The Riemann Problem for Fluid Flows in a Nozzle with Discontinuous Cross-Section

The system of balance laws describing a compressible fluid flow a nozzle forms a non-strictly hyperbolic system of partial equations which, also, is not fully conservative to the effect of the geometry. First, we investigate the properties of the system and determine all possible wave. Second, we construct analytically the solutions of Riemann problem for any values of the left-and right-handed. For certain values we obtain up to three solution whose is carefully described here. In some range of Riemann, no solutions exists. When three solutions are avialable, exactly one of them contains two stationary waves which are in the physical space. We include also numerical plots these solutions.