Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations

Gallouët, T.; Herbin, R.; Latché, J.-C.; Maltese, D.

doi:10.1090/mcom/3260

Convergence of the MAC scheme for the compressible stationary Navier-Stokes equations
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by T. Gallouët, R. Herbin, J.-C. Latché and D. Maltese;

Math. Comp. 87 (2018), 1127-1163

DOI: https://doi.org/10.1090/mcom/3260

Published electronically: September 19, 2017

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Abstract:

We prove in this paper the convergence of the marker and cell (MAC) scheme for the discretization of the steady state compressible and isentropic Navier-Stokes equations on two- or three-dimensional Cartesian grids. Existence of a solution to the scheme is proven, followed by estimates on approximate solutions, which yield 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 and momentum balance equations, as well as the equation of state, which is the main difficulty of this study.

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