On the spatial convergence and transient behaviour of lattice Boltzmann methods for modelling fluids with yield stress

TL;DR

This study compares two lattice Boltzmann formulations for modeling yield-stress fluids, analyzing their convergence, transient behavior, and effects of lattice symmetry and Burnett stresses, with the implicit model showing advantages in dynamic flows.

Contribution

It introduces and compares a Papanastasiou-regularized and a locally-implicit lattice Boltzmann model for viscoplastic fluids, highlighting their performance differences.

Findings

Implicit model better captures transient and inertial behaviors.

Lattice choice and Burnett stresses influence model accuracy.

Both models perform similarly in creeping flows.

Abstract

In this paper, the performance of two lattice Boltzmann method formulations for yield-stress (i.e. viscoplastic) fluids has been investigated. The first approach is based on the popular Papanastasiou regularisation of the fluid rheology in conjunction with explicit modification of the lattice Boltzmann relaxation rate. The second approach uses a locally-implicit formulation to simultaneously solve for the fluid stress and the underlying particle distribution functions. After investigating issues related to the lattice symmetry and non-hydrodynamic Burnett stresses, the two models were compared in terms of spatial convergence and their behaviour in transient and inertial flows. The choice of lattice and the presence of Burnett stresses was found to influence the results of both models, however the latter did not significantly degrade the velocity field. Using Bingham flows in ducts and synthetic porous media, it was found that the implicitly-regularised model was superior in capturing transient and inertial fluid behaviour. This result presents potential implications for the application of the Papanastasiou-regularised model in such scenarios. In creeping flows the performance of both models was found to be both similar and satisfactory.