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A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem

Published online by Cambridge University Press:  10 August 2011

M. Farhloul  and
A. Zine
M. Farhloul
Affiliation:
Département de Mathématiques et de Statistique, Université de Moncton Moncton, N.B., E1A 3E9, Canada
A. Zine*
Affiliation:
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
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Abstract

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.

Keywords

Oldroyd–Stokes problemnon–isothermdual mixed formulation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 130 - 156
Copyright
© EDP Sciences, 2011

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