A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow

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–Bulkle...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2021-11, Vol.55 (6), p.2679-2703
Main Author: Gazca-Orozco, Pablo Alexei
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Banach spaces
Constitutive relationships
Finite element analysis
Finite element method
Fluid flow
Function space
Hypotheses
Incompressible flow
Mathematical analysis
Methods
Newton methods
Newtonian fluids
Non Newtonian fluids
Numerical analysis
Regularization
Shear stress
Velocity
Velocity gradient
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2021068