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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Nathan Shourick 1, 2; Ibrahim Cheddadi 2; Pierre Saramito 1
@article{CRMATH_2023__361_G11_1767_0, author = {Nathan Shourick and Ibrahim Cheddadi and Pierre Saramito}, title = {A new framework for shallow approximations of incompressible flows}, journal = {Comptes Rendus. Math\'ematique}, pages = {1767--1783}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.526}, language = {en}, }
TY - JOUR AU - Nathan Shourick AU - Ibrahim Cheddadi AU - Pierre Saramito TI - A new framework for shallow approximations of incompressible flows JO - Comptes Rendus. Mathématique PY - 2023 SP - 1767 EP - 1783 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.526 LA - en ID - CRMATH_2023__361_G11_1767_0 ER -
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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