The Selective Catalytic Reduction (SCR) is a promising approach to meet future legislation regarding the nitric oxide emissions of diesel engines. In automotive applications a liquid urea-water solution (UWS) is injected into the hot exhaust gas. It evaporates and decomposes to ammonia vapor acting as the reducing agent. Significant criteria for an efficient SCR system are a fast mixture preparation of the UWS and a high ammonia uniformity at the SCR catalyst. Multiphase CFD simulation is capable to support the development of this process. However, major challenges are the correct description of the liquid phase behavior and the simulation of the ammonia vapor mixing in the turbulent exhaust gas upstream of the SCR catalyst.This paper presents a systematic study of the impact of the turbulence model and the numerical spatial discretization scheme on the prediction of the turbulent mixing process of the gaseous ammonia. The simulations are carried out for an exhaust system with a mixing element that creates turbulent swirl flow in the mixing pipe. Numerical results are validated with back pressure measurements at the mixer and CLD measurements of the spatial distribution of the reduced NOx concentration at the catalyst outlet.The study proves the high impact of an advanced second-order differencing scheme on the species transport. Furthermore it shows that Reynolds-averaged k-ε models systematically underestimate the turbulence level in the swirl flow and, in consequence, the turbulent diffusion and uniformity of the ammonia vapor at the catalyst. In contrast, a Reynolds-Stress model leads to improved predictions by accounting for the anisotropic character of turbulence in the swirl flow. In combination with detailed submodels of the liquid phase dynamics and -evaporation a correct prediction of the ammonia homogenization for a wide range of operating conditions can be achieved. By this means a good correlation with measured ammonia uniformity indices and the mixing element"s back pressure behavior can be observed. The described numerical method therefore allows for a predictive evaluation and optimization of SCR-mixing systems.