基于格子Boltzmann方法的顶盖驱动流数值模拟

Numerical Simulation of Overhead-Driven Flow Based on the Lattice Boltzmann Method

摘要: 格子Boltzmann方法是一种从介观角度来模拟流体宏观行为的方法，通过在时间和空间上使用完全离散的动力学模型来实现。利用Chapman-Enskog多尺度展开技术，我们可以将基本模型恢复到符合标准的不可压Navier-Stokes方程，给出了具体的求解过程。对于格子Boltzmann方程的边界处理，我们采用非平衡外推格式并给出了详细的推导说明。对于顶盖方腔驱动流问题，我们使用此方法进行了数值模拟，以及对模拟结果进行了分析和讨论。通过与已有的试验及数值研究结果对比，进行了鲁棒性分析，验证了使用格子Boltzmann方法模拟顶盖方腔驱动流的正确性、准确性和稳定性。

Abstract: Lattice Boltzmann method is a method to simulate the macroscopic behavior of fluid from a mesoscopic perspective, which is realized by using a completely discrete dynamic model in time and space. Using Chapman-Enskog multi-scale expansion technology, we can restore the basic mod-el to the standard incompressible Navier-Stokes equation, and give the specific solution process. For the boundary treatment of lattice Boltzmann equation, we use the non-equilibrium extrapolation scheme and give a detailed derivation. For the problem of driving flow in the square cavity of the top cover, we use this method to carry out numerical simulation, and analyze and discuss the simu-lation results. By comparing with the existing experimental and numerical results, the robustness analysis is carried out to verify the correctness, accuracy and stability of using the lattice Boltzmann method to simulate the driving flow in the square cavity of the top cover.