High-order relaxation methods for nonequilibrium two-phase flow equations
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 25 December 2023
Issue publication date: 27 February 2024
Abstract
Purpose
The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.
Design/methodology/approach
The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.
Findings
The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.
Originality/value
While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.
Keywords
Acknowledgements
The study was carried out within the framework of the research project between Nouh Izem, Ibn Zohr University, Agadir, Morocco, Mohammed Seaid, University of Durham, Durham, UK, and Dia Zeidan, German Jordanian University, Amman, Jordan. The assistance from the honorable authors universities is highly appreciated.
Declaration of competing interest: The authors declare no conflict of interest to announce.
Author contributions:
Fatima Herbate: Investigation, Code development, Visualization, Methodology, Conceptualization, Writing – original draft. Nouh Izem: Conceptualization, Funding acquisition, Supervision, Writing – review and editing. Mohammed Seaid: Validation, Supervision, Conceptualization, Methodology, Writing – review and editing. Dia Zeidan: Supervision, Project administration, Conceptualization, Validation, Writing – review and editing.
Citation
Harbate, F., Izem, N., Seaid, M. and Zeidan, D. (2024), "High-order relaxation methods for nonequilibrium two-phase flow equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 34 No. 3, pp. 1399-1423. https://doi.org/10.1108/HFF-06-2023-0344
Publisher
:Emerald Publishing Limited
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