Keywords: Boltzmann method, immersed boundary-lattice, IB-LBM, sedimentation, fluidization, pressure distribution function.

In this paper, a direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM) is developed to simulate sedimentation and fluidization problems. This method uses the pressure-based lattice Boltzmann method 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. For sedimentation problems, the flowfield of 1260 particles in a box is demonstrated to investigate phenomena. For the fluidization area, the flowfield of one particle in a box is validated. Then 400 (20x20) particles with different sizes and densities in a two-dimensional-like narrow box are investigated. After this, 500 (5x5x20) particles in a wider box are also represented with different density. The numerical results show that the comparison between average hydraulic gradient and theoretical data is good.

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