A van Leer-Type Numerical Scheme for the Model of a General Fluid Flow in a Nozzle with Variable Cross Section

Abstract

A van Leer-type numerical scheme for the model of a general fluid in a nozzle with variable cross section is presented. The model is nonconservative, making it hard for standard numerical schemes. Exact solutions of local Riemann problems are incorporated in the construction of this scheme. The scheme can work well in regions of resonance, where multiple waves are colliding. Numerical tests are conducted, where we compare the errors and orders of accuracy for approximating exact solutions between this scheme and a Godunov-type scheme. Results from numerical tests show that this van Leer-type scheme has a much better accuracy than the Godunov-type scheme.

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Acknowledgements

The authors are thankful to the referee for his/her very constructive comments and fruitful discussions.

Funding

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2016.15.

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Correspondence to Mai Duc Thanh.

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Thanh, M.D., Cuong, D.H. A van Leer-Type Numerical Scheme for the Model of a General Fluid Flow in a Nozzle with Variable Cross Section. Acta Math Vietnam 43, 503–547 (2018). https://doi.org/10.1007/s40306-017-0242-z

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Keywords

  • Numerical approximation
  • van Leer-type scheme
  • Fluid
  • Nozzle
  • Shock
  • Nonconservative
  • Riemann solver

Mathematics Subject Classification (2010)

  • 35L65
  • 65M06
  • 76T10