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Physics-to-Geometry Transformation to Construct Identities between Reynolds Stresses

Author

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  • Sungmin Ryu

    (Department of Mechanical Engineering, Incheon National University, Academy-ro 119, Incheon 22012, Republic of Korea)

Abstract

Modeling has become firmly established as a methodology to close the Reynolds-averaged Navier–Stokes (RANS) equations, owing to theoretical and empirical efforts towards a complete formulation of the Reynolds stress tensor and, recently, breakthroughs in data-processing technology. However, mathematical exactness is not generally ensured by modeling, which is an intrinsic reason why the reliability of RANS closure models is not supposed to be consistent for all kinds of turbulent flow. Rather than straightforwardly overcoming this inherent limitation, most of the studies to date were reasonably directed towards broadening the range of turbulent flows, where reliable prediction accuracy can be obtained via modeling. In this paper, we present three identities between components of the Reynolds stress tensor, constructed via spatial mapping on the basis of the differential version of the Gauss–Bonnet formula. Further, we present a constraint condition that gives a set of equations as numerous as the parameters within a RANS model.

Suggested Citation

  • Sungmin Ryu, 2023. "Physics-to-Geometry Transformation to Construct Identities between Reynolds Stresses," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3698-:d:1227013
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    References listed on IDEAS

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    1. Sungmin Ryu, 2023. "A Differential Relation of Metric Properties for Orientable Smooth Surfaces in ℝ 3," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
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    Cited by:

    1. Sungmin Ryu, 2023. "A Mathematically Exact and Well-Determined System of Equations to Close Reynolds-Averaged Navier–Stokes Equations," Mathematics, MDPI, vol. 11(24), pages 1-9, December.

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