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

06/28/2021
by   Daniel Castanon Quiroz, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 23

03/30/2020

A Hybrid High-Order method for creeping flows of non-Newtonian fluids

In this paper, we design and analyze a Hybrid High-Order discretization ...
12/08/2019

An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods

In this work, we introduce a novel abstract framework for the stability ...
04/30/2021

Design and analysis of the Extended Hybrid High-Order method for the Poisson problem

We propose an Extended Hybrid High-Order scheme for the Poisson problem ...
12/09/2020

Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems

We derive novel error estimates for Hybrid High-Order (HHO) discretizati...
02/12/2021

Robust Hybrid High-Order method on polytopal meshes with small faces

We design a Hybrid High-Order (HHO) scheme for the Poisson problem that ...
01/22/2021

Implicit shock tracking for unsteady flows by the method of lines

A recently developed high-order implicit shock tracking (HOIST) framewor...
09/02/2020

A high-order approach to elliptic multiscale problems with general unstructured coefficients

We propose a multiscale approach for an elliptic multiscale setting with...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.