Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part III.aFNS theory validation

What is it about?

CFD capability advancement unstagnation: aFNS theory contribution to CFD advancement unstagnation is documented in three parts. Mathematical formalities and resolution of the numerous algorithmic issues required for aFNS theory PDE system to be bounded domain well-posed constitute Part I. Part II details validation of the optimal Galerkin weak form aFNS theory CFD algorithm coupling with BCE and DBC resolution Galerkin algorithms including asymptotic error estimate and convergence quantification. Part III documents aFNS theory coupled resolution CFD algorithm validation for the virtual fluid dynamics laboratory, a thermal-incompressible NS manufactured statement characterized by steady to unsteady, eventually multi-scale chaotic periodic thermal-velocity vector fields explicitly Re-dependent. For assured laminar Re specifications, aFNS theory CFD code generates a posteriori data quantifying the steady to unsteady, multi-scale transition process, also validation via linear stability theory predicted critical Re and nil impact on genuinely laminar NS predictions. Thereafter, for Re specifications ranging laminar to not-assured laminar, a posteriori data quantify aFNS theory annihilation of NS CFD algorithm generated large wave number spectral content. A sufficiently large Re specification leads to first principles (modeling free!) prediction of unsteady, periodic thermal wall jet profile transitioning-from-laminar, followed by separation and turbulent profile reattachment, then relaminarization. These data additionally enable O(1; 2; 3) state variable scaled significance validation and fully quantify aFNS theory generated O(2; 3) state variable distributions,  the gaussian filter uniform measure.

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