Abstract
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.
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The authors would like to thank the reviewers for their very constructive comments and fruitful discussions. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number “101.02-2019.306”.
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Communicated by Yong Zhou.
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Thanh, M.D., Vinh, D.X. The Riemann Problem with Phase Transitions for Fluid Flows in a Nozzle. Bull. Malays. Math. Sci. Soc. 44, 2271–2317 (2021). https://doi.org/10.1007/s40840-020-01059-7
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DOI: https://doi.org/10.1007/s40840-020-01059-7