Finite Element Discretization of the Giesekus Model for Polymer Flows

Roland Becker () and Daniela Capatina ()
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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

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 135-143 from Springer

Abstract: 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.

Keywords: Finite Element Discretization; Lyapunov Equation; Algebraic Riccati Equation; Weissenberg Number; Viscous Stress Tensor (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_13

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DOI: 10.1007/978-3-642-11795-4_13

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