The simulation of non-Newtonian fluids is a challenging task from theoretical and numerical points of view. Different numerical methods has been used to study this class of fluids. In this article, a novel numerical scheme based on lattice Boltzmann method is presented for the simulation of White–Metzner (WM) fluid flows, where two types of distribution functions are defined for the evolution of momentum and stress, respectively. We study the accuracy, and the influence of different parameters on the flow on different benchmarks: we validate our model first for a two-dimensional planar channel, and then we investigate in details the behavior of WM fluid flows in a square lid driven cavity. In the numerical results, we give a very detailed investigation to elaborate the effect over a large range of each parameter on the flow field.

中文翻译：

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用于模拟 White-Metzner 流体流动的格子 Boltzmann 方法

从理论和数值的角度来看，非牛顿流体的模拟是一项具有挑战性的任务。已使用不同的数值方法来研究此类流体。在本文中，提出了一种基于格子 Boltzmann 方法的新型数值方案，用于模拟 White-Metzner (WM) 流体流动，其中分别为动量和应力的演变定义了两种分布函数。我们研究了准确性以及不同参数对不同基准上流动的影响：我们首先针对二维平面通道验证了我们的模型，然后我们详细研究了方形盖驱动腔中 WM 流体流动的行为。在数值结果中，我们进行了非常详细的研究，以阐述每个参数在大范围内对流场的影响。