NAVIER-STOKES SOLVER FOR COMPLEX 3-DIMENSIONAL TURBULENT FLOWS ADOPTING NONLINEAR MODELING OF THE REYNOLDS STRESSES

A non-linear modelling of the Reynolds stresses has been incorporated into a Navier-Stokes solver for complex three-dimensional geometries. A k-epsilon model, adopting a modelling of the turbulent transport whi ch is not based on the eddy viscosity, has been written in generalised co-ordinates and solved with a finite volume approach, using both a G MRES 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 evaluate d through comparison with the experimental data. The computational pro cedure is implemented for the flow analysis in a 90 degrees square sec tion bend and the obtained results show that with the non-linear model ling a much better agreement with the measured data is obtained, both for the velocity and the pressure. The importance of the convection sc heme is also discussed, showing how the effect of the non-linear corre ction added to the Reynolds stresses is effectively hidden by the addi tional numerical diffusion introduced by a low-order convection scheme as the first-order upwind scheme, thus making the use of higher order schemes necessary. (C) 1998 John Wiley & Sons, Ltd.