Abstract
This paper presents a Roe-type numerical scheme for the model of fluid flows in a nozzle with variable cross-section. The proposed scheme is built using the Roe method combined with stationary contact jumps at interfaces. The scheme is proven to capture smooth stationary waves precisely and preserve the positivity of the fluid's density. The numerical tests show that this approach can give considered accuracy to the exact solutions, except where the exact solution crosses a sonic surface.
Funding Statement
This research is funded by Ho Chi Minh City University of Education under grant number CS.2023.19.01.
Citation
Dao Huy Cuong. Ngo Nguyen Quoc Bao. Nguyen Duy Khang. Nguyen Nhat Nam. "Well-balanced and Positivity-preserving Roe-type Numerical Scheme for the Model of Fluid Flows in a Nozzle with Variable Cross-section." Taiwanese J. Math. 28 (1) 55 - 68, February, 2024. https://doi.org/10.11650/tjm/230804
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