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Simulation numérique des écoulements de liquides polymères

Julie Joie 1, 2
1 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
Abstract : There exist few commercial codes for the simulation of polymer flows. The difficulties stem from the intrinsec properties of polymers which are viscoelastic non-Newtonian. This implies a coupling between the viscoelasticity of the liquid and the flow, quantified by the Weissenberg number. The source of the problem is the breakdown in the convergence of the algorithms at critical values of this number. This work is devoted to the development of robust numerical schemes for the simulation of polymer flows, mainly considering the Giesekus model. We have first focused on the Stokes problem and we proposed a discontinuous Galerkin method less expensive and more robust than the classical Interior Penalty method. We carried out an a priori and a posteriori error analysis and we highlighted the connections between our dG method and nonconforming finite elements. Then, we have considered the three-fields Giesekus model. The velocity and the pressure are approximated by nonconforming finite elements, whereas the stress tensor is treated by discontinuous finite elements and an upwinding scheme of Lesaint-Raviart type. The analysis for triangular and quadrilateral meshes has been performed for the underlying Stokes problem. All the schemes have been implemented in the C++ library Concha. Comparisons with experimental data have been carried out illustrating the good behaviour of the Giesekus model. Moreover, comparisons with the commercial code Polyflow and a semi-analytical solution have also been performed, validating our numerical schemes. We obtained realistic simulations for high Weissenberg numbers on typical benchmark problems such as flows past a cylinder, 4:1 and 4:1:4 contractions.
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Julie Joie. Simulation numérique des écoulements de liquides polymères. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2010. Français. ⟨tel-00546708v2⟩

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