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A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour

Abstract : In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection laws, that are associated with possibly different Sobolev exponents r ∈ (1, ∞) and s ∈ (1, ∞). After providing a novel weak formulation of the continuous problem, we study its well-posedness highlighting how a subtle interplay between the exponents r and s determines the existence and uniqueness of a solution. We next design an HHO scheme based on this weak formulation and perform a comprehensive stability and convergence analysis, including convergence for general data and error estimates for shear-thinning fluids and small data. The HHO scheme is validated on a complete panel of model problems.
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https://hal.archives-ouvertes.fr/hal-03273118
Contributor : André Harnist Connect in order to contact the contributor
Submitted on : Sunday, January 9, 2022 - 4:21:14 PM
Last modification on : Friday, August 5, 2022 - 10:51:50 AM

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Daniel Castanon Quiroz, Daniele Antonio Di Pietro, André Harnist. A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2021, ⟨10.1093/imanum/drab087⟩. ⟨hal-03273118v3⟩

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