Lattice Boltzmann method for the simulation of White–Metzner fluid flows

Abstract

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.