非牛顿流体流动的格子Boltzmann方法研究进展

格子玻尔兹曼方法（lattice Boltzmann method，LBM）能够直接计算局部剪切速率并可以达到二次精度，因此在非牛顿流动数值模拟中展现出一定优势。尽管已证实LBM 对于非牛顿流动的适用性，但是LBM 需要通过即时调节BGK（Bhatnagar-Gross-Krook）碰撞项中的松弛时间来实时反映黏度改变，当松弛时间接近1/2 时，迭代会出现数值不稳定现象。该文对LBM 在非牛顿流体研究中的进展进行了总结，介绍了增加数值稳定性的方法并对结果的精度进行了比较，在此基础上对LBM 在非牛顿研究中的进一步发展进行了展望。

THE RESEARCH PROGRESS OF LATTICE BOLTZMANN METHOD IN NON-NEWTONIAN FLUID FLOW

LBM (lattice Boltzmann method) allows straightforward calculations of the local shear rate to the second-order accuracy, so it has some advantages in the simulation of the non-Newtonian behavior of flows． Although the suitability of LBM for the non-Newtonian flow has been well demonstrated, the algorithms are mainly through instantaneously regulating the local relaxation time in the BGK (Bhatnagar-Gross-Krook) approximated collision term to match its corresponding viscosity for reflecting the effect of the local rheology variation．This approach, however, might cause some numerical instabilities when the relation time is close to 1/2．In this paper, the advances of LBM applied to generalized Newtonian flows are reviewed．The methods to mitigate numerical instabilities are described and the results are compared．Several ways of extending LBM to viscoelastic flows in the literature are introduced．Finally the prospective developments of LBM for non-Newtonian flows are suggested．