A numerical approximation with WLS/SUPG algorithm for solving White-Metzner viscoelastic flows

摘要

In this paper, we consider a numerical method for the White-Metzner model of viscoelastic fluid flows by a combination of the weighted least-squares (WLS) method and the streamline upwind/Petrov-Galerkin (SUPG) method. The constitutive equation is decoupled from the momentum and continuity equations, and the approximate solution is computed iteratively by solving the Stokes-like problem and a linearized constitutive equation using WLS and SUPG, respectively. The elastic viscous split stress formulation (EVSS) introduced in [27] is used for the discretization of the constitutive equation. An a priori error estimate for the WLS/SUPG method is derived and numerical results supporting the estimate are presented. We encounter no limit of the Weissenberg number for all values of s satisfying 0 epsilon 1, a dimensionless material parameter, in our calculations. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.