| Issue |
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
|
|
|---|---|---|
| Page(s) | 2045 - 2073 | |
| DOI | https://doi.org/10.1051/m2an/2021051 | |
| Published online | 01 October 2021 | |
A hybrid high-order method for creeping flows of non-Newtonian fluids
1
MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
2
MAG, Univ Montpellier, CNRS, Montpellier, France
* Corresponding author: harnist.andre@outlook.fr
Received:
5
November
2020
Accepted:
20
August
2021
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for scalar Leray–Lions problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau–Yasuda models. Numerical examples complete the exposition.
Mathematics Subject Classification: 65N08 / 65N30 / 65N12 / 35Q30 / 76D05
Key words: Hybrid High-Order methods / non-Newtonian fluids / power-law / Carreau–Yasuda law / discrete Korn inequality
© The authors. Published by EDP Sciences, SMAI 2021
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