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

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 expon...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Daniel Castanon Quiroz, Di Pietro, Daniele Antonio, Harnist, André
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.01.2022
Subjects
Computational fluid dynamics
Computer Science - Numerical Analysis
Convergence
Exponents
Fluid flow
Incompressible flow
Mathematics - Analysis of PDEs
Mathematics - Numerical Analysis
Newtonian fluids
Non Newtonian fluids
Shear thinning (liquids)
Stability analysis
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.14950