Immersed Boundary-Finite Difference Lattice Boltzmann Method for Liquid-Solid Two-Phase Flows

Abstract

An immersed boundary method based on a finite difference lattice Boltzmann method (IB-FDLBM) is presented. The FDLBM solves the discrete Boltzmann equation including an additional collision term by using finite difference schemes. The additional term works as a negative viscosity in the macroscopic level and allows us to alter the fluid viscosity while keeping the other relevant parameters of the simulation fixed. The immersed boundary method employs a direct-forcing method, which utilizes external forces at Lagrangian points embedded on immersed boundaries to impose the no-slip boundary condition. Several benchmark simulations are carried out to validate the developed method, i.e., flows past a circular cylinder, a falling particle, and interaction between two falling particles. Couette flows between a stationary and a rotating cylinder are also simulated at various values of the relaxation time for collision. The main conclusions obtained are as follows: (1) steady flows past a stationary circular cylinder are well predicted, (2) the motions of particles falling through liquids predicted using IB-FDLBM quantitatively agree well with those obtained using immersed boundary methods based on the lattice Boltzmann equation (IB-LBM), (3) the developed method well predicts the interaction between two particles falling through a liquid, e.g., the drafting-kissing-tumbling motion, and (4) distortion of velocity fields in circular Couette flows at high relaxation times is removed by the additional collision term.

Keywords

• immersed boundary
• finite difference lattice boltzmann method
• falling particles
• circular couette flow