A new efficient finite-difference scheme for solving turbulence
k-ε equations-Turbulence U-scheme has been developed.This method was combined with the solver of Navier-Stokes discreted by a modified Beam-Warming scheme to investigate three-dimensional turbulent internal flow in S-shaped duct.Many numerical experiments and practical applications show that this method provides detailed flow field and parameters for engineering design.As a special example,a numerical simulation has been completed for an S-shaped duct including separation,secondary flow,vortices etc.The comparison of its results with the flow patterns in the circular section s-shaped duct shows a good agreement in essence.