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Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 503–547 | Cite as

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

  • Mai Duc Thanh
  • Dao Huy Cuong
Article
  • 64 Downloads

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.

Keywords

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

Mathematics Subject Classification (2010)

35L65 65M06 76T10 

Notes

Acknowledgements

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

Funding Information

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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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of MathematicsInternational University (VNU-HCM)Ho Chi Minh CityVietnam
  2. 2.Nguyen Huu Cau High SchoolHo Chi Minh CityVietnam
  3. 3.Department of Mathematics and Computer ScienceUniversity of Science (VNU-HCM)Ho Chi Minh CityVietnam

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