Assessment of polymer feedback coupling approaches in simulation of viscoelastic fluids using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has emerged as a popular approach to simulate complex non-Newtonian fluid mechanics problems, such those involving viscoelastic fluids. In these cases, the LBM solver often requires modelling additional non-linear and non-ideal hydrodynamic contributions flow resulting from addition of polymer molecules. These contributions, commonly referred feedback, are either incorporated directly in stress (pressure method) or alternatively momentum field forcing contribution (forcing method). choice coupling previous works been strongly speculated impact numerical accuracy stability solvers for fluids, however no formal comparison conducted. this work, we compare two feedback approaches, well various schemes used method, namely, explicit (EF) scheme (He et al., 1998), Guo al. (Guo 2002), exact-difference-method (EDM) (Kupershtokh 2009). First, through theoretical recovering macroscopic equations, show that both EF retain exact representation up second-order, whereas EDM includes error terms. Similarly, pressure retains unphysical terms, which known violate Galilean invariance. Through tests, steady time-dependent Poiseuille four-roll mill problem under transient regimes, it is shown enhanced at varying elastic effects. Alternatively, owing violation invariance, proved be unstable even moderate obtained results useful determining optimal when simulating fluids using LBM, further testing generality findings on approaches