Comptes Rendus
Équations aux dérivées partielles, Mécanique
A new framework for shallow approximations of incompressible flows
Nathan Shourick1, 2  ; Ibrahim Cheddadi2 ; Pierre Saramito1
1 Lab. Jean Kuntzmann – CNRS and Université Grenoble-Alpes, F-38041 Grenoble, France
2 Univ. Grenoble Alpes, CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, 38000 Grenoble, France
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1767-1783.

A new framework for the asymptotic analysis of incompressible flows of complex non-Newtonian materials is presented in this paper. It allows both to avoid redundant mathematical hypotheses and to dramatically reduce the amount of tedious formal calculations. The starting point of the proposed framework is a generic equation, easily adaptable to most problems of continuum mechanics, for which a thin-layer approximation is developed. We then show how to treat the so-called Gordon–Schowalter derivative, a general objective time derivative involved in non-Newtonian viscoelastic fluids. As a proof of concept of our framework, we apply it to the Maxwell viscoelastic model.

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DOI : 10.5802/crmath.526
Classification : 35Q35
Nathan Shourick 1, 2 ; Ibrahim Cheddadi 2 ; Pierre Saramito 1

1 Lab. Jean Kuntzmann – CNRS and Université Grenoble-Alpes, F-38041 Grenoble, France
2 Univ. Grenoble Alpes, CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, 38000 Grenoble, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A new framework for shallow approximations of incompressible flows},
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     language = {en},
}
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Nathan Shourick; Ibrahim Cheddadi; Pierre Saramito. A new framework for shallow approximations of incompressible flows. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1767-1783. doi : 10.5802/crmath.526. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.526/

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