Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part II. Resolution algorithms, validations

ABSTRACT

For uniform measure δ Gaussian filter, Part I derives the totally analytical aFNS theory closing rigorously space filtered Navier–Stokes (NS) partial differential equation (PDE) system absent a Reynolds number (Re) assumption. aFNS theory state variable is scaled O(1; δ²; δ³) via classic fluid mechanics perturbation theory which also identifies the O(δ²) elliptic PDE system. Filter penetration of domain bounding surfaces requires O(1) PDE system inclusion of boundary commutation error (BCE) integrals. For the O(1; δ²), PDE system to be bounded domain well-posed requires derivation of domain encompassing nonhomogeneous Dirichlet boundary conditions (DBC). Resolution of BCE and DBC requirements is theorized via O(δ⁴) approximate deconvolution (AD) Galerkin differential definition weak form algorithms. Amenable to any space-time discretization, detailed is aFNS theory insertion in the optimal Galerkin weak form CFD algorithm, finite element linear tensor product basis implemented. Coupled Galerkin CFD/BCE/DBC code a posteriori data reported herein validate theory resolution algorithms including accuracy/convergence assessments.

Acknowledgments

During the dissertation project, the first author served as HPC Graduate Assistant in the Joint Institute for Computational Sciences (JICS), a collaboration between the US DOE Oak Ridge National Laboratory and the University of Tennessee/Knoxville (UTK). Dissertation project coordination was through the UTK College of Engineering CFD Laboratory.