Volume 55, Number 6, November-December 2021
|2679 - 2703
|11 November 2021
A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow
Department of Mathematics, FAU Erlangen-Nürnberg, 91058 Erlangen, Germany
Accepted: 12 October 2021
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.
Mathematics Subject Classification: 65N30 / 65J99 / 76A05
Key words: Semismooth Newton methods / non-Newtonian / Bingham fluids / finite element method
© The authors. Published by EDP Sciences, SMAI 2021
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