Su Jin, Ouyang Jie, Wang Xiaodong, Yang Binxin
School of Science, Northwestern Polytechnical University, Xi'an 710129, Shaanxi, PR China.
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, Shanxi, PR China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):053304. doi: 10.1103/PhysRevE.88.053304. Epub 2013 Nov 4.
We developed a lattice Boltzmann method coupled with the Oldroyd-B constitutive equation to simulate a viscoelastic fluid. In this work, the flow field of the solvent is solved using an incompressible lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model, while the advection operator of the polymer stress tensor is directly calculated with the help of the particle distribution functions. Specifically, we present a numerical scheme for the advection of the polymer stress tensor through the truncation of second-order Taylor expansion, which does not need to introduce the extra distribution functions and has better numerical accuracy. We consider two types of numerical tests to examine the performance of the presented method, including a two-dimensional (2D) channel flow and the 4:1 contraction problem. Our numerical results for the 2D channel flow agree well with the analytical results and some experimental results reported in the previous studies. Moreover, the numerical results also indicate that the current method can capture some complex rheological behaviors of the 4:1 contraction flow.
我们开发了一种结合Oldroyd-B本构方程的格子玻尔兹曼方法来模拟粘弹性流体。在这项工作中，溶剂的流场使用不可压缩的格子玻尔兹曼 Bhatnagar-Gross-Krook（BGK）模型求解，而聚合物应力张量的对流算子借助粒子分布函数直接计算。具体而言，我们通过截断二阶泰勒展开式提出了一种聚合物应力张量对流的数值格式，该格式无需引入额外的分布函数且具有更好的数值精度。我们考虑了两种数值测试来检验所提出方法的性能，包括二维（2D）通道流和4:1收缩问题。我们对二维通道流的数值结果与先前研究中报道的解析结果和一些实验结果吻合良好。此外，数值结果还表明当前方法能够捕捉4:1收缩流的一些复杂流变行为。
