Decoupled algorithm for solving Phan-Thien–Tanner viscoelastic fluid by finite element method

In this paper we present a decoupled algorithm for the viscoelastic fluid flow obeying the Phan-Thien–Tanner (PTT) differential model. The method consists to solve alternatively a Stokes-like problem by weighted least-squares (WLS) finite element method, and the constitutive equation by streamline upwind Petrov–Galerkin (SUPG) method. A priori error estimate for the WLS/SUPG finite element method is derived. The existence and uniqueness of the approximate solution are obtained using fixed point techniques. We show that the mapping of the decoupled algorithm is locally contracting. The planar channel flow problem is used to illustrate our theoretical results. We encounter no limit of the Weissenberg number for reasonable values of εε, a dimensionless material parameter, in our calculations.