An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows
A time-consistent upwind difference scheme with a preconditioned numerical flux for unsteady gas-liquid multiphase flows is presented and applied to the analysis of cavitating flows. The fundamental equations were formulated in general curvilinear coordinates to apply to diverse flow fields. The pre...
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2025-02-01
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| author | Tianmu Zhao Byeongrog Shin |
| author_facet | Tianmu Zhao Byeongrog Shin |
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| description | A time-consistent upwind difference scheme with a preconditioned numerical flux for unsteady gas-liquid multiphase flows is presented and applied to the analysis of cavitating flows. The fundamental equations were formulated in general curvilinear coordinates to apply to diverse flow fields. The preconditioning technique was applied specifically to the numerical dissipation terms in the upwinding process without changing the time derivative terms to maintain time consistency. This approach enhances numerical stability in unsteady multiphase flow computations, consistently delivering time-accurate solutions compared to conventional preconditioning methods. A homogeneous gas-liquid two-phase flow model, third-order Runge-Kutta method, and the flux difference splitting upwind scheme coupled with a third-order MUSCL TVD scheme were employed. Numerical tests of two-dimensional gas-liquid single- and two-phase flows over backward-facing step with different step height and flow conditions successfully demonstrated the capability of the present scheme. The calculations remained stable even for flows with a very low Mach number of 0.001, typically considered incompressible flows, and the results were in good agreement with the experimental data. In addition, we analyzed unsteady cavitating flows at high Reynolds numbers and confirmed the effectiveness and applicability of the present scheme for calculating unsteady gas-liquid two-phase flows. |
| format | Article |
| id | doaj-art-e06c692419ac4178a8b8570d84272d55 |
| institution | DOAJ |
| issn | 2311-5521 |
| language | English |
| publishDate | 2025-02-01 |
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| spelling | doaj-art-e06c692419ac4178a8b8570d84272d552025-08-20T03:12:20ZengMDPI AGFluids2311-55212025-02-011023810.3390/fluids10020038An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase FlowsTianmu Zhao0Byeongrog Shin1Interdisciplinary Graduate School of Agriculture and Engineering, University of Miyazaki, Miyazaki 889-2192, JapanDepartment of Mechanical Engineering, University of Miyazaki, Miyazaki 889-2192, JapanA time-consistent upwind difference scheme with a preconditioned numerical flux for unsteady gas-liquid multiphase flows is presented and applied to the analysis of cavitating flows. The fundamental equations were formulated in general curvilinear coordinates to apply to diverse flow fields. The preconditioning technique was applied specifically to the numerical dissipation terms in the upwinding process without changing the time derivative terms to maintain time consistency. This approach enhances numerical stability in unsteady multiphase flow computations, consistently delivering time-accurate solutions compared to conventional preconditioning methods. A homogeneous gas-liquid two-phase flow model, third-order Runge-Kutta method, and the flux difference splitting upwind scheme coupled with a third-order MUSCL TVD scheme were employed. Numerical tests of two-dimensional gas-liquid single- and two-phase flows over backward-facing step with different step height and flow conditions successfully demonstrated the capability of the present scheme. The calculations remained stable even for flows with a very low Mach number of 0.001, typically considered incompressible flows, and the results were in good agreement with the experimental data. In addition, we analyzed unsteady cavitating flows at high Reynolds numbers and confirmed the effectiveness and applicability of the present scheme for calculating unsteady gas-liquid two-phase flows.https://www.mdpi.com/2311-5521/10/2/38upwind difference schemenumerical dissipationgas-liquid multiphase flowlow Mach numberpreconditioning |
| spellingShingle | Tianmu Zhao Byeongrog Shin An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows Fluids upwind difference scheme numerical dissipation gas-liquid multiphase flow low Mach number preconditioning |
| title | An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows |
| title_full | An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows |
| title_fullStr | An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows |
| title_full_unstemmed | An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows |
| title_short | An Application of Upwind Difference Scheme with Preconditioned Numerical Fluxes to Gas-Liquid Two-Phase Flows |
| title_sort | application of upwind difference scheme with preconditioned numerical fluxes to gas liquid two phase flows |
| topic | upwind difference scheme numerical dissipation gas-liquid multiphase flow low Mach number preconditioning |
| url | https://www.mdpi.com/2311-5521/10/2/38 |
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