Decoupled approach for the problem of viscoelastic fluid flow of PTT model I: continuous stresses

We present in this work a numerical analysis of a decoupled approach with continuous stresses for the viscoelastic fluid flows obeying the PTT model. The Streamline Upwind Petrov–Galerkin is used to treat the transport part of the equations. This model introduces supplementary difficulties linked to the non-linearities of the exponential type present in the constitutive equation. In exchange, it seems to be more realistic and gives best numerical results. The method is tested on the classical benchmark problem: Stick–Slip flow. Numerical results show that our method is remarkably stable and no upper Weissenberg limit number was encountered for reasonable values of ϵ, a material-depending parameter.