Solid-fluid boundaries in particle suspension simulations via the lattice Boltzmann method

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Abstract
We study several possible treatments of the solid-fluid boundary in lattice Boltzmann simulations of solid-particle suspensions. Our aim is to avoid the complications of the boundary rule pioneered by Ladd [J. Fluid Mech. 271, 285 (1994); 271, 311 (1994)], introduced by treating the solid-fluid interactions on the links between lattice nodes rather than on the lattice nodes themselves. We show that simply treating the interactions in a similar manner on the lattice nodes is not a valid alternative due to the presence of nonrelaxing fluid distributions that do not allow steady flows to be reached. After showing the failure of the so-called ‘‘forcing method,’’ in which the lattice velocity distributions inside the solid particle are forced to represent the local solid body velocity, we introduce a boundary treatment at the lattice nodes. In combination with two further simplifications in the general algorithm, this method produces results comparable to those obtained with Ladd’s boundary rule, especially in the computations of bulk transport coefficients of solid-particle suspensions. When used together with a fluctuating lattice Boltzmann method, it allows for the fluctuation-dissipation theorem to be obeyed exactly at all solid-particle volume fractions.