Open Access
2024 A Well-balanced and Positivity-preserving Godunov-type Numerical Scheme for a Spray Model
Dao Huy Cuong, Mai Duc Thanh
Author Affiliations +
Taiwanese J. Math. Advance Publication 1-33 (2024). DOI: 10.11650/tjm/240608


Computational exact Riemann solvers are constructed for a spray model. The model is characterized by a system of balance laws with nonconservative terms in the equations for conservations of momentum and energy. The proposed scheme is combined from an upwind scheme for the equation of the volume fraction evolution and a Godunov-type scheme for the governing equations. The numerical results show that the scheme provides us with the convergence and it possesses a good accuracy, even when resonant phenomena occur. It is interesting to see that the proposed scheme is well-balanced, and preserves the positivity of density, of volume fraction, and the $C$-property.

Funding Statement

This research is funded by Vietnam National University HoChiMinh City (VNU-HCM) under grant number B2023-28-07.


We are grateful to the reviewers for their very constructive comments and helpful suggestions.


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Dao Huy Cuong. Mai Duc Thanh. "A Well-balanced and Positivity-preserving Godunov-type Numerical Scheme for a Spray Model." Taiwanese J. Math. Advance Publication 1 - 33, 2024.


Published: 2024
First available in Project Euclid: 9 July 2024

Digital Object Identifier: 10.11650/tjm/240608

Primary: 35L65 , 65M08 , 76N15

Keywords: Godunov-type scheme , nonconservative , resonance , spray model , two-phase flow , well-balanced scheme

Rights: Copyright © 2024 The Mathematical Society of the Republic of China

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