A comparative study of boundary conditions for lattice Boltzmann simulations of high Reynolds number flows

Kainan Hu,Jianping Meng,Hongwu Zhang,Xiao-Jun Gu,David R Emerson,Yonghao Zhang

doi:10.1016/j.compfluid.2017.06.008

Abstract

Four commonly-used boundary conditions in lattice Boltzmann simulation, i.e. the bounce-back, non-equilibrium bounce-back, non-equilibrium extrapolation, and the kinetic boundary condition, have been systematically investigated to assess their accuracy, stability and efficiency in simulating high Reynolds number flows. For the classical lid-driven cavity flow problem, it is found that the bounce-back scheme does not influence the simulation accuracy in the bulk region if the boundary condition is properly implemented to avoid generating non-physical slip velocity. Although the kinetic boundary condition naturally produces physical slip velocity at the wall, it gives overall satisfactory predictions of the center-line velocity profile and the vortex center locations for the Reynolds numbers considered. For the cavity flow problem, all four boundary conditions show minimal difference in the computing time needed to reach a steady state. This is surprising because the kinetic boundary condition is significantly different from the other three schemes which are designed specifically for no-slip boundary conditions. The bounce-back scheme is the most computationally efficient in updating boundary points, which is particularly attractive if there are a large number of solid bodies in the flow field. For the numerical stability, we further test the pressure-driven channel flow with or without a enclosed square cylinder. Overall, the kinetic boundary condition is the most stable of the four schemes. The non-equilibrium extrapolation scheme presents excellent stability second to the kinetic boundary condition for the lid-driven cavity flow. In comparison with other threes schemes, the stability of non-equilibrium bounce-back scheme appears to be less satisfactory for both flows.

Highlights

The lattice Boltzmann (LB) method has been developed into an efficient mesoscopic simulation tool for fluid dynamics [1], which has shown its strength in simulating multi-phase and multicomponent flows [2], and flows in porous media [3]
We have investigated the accuracy, stability, and efficiency of four popular boundary conditions for LB simulation of flows with high Reynolds numbers
The slip velocity given by the kinetic boundary condition (KBC) has no significant effect on the Reynolds numbers considered

Summary

Introduction

The lattice Boltzmann (LB) method has been developed into an efficient mesoscopic simulation tool for fluid dynamics [1], which has shown its strength in simulating multi-phase and multicomponent flows [2], and flows in porous media [3]. The kinetic boundary condition (KBC) is of great interest for the LB method [13] This scheme can induce physically realistic slip velocity at a wall boundary, and has been often used in the discrete velocity method (DVM) [14] for rarefied gas flows, e.g., [15]. It was shown that the BB scheme may induce a numerical slip velocity and cause different order of errors depending on its implementation (e.g.,“on-grid” or “halfway”) While this artificial slip velocity can be eliminated for simple geometries [19], we will investigate the performance of the BB scheme without the deficiency. We will focus on accuracy, efficiency, and stability of the BB, NEEP NEBB and the KBC schemes for high Reynolds number flows. For the flow around a square cylinder, we will primarily investigate their numerical stability

Lattice Boltzmann equation and D2Q9 lattice model

Boundary conditions

Stability for flow around a square cylinder

Findings

Concluding remarks