A direct-forcing pressure-based lattice Boltzmann method for solving fluid-particle interaction problems

A direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate fluid-particle interaction problems. This method uses the pressure-based LBM to solve the incompressible flow field and the immersed boundary method to handle the fluid-particle interactions. The pressure-based LBM uses the pressure distribution functions instead of the density distribution functions as the independent dynamic variables. The main idea is to explicitly eliminate the compressible effect due to the density fluctuation. In the IB method, a direct-forcing method is introduced to capture the particle motion. It directly computes an IB force density at each lattice grid from the differences between the pressure distribution functions obtained by the LBM and the equilibrium pressure distribution functions computed from the particle velocity. By applying this direct-forcing method, the IB-LBM becomes a purely LBM version. Also, by applying the Gauss theorem, the formulas for computing the force and the torque acting on the particle from the flows are derived from the volume integrals over the particle volume instead of from the surface integrals over the particle surface. The order of accuracy of the IB-LBM is demonstrated on the errors of velocity field, wall stress, and gradients of velocity and pressure. As a demonstration of the efficiency and capabilities of the new method, sedimentation of a large number of spherical particles in an enclosure is simulated.