Enhanced double distribution function lattice Boltzmann method for simulation of viscoelastic and shear-thinning fluids flow

Abstract

In this study, we use a two-dimensional multiple relaxation time (MRT) approach for simulating polymeric fluids. A correction term is introduced into the source term to remove non-physical terms and improve numerical accuracy of the simulations. The correction term preserves the locality of the collision process and ensures numerical stability across a range of Weissenberg numbers when coupled with non-linear constitutive equations.

This approach is applied to the Phan-Thien-Tanner (PTT) model and the Oldroyd-B model, where the first exhibits viscoelastic and shear-thinning behavior while the second is purely viscoelastic. To evaluate the numerical accuracy and stability of the proposed MRT-LBM approach, we apply it to planar Poiseuille flow as well as simplified four-roll mill benchmarks. In the case of the four-roll mill, we specifically examine the effects of shear-thinning and viscoelasticity in steady elongational flows and their transitions to oscillatory and chaotic or turbulent behaviors, known as elastic instability. Our results indicate that the non-linearity in the stress-strain rate relationship and the microstructural dynamics of polymer chains, as described by non-linear constitutive models, make the standard BGK-LBM approach incapable to accurately capture the complex behavior of polymers without introducing numerical artifacts. On the other hand the MRT-LBM method maintains numerical stability and accuracy across a broad range of Weissenberg (up to $Wi=20$) and should therefore be the method of choice when simulating these types of flows.