Convergence of the MAC scheme for the incompressible Navier-Stokes equations with variable density and viscosity
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- by L. Batteux, T. Gallouët, R. Herbin, J. C. Latché and P. Poullet HTML | PDF
- Math. Comp. 92 (2023), 1595-1631 Request permission
Abstract:
The present paper addresses the convergence of the implicit Marker-and-Cell scheme for time-dependent Navier–Stokes equations with variable density and density-dependent viscosity and forcing term. A priori estimates on the unknowns are obtained, and thanks to a topological degree argument, they lead to the existence of an approximate solution at each time step. Then, by compactness arguments relying on these same estimates, we obtain the convergence (up to the extraction of a subsequence), when the space and time steps tend to zero, of the numerical solutions to a limit; this latter is shown to be a weak solution to the continuous problem by passing to the limit in the scheme.References
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Additional Information
- L. Batteux
- Affiliation: LAMIA, Université des Antilles, Campus de Fouillole, BP 250, F-97159 Pointe-à-Pitre, Guadeloupe, France
- MR Author ID: 1451741
- ORCID: 0000-0003-3162-402X
- Email: lea.batteux@univ-antilles.fr
- T. Gallouët
- Affiliation: I2M UMR 7373, Aix-Marseille Université, CNRS, Ecole Centrale de Marseille, 39 rue Joliot Curie, 13453 Marseille, France
- Email: thierry.gallouet@univ-amu.fr
- R. Herbin
- Affiliation: I2M UMR 7373, Aix-Marseille Université, CNRS, Ecole Centrale de Marseille, 39 rue Joliot Curie, 13453 Marseille, France
- MR Author ID: 244425
- ORCID: 0000-0003-0937-1900
- Email: raphaele.herbin@univ-amu.fr
- J. C. Latché
- Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France
- MR Author ID: 715367
- Email: jean-claude.latche@irsn.fr
- P. Poullet
- Affiliation: LAMIA, Université des Antilles, Campus de Fouillole, BP 250, F-97159 Pointe-à-Pitre, Guadeloupe, France
- MR Author ID: 623789
- ORCID: 0000-0003-3085-4368
- Email: pascal.poullet@univ-antilles.fr
- Received by editor(s): January 19, 2022
- Received by editor(s) in revised form: September 12, 2022, October 14, 2022, and October 14, 2022
- Published electronically: February 17, 2023
- © Copyright 2023 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 1595-1631
- MSC (2020): Primary 35Q30, 65M08, 65N12, 76M12
- DOI: https://doi.org/10.1090/mcom/3803
- MathSciNet review: 4570335