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arXiv · 2106.14950

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

Daniel Castanon Quiroz·Daniele Antonio Di Pietro·André Harnist
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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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Daniel Castanon Quiroz, Daniele Antonio Di Pietro, André Harnist. 2021-06-28. A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. https://doi.org/10.1093/imanum%2Fdrab087

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