Lattice Boltzmann method coupled with the Oldroyd-B constitutive model for a viscoelastic fluid

Abstract

We developed a lattice Boltzmann method coupled with the Oldroyd-B constitutive equation to simulate a viscoelastic fluid. In this work, the flow field of the solvent is solved using an incompressible lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model, while the advection operator of the polymer stress tensor is directly calculated with the help of the particle distribution functions. Specifically, we present a numerical scheme for the advection of the polymer stress tensor through the truncation of second-order Taylor expansion, which does not need to introduce the extra distribution functions and has better numerical accuracy. We consider two types of numerical tests to examine the performance of the presented method, including a two-dimensional (2D) channel flow and the 4:1 contraction problem. Our numerical results for the 2D channel flow agree well with the analytical results and some experimental results reported in the previous studies. Moreover, the numerical results also indicate that the current method can capture some complex rheological behaviors of the 4:1 contraction flow.

Simulations of viscoelastic fluids using a coupled lattice Boltzmann method: Transition states of elastic instabilities

“…The motivation of this paper is to generalize a coupled lattice Boltzmann method with double-type particle speeds (CLBM-DTPS) to simulate those instabilities. Different from some traditional coupled lattice Boltzmann methods, [22][23][24][25][26] two types of distribution functions are defined with two different particle speeds for the coupled lattice Boltzmann solvers, which could distinguish the time scales between the momentum and stress tensor evolution. Our main intention is to explore some possibility of factors for elastic instabilities by making use of the mesoscopic method.…”

A Lattice Boltzmann Method and Asynchronous Model Coupling for Viscoelastic Fluids

“…In addition, as the Wi number increased, for the viscoelastic flows through contractions, we show that the prediction of our presented method can reproduce the same numerical results that were reported by previous studies. The main advantage of current method is that it can be applied to simulate the complex phenomena of the viscoelastic fluids.lattice Boltzmann method have been devised to solve the equations of an Oldroyd-B viscoelastic fluid in the reference [21], which did not need to adding extra distribution functions for the stress tensor. The coupled systems of the viscoelastic fluid include the macro scale constitutive equation and the mesoscopic lattice Boltzmann equation.…”

“…There is a more disparity in timescales between the macro solver and meso solver. To distinguish this different time scale and enhance the computational efficiency, the asynchronously coupled method [22,23] was applied for the coupling time in reference [21]. That means, the data between macro constitutive equation and the lattice Boltzmann equation exchange at every time step.…”

“…lattice Boltzmann method have been devised to solve the equations of an Oldroyd-B viscoelastic fluid in the reference [21], which did not need to adding extra distribution functions for the stress tensor. The coupled systems of the viscoelastic fluid include the macro scale constitutive equation and the mesoscopic lattice Boltzmann equation.…”

Numerical Simulation of Sudden Contraction Flow for Viscoelastic Fluids with the Lattice Boltzmann Method

“…In 2010, Malaspinas [10] introduced dual distribution function to simulate Oldroyd-B fluid. In this work, the configuration tensor was used instead of stress tensor [11,12] in the Oldroyd-B constitutive model, and the convection diffusion lattice Boltzmann model [13] was used to solved the configuration tensor component, then the stress tensor could be obtained through the configuration tensor.…”