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On the solution to the Riemann problem for the compressible duct flow

by Andrianov, N., Warnecke, G..

Series: 2003-08, Preprints

35L65 Conservation laws
35L67 Shocks and singularities
76N99 None of the above, but in this section

The quasi-one-dimensional Euler equations in a duct of variable cross-section are probably one of the
most simplest non-conservative systems. We consider the Riemann problem for it and discuss its properties. In
particular, for some initial conditions, the solution to the Riemann problem appears to be non-unique. In order to
rule out the non-physical solutions, we provide 2D computations of the Euler equations in a duct of corresponding
geometry and compare it with the 1D results. Then, the physically relevant 1D solutions satisfy a kind of entropy
rate admissibility criterion. Finally, we present a procedure for finding an exact solution to the Riemann problem
and construct a Godunov-type method on its basis.

Nozzle flow, nonstrictly hyperbolic, resonance, Godunov method