Compressibility

Finite volume method

Riemann solver

Applied mathematics

Computer science

Mathematical optimization

Solver

Classical mechanics

Physics

Riemann hypothesis

Mathematics

Mathematical analysis

Moment (physics)

Mechanics

An approximate Riemann solver is presented in this contribution, which enables to compute turbulent compressible flows using an objective realisable second order closure. 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, a result of existence and uniqueness of the one dimensional Riemann problem is then given. This result enables to construct exact or approximate Riemann type solvers. An approximate Riemann solver, which is based on Gallouet's recent proposal is eventually presented. Some computations of shock tube experiments are then discussed.

An approximate Riemann solver to compute compressible flows using second-moment closures