A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour - Archive ouverte HAL Access content directly
Journal Articles IMA Journal of Numerical Analysis Year : 2021

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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Dates and versions

hal-03273118 , version 1 (28-06-2021)
hal-03273118 , version 2 (01-07-2021)
hal-03273118 , version 3 (09-01-2022)

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Daniel Castanon Quiroz, Daniele 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, 2021, 43 (1), pp.144-186. ⟨10.1093/imanum/drab087⟩. ⟨hal-03273118v3⟩
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