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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2017; 54(1): 141-175

Online first article October 14, 2016      Printed January 1, 2017

https://doi.org/10.4134/JKMS.j150616

Copyright © The Korean Mathematical Society.

A high-resolution van Leer-type scheme for a model of fluid flows in a nozzle with variable cross-section

Dao Huy Cuong and Mai Duc Thanh

University of Science (VNU-HCM), International University (VNU-HCM)

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We present a high-resolution van Leer-type numerical scheme for the isentropic model of fluid flows in a nozzle with variable cross-section. Basically, the scheme is an improvement of the Godunov-type scheme. The scheme is shown to be well-balanced, as it can capture exactly equilibrium states. Numerical tests are conducted which include comparisons between the van Leer-type scheme and the Godunov-type scheme. It is shown that the van Leer-type scheme achieves a very good accuracy for initial data belong to both supersonic and supersonic regions, and the exact solution eventually possesses a resonant phenomenon.

Keywords: shock wave, nonconservative, numerical approximation, Riemann problem, Godunov scheme, van Leer scheme, accuracy

MSC numbers: Primary 35L65, 74XX; Secondary 76N10, 76L05

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