Abstract
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.
Highlights
Over the last few decades, there has been substantial development in the numerical simulation of viscoelastic fluids, which are commonly encountered in many important industries, such as oil and chemical engineering
Since 1990s, Qian [11] and Giraud [12] have been developed the lattice Boltzmann method to account for non-Newtonian behaviors, but they did not focus on the model with strong elastic effects
For viscoelastic fluids at high Weissenberg number (Wi) number, the computational stability of asynchronously coupling is greatly affected by the polymer stress as the elasticity interaction becomes relatively large
Summary
Over the last few decades, there has been substantial development in the numerical simulation of viscoelastic fluids, which are commonly encountered in many important industries, such as oil and chemical engineering. The numerical solution of the viscoelastic constitutive models is a tremendous challenge, due to breakdown in convergence of algorithms when the Weissenberg number (Wi, is a non-dimensional number characterizing the effect of elasticity on the flow) is increased [1,2]. Many researchers have already had some attempts to develop robust and stable numerical algorithm to solve viscoelastic fluid flows at moderately high values of Wi number, such as discontinuous Galerkin method [4], finite-volume methods [5,6,7], and the lattice. Since 1990s, Qian [11] and Giraud [12] have been developed the lattice Boltzmann method to account for non-Newtonian behaviors, but they did not focus on the model with strong elastic effects. Several approaches have been proposed to incorporate constitutive equations in lattice
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call