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Communication Dans Un Congrès Année : 2017

Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem

Résumé

We prove in this paper the convergence of the marker-and-cell (MAC) scheme for the discretization of the semi-stationary compressible Stokes equations on two or three dimensional Cartesian grids. Existence of a solution to the scheme is stated, followed by estimates on approximate solutions, which yields the convergence of the approximate solutions, up to a subsequence, and in an appropriate sense. We then prove that the limit of the approximate solutions satisfies the mass balance and mass momentum equations, as well as the equation of state, which is the main difficulty of this study.
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Dates et versions

hal-01620080 , version 1 (20-10-2017)

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Thierry Gallouët, Raphaèle Herbin, David Maltese, Antonin Novotny. Convergence of the marker-and-cell scheme for the semi-stationary compressible Stokes problem. 6th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN), Univ Pau; CNRS; Univ Mohammed I; CNRST; Univ Granada; Int Assoc Math & Comp Simulat, Jun 2015, Pau, France. pp.325 - 349, ⟨10.1016/j.matcom.2016.10.003⟩. ⟨hal-01620080⟩
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