The lattice-Boltzmann method is a technique for simulating the time-dependent motions of a simple fluid. Introducing rigid particles and imposing the correct boundary conditions at the solid/fluid interface allows the many-body, time-dependent hydrodynamic interactions between particles to be computed. Rather than simulating truly solid particles, a computationally convenient method for doing this uses hollow objects filled with the model fluid. We propose a simple modification of this "internal fluid" method. For computational convenience our method keeps the fluid inside the object. Its behaviour is modified, however, in such a way that it does not perturb the dynamics of the particle. The equations of motion for the solid particles are then modified in such a way that the microscopic conservation laws for mass and momentum are satisfied. Comparing both the time-dependent (rotational and translational) motion of an isolated spherical particle and the viscosity of a concentrated suspension of hard spheres against known results for solid particles, we examine artifacts attributable to the "internal" fluid. Using our modified approach, we show that these artifacts are no longer present and the behaviour of truly solid particles is recovered.
J. Comput. Phys.

Heemels, M. W, Hagen, M. H. J, & Lowe, C. P. (2000). Simulating solid colloidal particles using the lattice-Boltzmann method. J. Comput. Phys., 164, 48–61. doi:10.1006/jcph.2000.6564