Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011Complex Fluids
|Page(s)||130 - 156|
|Published online||10 August 2011|
A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem
Département de Mathématiques et de Statistique, Université de
Moncton Moncton, N.B., E1A
2 Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Institut Camille Jordan 36, rue Guy de Collongue, 69134 Ecully, France
⋆ Corresponding author. E-mail: Abdel-Malek.Zine@ec-lyon.fr
We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and polymeric components of the extra-stress tensor, as well as the heat flux. Furthermore, it has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass.
Mathematics Subject Classification: 65N30 / 65N15 / 76D07
Key words: Oldroyd–Stokes problem / non–isotherm / dual mixed formulation
© EDP Sciences, 2011
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