Comptes Rendus
Nonlinear iterative approximation of steady incompressible chemically reacting flows
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 431-455.

We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. We prove that the weak solution, whose existence was already established in the literature, is unique, given some strengthened assumptions on the diffusive flux and the stress tensor, for small enough data. We then show that the uniqueness result can be applied to a model describing the synovial fluid. Furthermore, in the latter context, we prove the convergence of a nonlinear iteration scheme; the proposed scheme is remarkably simple and it amounts to solving a linear Stokes–Laplace system at each step. Numerical experiments are performed, which confirm the theoretical findings.

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DOI: 10.5802/crmeca.127
Keywords: Fixed point iteration, Incompressible flow, Non-Newtonian fluids, Chemically reacting flow, Synovial fluid

Pablo Alexei Gazca-Orozco 1; Pascal Heid 2; Endre Süli 2

1 Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech Republic
2 Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Pablo Alexei Gazca-Orozco; Pascal Heid; Endre Süli. Nonlinear iterative approximation of steady incompressible chemically reacting flows. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 431-455. doi : 10.5802/crmeca.127. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.127/

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