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

Abstract

ABSTRACTFor 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.