Lattice Boltzmann (LB) method, which is a mesoscopic numerical method, has been considered as a powerful tool to study microscale gas and liquid flows. Boundary slip phenomenon, which is a significant feature of both microscale gas and liquid flows, has been extensively studied by the LB method in the past decade. However, most of the previous works have focused on the microchannel flows and studies on the microtube flows are very rare. In this paper, we investigate the widely used slip boundary conditions, i.e., combined bounce-back and specular-reflection (BS) scheme, combined Maxwell-diffusion and specular-reflection (MS) scheme, and combined Maxwell-diffusion and bounce-back (MB) scheme, for the axisymmetric LB model with multi-relaxation-time (MRT) in detail. In order to realize the Navier slip boundary condition for liquid flows, we put forward to a reasonable strategy for determining the combination coefficients and the relaxation time. The proposed boundary schemes are validated by some numerical tests including the Hagen–Poiseuille flow, axisymmetric Womersley flow, Poiseuille flow in a circular annulus, and Womersley flow in a circular annulus. Numerical results are consistent with the analytical solutions, which demonstrate that the proposed boundary schemes are suitable for microscale liquid flows in microtube.

格子玻尔兹曼 (LB) 方法是一种细观数值方法，被认为是研究微尺度气体和液体流动的有力工具。边界滑移现象是微尺度气体和液体流动的显着特征，在过去十年中已通过 LB 方法进行了广泛的研究。然而，以前的大部分工作都集中在微通道流动上，对微管流动的研究非常少见。在本文中，我们研究了广泛使用的滑移边界条件，即组合反弹和镜面反射 (BS) 方案、组合麦克斯韦扩散和镜面反射 (MS) 方案以及组合麦克斯韦扩散和反弹(MB) 方案，详细用于具有多重松弛时间 (MRT) 的轴对称 LB 模型。为实现液体流动的 Navier 滑移边界条件，我们提出了确定组合系数和松弛时间的合理策略。提出的边界方案通过一些数值试验得到验证，包括 Hagen-Poiseuille 流、轴对称 Womersley 流、圆形环中的 Poiseuille 流和圆形环中的 Womersley 流。数值结果与解析解一致，表明所提出的边界方案适用于微管中的微尺度液体流动。