We propose a semismooth Newton method for non-Newtonian models of incompressible flow where the constitutive relation between the shear stress and the symmetric velocity gradient is given implicitly; this class of constitutive relations captures for instance the models of Bingham and Herschel–Bulkley. The proposed method avoids the use of variational inequalities and is based on a particularly simple regularisation for which the (weak) convergence of the approximate stresses is known to hold. The system is analysed at the function space level and results in mesh-independent behaviour of the nonlinear iterations.
Keywords: Semismooth Newton methods, non-Newtonian, Bingham fluids, finite element method
@article{M2AN_2021__55_6_2679_0,
author = {Gazca-Orozco, Pablo Alexei},
title = {A semismooth {Newton} method for implicitly constituted {non-Newtonian} fluids and its application to the numerical approximation of {Bingham} flow},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2679--2703},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/m2an/2021068},
mrnumber = {4337453},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021068/}
}
TY - JOUR AU - Gazca-Orozco, Pablo Alexei TI - A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2679 EP - 2703 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021068/ DO - 10.1051/m2an/2021068 LA - en ID - M2AN_2021__55_6_2679_0 ER -
%0 Journal Article %A Gazca-Orozco, Pablo Alexei %T A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2679-2703 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021068/ %R 10.1051/m2an/2021068 %G en %F M2AN_2021__55_6_2679_0
Gazca-Orozco, Pablo Alexei. A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2679-2703. doi: 10.1051/m2an/2021068
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