Finite Volume-Based Numerical Investigation of Power-Law and QUICK Interpolation Schemes in Analyzing Confined Buoyancy-Driven Turbulent Flow Field

Jane Gatwiri, Stephen Karanja and Eustace Mwenda
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Jane Gatwiri: Meru University of Science and Technology, Kenya
Stephen Karanja: Meru University of Science and Technology, Kenya
Eustace Mwenda: Meru University of Science and Technology, Kenya

European Journal of Mathematics and Statistics, 2026, vol. 7, issue 1, 22-30

Abstract: Turbulent natural convection in confined settings is a common phenomenon in many thermal and engineering systems. Therefore, an accurate prediction of the flow field is essential for a reliable performance evaluation. Among the numerous prediction approaches, numerical methods are used, which largely complement experimentation. Confined buoyancy-driven turbulent flows are largely analyzed using the finite volume discretization approach owing to its strong conservation properties and flexibility in handling complex computational domains. However, the accuracy of finite volume-based numerical simulations largely depends on the interpolation scheme used to approximate the flow variables at the control volume faces. Consequently, a careful assessment of interpolation schemes is essential for improving numerical predictions. This study presents a scientific evaluation of the performance of the power-law and QUICK interpolation techniques in simulating the turbulent natural convection of air in a square cavity. Pressure-velocity coupling was attained using the pressure-implicit with splitting of operators; (PISO) algorithm, while turbulence was resolved using the SST k–ω turbulence model. The schemes were assessed based on numerical stability, convergence behavior, artificial diffusion, and their effectiveness in predicting primary flow and turbulence features in the interpolation of temperature, velocity, turbulent kinetic energy, and turbulent eddy viscosity across the faces of control volumes. The flow profiles were validated using experimental data. The numerical findings demonstrated that the QUICK scheme consistently provided superior predictions compared to the power-law interpolation scheme for all examined variables. These findings demonstrate that for the numerical analysis of confined buoyancy-driven turbulent flows at high Rayleigh numbers, QUICK offers improved reliability and accuracy compared to the power-law scheme.

Keywords: Finite volume; interpolation; natural convection (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:7:y:2026:i:1:id:70297

DOI: 10.24018/ejmath.2026.7.1.70297

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