# Riemann Problem for van der Waals Fluids in Nozzle with Cross-Sectional Jump

• Duong Xuan Vinh
• Mai Duc Thanh
Article

## Abstract

The Riemann problem for isentropic van der Waals fluid flows in a nozzle with discontinuous cross-section is investigated. The pressure, expressed as a function of the density, is increasing and admits two inflection points. The model is not strictly hyperbolic, and the characteristic fields are not genuinely nonlinear. Since the model is written in Eulerian coordinates, it is hard to directly examine the Liu entropy condition. There may exist up to four stationary jumps from a given state. After imposing the admissibility criterion, two admissible stationary jumps may also co-exist. This leads to the multiple solutions of the Riemann problem for van der Waals fluids.

## Keywords

Shock Nozzle van der Waals fluid Riemann problem Entropy condition

## Mathematics Subject Classification

35L40 35L65 76L05 76N10

## Notes

### Acknowledgements

The authors would like to thank the Reviewers for their very constructive comments and helpful suggestions. This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2018-28-01.

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