by Andrianov, N., Warnecke, G..

**Series:** 2003-08, Preprints

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

**Abstract:**

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.

**Keywords:**

Nozzle flow, nonstrictly hyperbolic, resonance, Godunov method