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- W4287070900 abstract "The present paper is focused on the proof of the convergence of the discrete implicit Marker-and-Cell (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." @default.
- W4287070900 created "2022-07-25" @default.
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- W4287070900 date "2021-07-21" @default.
- W4287070900 modified "2023-09-27" @default.
- W4287070900 title "Convergence of the implicit MAC-discretized Navier--Stokes equations with variable density and viscosity on non-uniform grids" @default.
- W4287070900 doi "https://doi.org/10.48550/arxiv.2107.10117" @default.
- W4287070900 hasPublicationYear "2021" @default.
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