Numerical simulation of polymer flows using non-conforming finite elements

In this paper, we are interested in the simulation of polymer flows for high-Weissenberg numbers. The high-Weissenberg number problem (HWNP) is one of the main difficulties encountered for the numerical simulation of such flows. We develop a numerical approach for two non-linear models: the affine Phan-Thien and Tanner model and the Giesekus model. We consider the 2D case and triangular and quadrilateral meshes. The velocity and the pressure are approximated by non-conforming finite elements while the stress tensor is approximated by P0 totally discontinuous finite elements. We have considered three popular test-cases: a simple channel, a 4:1 abrupt contraction and a cylinder. Comparisons with analytical solutions and experiences are performed, illustrating the good behavior of our code. Moreover, for the Oldroyd-B model, we have performed comparisons of drag values with data given in the literature. We have been able to obtain simulations for large values of Weissenberg number (Wi>21 for the 4:1 contraction), our approach gives a realistic description of polymer flows.