Implementation of Lees-Edwards periodic boundary conditions for three-dimensional lattice Boltzmann simulation of particle dispersions under shear flow

In this research, the three-dimensional implementation of the Lees-Edwards boundary condition is presented and discussed for the simulation of particulate suspensions. The proposed method is based on the lattice Boltzmann and smoothed profile method for flow and particle motion simulation. This approach eliminates Galilean invariance errors when the particle crosses Lees-Edwards boundaries. Two important issues of particle crossing shear boundaries and corners of a computational domain are discussed in detail. Forces and torques evaluation for a particle that crosses boundaries need special treatment due to the division of the particle into two, four, and eight parts as it traverses one edge, and the intersection of two and three boundaries, respectively. The validation of the present method is performed by using some benchmarks. Furthermore, due to the ability of this algorithm to perform in parallel mode, a CUDA code based on the GPU platform is used to accelerate the computations. The results show that the parallel processing of this method on GPU significantly accelerates the computations.