Immersed Boundary-Finite Difference Lattice Boltzmann Method Using Two Relaxation Times

Abstract

Immersed boundary-lattice Boltzmann methods (IB-LBM) with the single-relaxation time (SRT) cause non-physical distortion in fluid velocity when the Reynolds number is low, i.e. the relaxation time τ is high, and IB-LBM requires high spatial resolution to stably simulate high Reynolds number flows. An immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using two-relaxation times (TRT) is therefore proposed in this study to simulate low and high Reynolds number flows stably and accurately. Benchmark problems such as circular Couette flows, flows past a circular cylinder and a sphere at various Reynolds numbers are carried out for validation. The main conclusions obtained are as follows: (1) TRT reduces numerical errors causing non-physical distortion in the fluid velocity at low Reynolds numbers, and accurate predictions are obtained when the parameter Λ, which is a function of the two relaxation times, is low, (2) for stable simulation the parameter Λ should be decreased as the Reynolds number increases, (3) implementation of TRT and the implicit direct forcing method into IB-FDLBM can solve two problems in simulation of low Reynolds number flows, i.e. non-physical velocity distortion and non-physical penetration of flow into the solid body, and (4) IB-FDLBM with TRT gives good predictions of the drag coefficients of a circular cylinder and a sphere in uniform flows for a wide range of the Reynolds number, Re, i.e., 0.1 ≤ Re ≤ 1x104.

Keywords

• immersed boundary
• finite difference lattice boltzmann method
• two-relaxation time collision operator
• low reynolds number flows