Comparative study of boundary treatment schemes in lattice Boltzmann method

Abstract

Suspension flows are frequently found in our daily lives, and their rheological properties are critical issues in many fields. In numerical simulations of suspension flows based on the two-way coupling approach, it is important to treat the no-slip boundary condition. The immersed boundary method (IBM) and interpolated bounce-back (IBB) scheme are representative schemes for satisfying the no-slip boundary condition in the lattice Boltzmann method. In the regard, the virtual flux method (VFM) has also been recently developed. In this study, the effect of pressure interpolation with arbitrary precision on numerical convergence was investigated and various methods were compared. Simulations of flows around a fixed cylinder, inertial migration of a single particle, and suspension flow were performed to compare the VFM with the multi direct forcing immersed boundary method and single-node second-order bounce-back scheme. Consequently, in the simulation of flows past a circular cylinder, we demonstrated that the convergence rate improved slightly when the pressure interpolation precision was increased. Moreover, in the suspension flow, using the VFM and IBB scheme reduced the computing time compared with using the IBM and allowed for more stable analysis at higher area fractions. The VFM can improve the numerical convergence rate by changing the pressure interpolation precision.

Keywords

• immersed boundary method
• interpolated bounce-back scheme
• no-slip boundary condition
• neumann boundary condition
• suspension rheology