AN ADAPTIVE VISCOELASTIC STRESS SPLITTING SCHEME AND ITS APPLICATIONS- AVSS SI AND AVSS/SUPG/

We report an adaptive viscoelastic stress splitting (AVSS) scheme, whi ch was found to be extremely robust in the numerical simulation of vis coelastic flow involving steep stress boundary layers. The scheme is d ifferent from the elastic viscous split stress (EVSS) in that the loca l Newtonian component is allowed to depend adaptively on the magnitude of the local elastic stress. Two decoupled versions of the scheme wer e implemented for the Upper Convected Maxwell (UCM) model: the streaml ine integration (AVSS/SI), and the streamline upwind Petrov-Galerkin ( AVSS/SUPG) methods of integrating the stress. The implementations were benchmarked against the known analytic Poiseuille solution, and no up per limiting Weissenberg number was found (the computation was stopped at Weissenberg number of O(10(4))). The flow past a sphere in a tube was solved next, giving convergent results up to a Weissenberg number of 3.2 with the AVSS/SI and 1.55 with the AVSS/SUPG (both were decoupl ed schemes; without the adaptive scheme, the limiting Weissenberg numb er for the decoupled streamline integration method was about 0.3). The se results show that the decoupled AVSS is more stable than the corres ponding EVSS, and the SI is more robust than SUPG in solving the const itutive equation of hyperbolic type. In addition, we found a very long stress wake behind the sphere, and a weak vortex in the rear stagnati on region at a Weissenberg number above W-i of about 1.6, which does n ot seem to increase in size or strength with increasing W-i.