# A HIGH-RESOLUTION VAN LEER-TYPE SCHEME FOR A MODEL OF FLUID FLOWS IN A NOZZLE WITH VARIABLE CROSS-SECTION

• Published : 2017.01.01

#### Abstract

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.

#### Acknowledgement

Supported by : Vietnam National University

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#### Cited by

1. A van Leer-Type Numerical Scheme for the Model of a General Fluid Flow in a Nozzle with Variable Cross Section pp.2315-4144, 2017, https://doi.org/10.1007/s40306-017-0242-z