmann method for partially saturated computational cells. International Journal of Modern Physics, 9(8):1189--1201, 1998],
which modifies the LB equation by an additional solid collision term weighted by the lattice solid fraction. We analyse two different PSC schemes with regard to its capability of accurately computating the hydrodynamic stresslet, which is essential to computing the stress, hence the rheology of suspensions of granular particles. Through simulations of single and pair particles in a simple shear flow field, we show that a commonly used solid collision term based on non-equilibrium bounce-back fails to correctly capture the stresslet, although can result in a numerically accurate hydrodynamic torque, when compared to the analytical solutions. In contrast,
a model using superposition, which has neither hitherto been analysed nor extensively applied, is demonstrated to be able to accurately calculate both the stresslet and the torque. We finally highlight the importance of using the correct model when simulating suspension rheology, showing the viscosity obtained in simulations of hundreds of mono-disperse particles at various solid fractions sheared homogeneously using the Lees-Edwards boundary condition.