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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2021

A hybrid high-order method for creeping flows of non-Newtonian fluids

Abstract

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for scalar Leray–Lions problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau–Yasuda models. Numerical examples complete the exposition.
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Dates and versions

hal-03362663 , version 1 (25-03-2020)
hal-03362663 , version 3 (01-10-2021)
hal-03362663 , version 2 (09-01-2022)

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Michele Botti, Daniel Castanon Quiroz, Daniele Antonio Di Pietro, André Harnist. A hybrid high-order method for creeping flows of non-Newtonian fluids. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (5), pp.2045-2073. ⟨10.1051/m2an/2021051⟩. ⟨hal-03362663v3⟩
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