LAUSR

Phase transitions in a model of van der Waals fluid flows in a nozzle with discontinuous cross-sectional area are investigated. The model admits a physically unstable elliptic region which causes phase transitions, and a jump in cross-sectional area which causes stationary contact waves. Compositions between waves in different characteristic fields are constructed differently in subsonic or supersonic regions. A new kind of waves is introduced which helps establish the existence of solutions of the Riemann problem. There are regions in which the Riemann problem admits a unique solution. Resonant phenomena occur when shock waves associated with different characteristic fields propagate with the same speed. Multiple solutions are also observed even in a strictly hyperbolic region not only by the modeling, but also by the type of a van der Waals fluid.