Abstract An algebraic Reynolds stress (ASM) turbulence model using a simplified pseudo-viscosity is incorporated with a non-orthogonal and non-staggered grid system using Cartesian velocity components with finite volume discretization. The accuracy and robustness of the method is shown by the prediction of complex turbulent flows in 8° and 20° included angle conical diffusers, with and without swirl. Both the ASM and the k - ϵ turbulence models predict the mean velocities accurately, while the ASM turbulence model gives better predictions of the Reynolds stresses than the k - ϵ turbulence model.