LAUSR

The numerical algorithms of viscoelastic flows can appear a tremendous challenge as the Weissenberg number (Wi) enlarged sufficiently. In this study, we present a generalized technique of time-stably advancing based on the coupled lattice Boltzmann method, in order to improve the numerical stability of simulations at a high Wi number. The mathematical models of viscoelastic fluids include both the equation of the solvent and the Oldroyd-B constitutive equation of the polymer. In the two-dimensional (2D) channel flow, the coupled method shows good agreements between the corresponding exact results and the numerical results obtained by our method. 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.