Implicit Lattice Boltzmann Method based Central Moments with a TR-BDF2 Time Integration for Shear Thinning Viscoelastic Flows

Shear thinning viscoelastic flows arise in various applications involving polymeric fluids. The viscoelastic stresses (VES) in such fluids are often represented by the Giesekus model with a quadratically nonlinear term to account for the shear thinning effects. We develop robust lattice Boltzmann methods (LBMs) using Fokker-Planck central moments-based collision steps for solving both the polymeric VES represented by the Giesekus model and the solvent fluid dynamics. To address the numerical stability issues at Weissenberg numbers effectively, we use a time-implicit formulation of the source terms in the LBM for the VES; it is based on a L-stable approach using the trapezoidal rule together with the second order backward difference (TR-BDF2) discretization and implemented via a Strang splitting method around the collision step, where the nonlinearity is accounted for via a local iterative scheme. The VES is then coupled with the LBM for the fluid motions via augmenting the equilibria used its collision step. We show the effectiveness of the resulting approach via simulations of various canonical single phase and two-phase shear thinning viscoelastic flows.