A Navier-Stokes solver for complex three-dimensional turbulent flows adopting non-linear modelling of the Reynolds stresses

Abstract

A non-linear modelling of the Reynolds stresses has been incorporated into a Navier–Stokes solver for complex three-dimensional geometries. A k–ε model, adopting a modelling of the turbulent transport which is not based on the eddy viscosity, has been written in generalised co-ordinates and solved with a finite volume approach, using both a GMRES solver and a direct solver for the solution of the linear systems of equations. An additional term, quadratic in the main strain rate, has been introduced into the modelling of the Reynolds stresses to the basic Boussinesq's form; the corresponding constant has been evaluated through comparison with the experimental data. The computational procedure is implemented for the flow analysis in a 90° square section bend and the obtained results show that with the non-linear modelling a much better agreement with the measured data is obtained, both for the velocity and the pressure. The importance of the convection scheme is also discussed, showing how the effect of the non-linear correction added to the Reynolds stresses is effectively hidden by the additional numerical diffusion introduced by a low-order convection scheme as the first-order upwind scheme, thus making the use of higher order schemes necessary. © 1998 John Wiley & Sons, Ltd.