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Convergence of the implicit MAC scheme of the incompressible Navier-Stokes equations with variable density and viscosity

Abstract : he present paper is focused on the proof of the convergence of the discrete implicit Marker-andCell (MAC) scheme for time-dependent Navier–Stokes equations with variable density and variable viscosity. The problem is completed with homogeneous Dirichlet boundary conditions and is discretized according to a non-uniform Cartesian grid. A priori-estimates on the unknowns are obtained, and along with a topological degree argument they lead to the existence of a solution of the discrete scheme at each time step. We conclude with the proof of the convergence of the scheme toward the continuous problem as mesh size and time step tend toward zero with the limit of the sequence of discrete solutions being a solution to the weak formulation of the problem. Finite volume methods; MAC scheme; incompressible Navier–Stokes equations; variable density and viscosity; transport equations.
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https://hal.univ-antilles.fr/hal-03312831
Contributor : Pascal Poullet Connect in order to contact the contributor
Submitted on : Monday, August 2, 2021 - 9:35:31 PM
Last modification on : Friday, September 30, 2022 - 9:44:08 AM

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  • HAL Id : hal-03312831, version 1

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Léa Batteux, Pascal Poullet, Thierry Gallouët, Raphaele Herbin, Jean-Claude Latche. Convergence of the implicit MAC scheme of the incompressible Navier-Stokes equations with variable density and viscosity. 2021. ⟨hal-03312831⟩

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