Section: New Results
Polymer modeling and numerical simulation
Participants : Roland Becker, Daniela Capatina, Didier Graebling, Julie Joie.
Our activities with respect to numerical simulations in this field have been two-fold in order to respond to the difficulties related to simulation of industrial polymer flows outlined in Section 4.2 .
First, we have been concerned with the theoretical understanding of the properties of the Giesekus model. As outlined above, energy estimates are crucial for the development of robust numerical schemes, see also the recent work on similar questions in the EPI MICMAC  ,  .
Second, we have implemented a mixed non-conforming/DG method for the Giesekus model in the lowest order case; the result of a computation of a 4:1-contraction, comparing Newtonian flow with Giesekus model, is shown in Figure 6 . In the same figure, a comparison of the computed profile in the channel with the one obtained by the PolyFlow®, both on a relatively coarse mesh, is shown. A precise study shows that the results are in good agreement for moderate Weissenberg numbers We ; the computation time is by a factor of two smaller for the preliminary version of our code based on triangular meshes. For We>20 , we were not able to get a converged solution with the commercial code, whereas our program yields stationary solutions up to .
In view of the extension to three space-dimensions, we are actually porting our approach to quadrilateral meshes. Further improvements are expected from the use of adaptivity, as well as from the implementation of adequate iterative solvers.
The long-term goal is to successively build up robust and efficient software tools in order to tackle design problems, such as the design of mixing devices. Our results have been presented in  ,  ,  .