THE RIEMANN PROBLEM FOR A NONISENTROPIC FLUID IN A NOZZLE WITH DISCONTINUOUS CROSS-SECTIONAL AREA

We present a full investigation of the Riemann problem for a nonisentropic polytropic fluid in a nozzle with piecewise constant cross-section. First, we introduce the concept of elementary waves which turn out to make up Riemann solutions. Second, we study a procedure to select admissible stationary waves relying on the monotone criterion. By projecting all the wave curves in the (p, u)-plane, we construct Riemann solutions. Existence of Riemann solutions can be obtained for large initial data. Furthermore, we establish the uniqueness of Riemann solutions in strictly hyperbolic domains. Our argument can lead to estimate regions where the Riemann problem admits a unique solution.