On current aspects of finite element computational fluid mechanics for turbulent flows

Abstract

Numerous configurations for fluid mechanics systems involve motion of the fluid predominantly in a single well-defined direction. Examples include the wide range of aerodynamics as well as most fluids handling systems. Furthermore, in most of these situations, the flow is nominally steady, in all probability turbulent, and usually three-dimensional. A class of problems fitting this description is amenable to numerical simulation under the ‘parabolic’ simplification, wherein an order-of-magnitude analysis is employed to approximate the subsonic, three-dimensional, steady time-averaged Navier-Stokes equations for directed flows. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm formulation. A parabolic transverse momentum equation set is constructed to enforce first-order continuity effects as a penalty constraint. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, and requires solving the parabolic form of the two-equation turbulent kinetic energy-dissipation equation system. The theoretical aspects regarding accuracy and convergence are summarized, including the efficiency of the penalty constraint concept. The formulational aspects of the algorithm are presented. Numerical results for definitive flow geometries are summarized to document the overall robustness of the developed algorithm.