A Spatially Filtering Approach for Direct Numerical Simulation of Fluid-Particle Systems with the Lattice Boltzmann Method

A mesoscopic framework that can model the interactions between particles and fluids at any state of granular matter is developed. In this new formalism, the particles are represented by virtual fluid volumes that move and deform simultaneously with the physical particles. A single distribution function is used to describe the response of physical and virtual fluids. By applying a spatial transformation in the local equations, the necessity of explicitly enforcing the no-slip boundary condition at moving interfaces is removed. The no-slip boundary condition is satisfied a priori at fluid-particle interfaces as long as the average collision operators are evaluated with sufficient accuracy. The proposed theoretical framework forms the basis for deriving numerical fluid-particle interaction schemes that retain the advantages of the lattice Boltzmann method. The derived numerical schemes were compared against the benchmark cases of particle sedimentation and particle migration in two dimensional channels.