Performance Assessment of Power-Law and First-Order Upwind Interpolation Schemes in Analyzing Confined Buoyancy-Driven Turbulent Flow Field Using the Finite Volume Method

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, 9-21

Abstract: Confined buoyancy-driven turbulent flows occur in many engineering and thermal systems. An accurate numerical resolution of the flow field is required to assess the performance of these systems. The finite volume method is a robust discretization scheme because it can adapt to both structured and unstructured flow domains. However, it must be coupled with an appropriate interpolation scheme that estimates the values of the flow variables across the boundaries of the finite volumes. Thus, the accuracy of finite volume-based numerical predictions of the flow field is strongly dependent on the choice of interpolation scheme. Therefore, assessing the performance of interpolation schemes within the finite volume framework is critical. This study provides a scientific evaluation of the performances of the power law and first-order upwind interpolation schemes in simulating confined buoyancy-driven turbulent flows using the finite volume method coupled with the pressure-implicit with splitting of operators algorithm, with turbulence closure provided by the shear stress transport (SST) k–ω turbulence model. The interpolation schemes were evaluated with respect to numerical stability, convergence characteristics, artificial diffusion, and their effectiveness in resolving dominant flow and turbulence features. The assessment of their performance was based on the predicted flow field against benchmark results. The results revealed that the first-order upwind scheme was more stable and had a higher convergence rate than the power law scheme. However, this scheme is overly diffusive, leading to smearing of gradients, thus spreading momentum and temperature too broadly across the cavity. The power law scheme more accurately captures flow, thermal, and turbulence structures, particularly turbulent kinetic energy and eddy viscosity fields, although with increased grid sensitivity. The numerical evidence obtained provides a stability–accuracy trade-off between the two interpolation schemes considered in this study. Therefore, for any analysis requiring a physically meaningful representation of natural convection at high Rayleigh numbers, the power law scheme provides far more reliable and accurate results than first-order upwind.

Keywords: Buoyancy; discretization; interpolation; turbulent (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:70242

DOI: 10.24018/ejmath.2026.7.1.70242

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