Communications in Mathematical Sciences

Volume 1 (2003)

Number 4

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

Pages: 763 – 797



Philippe G. Lefloch

Mai Duc Thanh


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

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