A lattice Boltzmann flux solver with log-conformation representation for the simulations of viscoelastic flows at high Weissenberg numbers

Abstract

In this work, a viscoelastic lattice Boltzmann flux solver (VLBFS) with log-conformation representation is proposed for simulating the incompressible flows of a viscoelastic fluid at high Weissenberg number conditions. Compared with the original lattice Boltzmann flux solver (LBFS), the present method has two main new features. First, the method solves the polymer constitutive equations with log-conformation representation. Second, an upwind-biased scheme is incorporated in the interpolation when performing flux reconstructions at the cell interface. With the aid of these two treatments, the numerical stability of VLBFS is significantly improved, making it capable of solving high Weissenberg number problems (HWNP). Compared with using the lattice Boltzmann method (LBM) to solve the viscoelastic fluid flow, VLBFS inherits the advantages of LBFS, such as flexible mesh generation, decoupling of the grid spacing and time interval, and low memory requirement. VLBFS can also precisely recover the macroscopic constitutive equation. The present method has been critically validated using three benchmark cases, namely, the plane Poiseuille flow, lid-driven cavity flow, and 4:1 abrupt planar contraction flow. The numerical results fully demonstrate the solver’s powerful ability in simulating HWNP.