Lattice-Boltzmann Method for Non-Newtonian Fluid Flows

TL;DR

This paper extends the Lattice-Boltzmann method to simulate non-Newtonian fluids, demonstrating its accuracy for shear-thinning and shear-thickening models and validating it against analytical and finite-element solutions.

Contribution

The paper introduces an ad hoc extension of the Lattice-Boltzmann method for non-Newtonian fluids and validates its accuracy in complex flow geometries.

Findings

Error decays linearly with lattice resolution

High accuracy near singular points in reentrant-flow geometry

Excellent agreement with finite-element solutions

Abstract

We study an ad hoc extension of the Lattice-Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear-rate is no-longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution.