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On the two-dimensional compressible isentropic Navier-Stokes equations. (English) Zbl 1048.35056

For compressible isentropic two-dimensional Navier-Stokes equations, the authors establish a convergence result for the time-discretized problem when the momentum and continuity equations are solved by the Galerkin method, without adding a penalization term in the continuity equation. The authors verify theoretical findings by direct numerical calculations performed by finite element Modulef software. Numerical results are given for a simplified square domain, and a real domain, the dam of Calacuccia (Corsica, France). Some connections with the shallow water model are indicated.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M10 Finite element methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography

Software:

Modulef
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Full Text: DOI Numdam EuDML

References:

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