On the convergence rate of the Kačanov scheme for shear-thinning fluids.
Carreau model
Energy contraction
Kačanov’s method
Non-Newtonian fluids
Power-law model
Journal
Calcolo
ISSN: 1126-5434
Titre abrégé: Calcolo
Pays: Italy
ID NLM: 9918284265606676
Informations de publication
Date de publication:
2022
2022
Historique:
received:
05
01
2021
revised:
13
10
2021
accepted:
14
10
2021
entrez:
13
12
2021
pubmed:
14
12
2021
medline:
14
12
2021
Statut:
ppublish
Résumé
We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.
Identifiants
pubmed: 34898682
doi: 10.1007/s10092-021-00444-3
pii: 444
pmc: PMC8627928
doi:
Types de publication
Journal Article
Langues
eng
Pagination
4Informations de copyright
© The Author(s) 2021.