Galilean invariance in the lattice-Boltzmann method and its effect on the calculation of rheological properties in suspensions

The lattice-Boltzmann method (LBM) provides an efficient simulation technique for the study of particle suspensions. These simulations provide an important tool in elucidating the effect of suspended particles on the rheology of suspensions. The most common solid–fluid boundary condition used in the LBM is the bounce-back operation, and as such, the errors introduced by this operation to the dynamics of the particles and the calculation of relevant rheological quantities must be quantified. This paper derives the Galilean invariant term in the standard bounce-back operation and shows the effect of this error on the calculation of particle dynamics and stresslet. In particular, an error is found in the calculation of normal stresses that may be significant in magnitude compared with typical values found in suspensions of rigid spherical particles. A correction is proposed, and simulation results are shown that verify the original assessment and show the reduction of error when using the proposed correction.