Nonlinear iterative approximation of steady incompressible chemically reacting flows
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 de...
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Académie des sciences
2022-09-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.127/ |
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| author | Gazca-Orozco, Pablo Alexei Heid, Pascal Süli, Endre |
| author_facet | Gazca-Orozco, Pablo Alexei Heid, Pascal Süli, Endre |
| author_sort | Gazca-Orozco, Pablo Alexei |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0573c2f41b5543c587df41a6d2269208 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2022-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-0573c2f41b5543c587df41a6d22692082025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342022-09-01351S143145510.5802/crmeca.12710.5802/crmeca.127Nonlinear iterative approximation of steady incompressible chemically reacting flowsGazca-Orozco, Pablo Alexei0https://orcid.org/0000-0001-9859-4238Heid, Pascal1https://orcid.org/0000-0003-4227-4053Süli, Endre2https://orcid.org/0000-0002-0812-6105Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, Prague 186 75, Czech RepublicMathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UKMathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UKWe 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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.127/Fixed point iterationIncompressible flowNon-Newtonian fluidsChemically reacting flowSynovial fluid |
| spellingShingle | Gazca-Orozco, Pablo Alexei Heid, Pascal Süli, Endre Nonlinear iterative approximation of steady incompressible chemically reacting flows Comptes Rendus. Mécanique Fixed point iteration Incompressible flow Non-Newtonian fluids Chemically reacting flow Synovial fluid |
| title | Nonlinear iterative approximation of steady incompressible chemically reacting flows |
| title_full | Nonlinear iterative approximation of steady incompressible chemically reacting flows |
| title_fullStr | Nonlinear iterative approximation of steady incompressible chemically reacting flows |
| title_full_unstemmed | Nonlinear iterative approximation of steady incompressible chemically reacting flows |
| title_short | Nonlinear iterative approximation of steady incompressible chemically reacting flows |
| title_sort | nonlinear iterative approximation of steady incompressible chemically reacting flows |
| topic | Fixed point iteration Incompressible flow Non-Newtonian fluids Chemically reacting flow Synovial fluid |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.127/ |
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