Section: Application Domains
Viscoelastic flows
Polymeric fluids are, from a rheological point of view, viscoelastic non-Newtonian fluids, see Figure 1 . Their non-Newtonian behavior can be observed in a variety of physical phenomena, which are unseen with Newtonian liquids and which cannot be predicted by the Navier-Stokes equations. The better known examples include the rod climbing Weissenberg effect, die swell and extrusion instabilities (cf. fig. 1). The rheological behavior of polymers is so complex that many different constitutive equations have been proposed in the literature in order to describe these phenomena, see for instance [62] . The choice of an appropriate constitutive law is still a central problem. We consider realistic constitutive equations such as the Giesekus model. In comparison to the classical models used in CFD, such as UCM or Oldroyd B fluids, the Giesekus model is characterized by a quadratic stress term.
Our aim is to develop new algorithms for the discretization of polymer models, which should be efficient and robust for We>10 . For this purpose, we will develop a mathematical approach based on recent ideas on discretizations preserving the positivity of the conformation tensor. This property is believed to be crucial in order to avoid numerical instabilities associated with large Weissenberg numbers. In order to develop monotone numerical schemes, we shall use recent discretization techniques such as stabilized finite element and discontinuous Galerkin methods. We intend to validate the codes to be developed at hand of academic benchmark problems in comparison with the commercial code PolyFlow®.
