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.
Keywords: Hybrid High-Order methods, non-Newtonian fluids, power-law, Carreau–Yasuda law, discrete Korn inequality
@article{M2AN_2021__55_5_2045_0,
author = {Botti, Michele and Castanon Quiroz, Daniel and Di Pietro, Daniele A. and Harnist, Andr\'e},
title = {A hybrid high-order method for creeping flows of {non-Newtonian} fluids},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2045--2073},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021051},
mrnumber = {4319602},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021051/}
}
TY - JOUR AU - Botti, Michele AU - Castanon Quiroz, Daniel AU - Di Pietro, Daniele A. AU - Harnist, André TI - A hybrid high-order method for creeping flows of non-Newtonian fluids JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2045 EP - 2073 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021051/ DO - 10.1051/m2an/2021051 LA - en ID - M2AN_2021__55_5_2045_0 ER -
%0 Journal Article %A Botti, Michele %A Castanon Quiroz, Daniel %A Di Pietro, Daniele A. %A Harnist, André %T A hybrid high-order method for creeping flows of non-Newtonian fluids %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2045-2073 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021051/ %R 10.1051/m2an/2021051 %G en %F M2AN_2021__55_5_2045_0
Botti, Michele; Castanon Quiroz, Daniel; Di Pietro, Daniele A.; Harnist, André. A hybrid high-order method for creeping flows of non-Newtonian fluids. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2045-2073. doi: 10.1051/m2an/2021051
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