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Finite Element Discretization of the Giesekus Model for Polymer Flows

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Roland Becker

    (INRIA Bordeaux Sud-Ouest & Université de Pau, IPRA, EPI Concha & LMA CNRS UMR 5142)

  • Daniela Capatina

    (INRIA Bordeaux Sud-Ouest & Université de Pau, IPRA, EPI Concha & LMA CNRS UMR 5142)

Abstract

We consider the Giesekus model for steady flows of polymeric liquids. This model, characterized by the presence in the constitutive law of a quadratic term in the stress tensor, yields a realistic behavior for shear, elongational and mixed flows. Its numerical approximation is achieved by means of Crouzeix–Raviart nonconforming finite elements for the velocity and the pressure, respectively piecewise constant elements for the stress tensor. Appropriate upwind schemes are employed for the convective terms, and the nonlinear discrete problem is solved by Newton’s method. We next investigate the positive definiteness of the discrete conformation tensor and show that under certain hypotheses, this property is preserved by Newton’s method. This allows us to attain the convergence of the algorithm for rather large Weissenberg numbers. Numerical tests validating the code are presented.

Suggested Citation

  • Roland Becker & Daniela Capatina, 2010. "Finite Element Discretization of the Giesekus Model for Polymer Flows," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 135-143, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_13
    DOI: 10.1007/978-3-642-11795-4_13
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