An approximate solution of the Riemann problem for a realisable second-moment turbulent closure

An approximate solution of the Riemann problem associated with a realisable and objective turbulent second-moment closure, which is valid for compressible flows, is examined. The main features of the continuous model are first recalled. An entropy inequality is exhibited, and the structure of waves...

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Bibliographic Details
Published in:Shock waves 2002-01, Vol.11 (4), p.245-269
Main Authors: Berthon, C., Coquel, F., Hérard, J.M., Uhlmann, M.
Format: Article
Language:English
Subjects:
Fluid mechanics
Mathematics
Mechanics
Physics
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Summary:An approximate solution of the Riemann problem associated with a realisable and objective turbulent second-moment closure, which is valid for compressible flows, is examined. The main features of the continuous model are first recalled. An entropy inequality is exhibited, and the structure of waves associated with the non-conservative hyperbolic convective system is briefly described. Using a linear path to connect states through shocks, approximate jump conditions are derived, and the existence and uniqueness of the one-dimensional Riemann problem solution is then proven. This result enables to construct exact or approximate Riemann-type solvers. An approximate Riemann solver, which is based on Gallouët's recent proposal is eventually presented. Some computations of shock tube problems are then discussed.
ISSN:0938-1287
1432-2153
DOI:10.1007/s001930100109