An artificial‐dissipation‐based fractional step scheme for upper‐convected Maxwell (UCM) fluid flow past a circular cylinder

Abstract

AbstractThe fully explicit characteristic‐based split (CBS) scheme is employed to solve viscoelastic flow problems. The upper‐convected Maxwell (UCM) model is employed in the present study. In addition to allowing equal‐order interpolations for pressure and velocity, the proposed method along with an appropriate artificial damping scheme is able to produce stable solutions for different Deborah numbers (De). The higher‐order time terms introduced by the simplified characteristic Galerkin approximation are sufficient to obtain stable solution at very low De, but an additional damping is essential to maintain positive definitiveness of the conformation tensor at higher De. We demonstrate the need for an additional damping by analysing the basic forward time central space scheme applied to the constitutive equations. A second‐order artificial damping is employed to counteract the negative dissipation introduced by the explicit time discretization. The example studied in this paper is the widely used and difficult problem of flow past a circular cylinder. The results presented show that the velocity and extra stresses converge easily to a steady state at lower De values. At higher De values, the convergence to steady state is slow due to the incremental way in which the artificial damping is added. Copyright © 2008 John Wiley & Sons, Ltd.