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.

研究了范德华流体在具有不连续截面积的喷嘴中流动的模型中的相变。该模型允许出现一个物理不稳定的椭圆形区域，该区域会引起相变，而截面积的跳跃会导致固定的接触波。在亚音速或超音速区域，不同特征场中的波之间的成分构造不同。引入了一种新的波动，它有助于建立黎曼问题解的存在性。黎曼问题在某些地区允许采用唯一的解决方案。当与不同特征场相关的冲击波以相同速度传播时，就会发生共振现象。即使在严格的双曲区域，也可以观察到多种解决方案，不仅通过建模，