Today numerical models are a major part of the diesel engine development. They are applied during several stages of the development process to perform extensive parameter studies and to investigate flow and combustion phenomena in detail. The models are divided by complexity and computational costs why the engineer has to decide which the best choice for his task is. 0D models are suitable for problems with large parameter spaces and multiple operating points, e.g. engine map simulation and parameter sweeps. Hence, one would prefer to incorporate physical models to improve the predictive capability of the model. This work focuses on turbulence and mixing modeling in the 0D direct injection stochastic reactor model. The model is based on a probability density function approach and incorporates sub models for direct fuel injection, vaporization, heat transfer, turbulent mixing and detailed chemistry. The advantage of the probability density function approach towards mean value models is its capability to account for temperature and mixture in-homogeneities. Notional particles are introduced each with its own temperature and composition. The particle condition is changed by mixing, injection, chemical reaction and heat transfer. Turbulent mixing is modeled using the Euclidean minimum spanning tree mixing model which requires a mixing frequency function as input. Therefore, a turbulence model is proposed to calculate the mixing frequency dependent on turbulent kinetic energy and its dissipation. The turbulence model accounts for swirl, squish and injection effects on turbulent kinetic energy which in term are depending on operating conditions. Finally, the 0D model is tested for 40 different operating points distributed over the engine map. The results show a close match of heat release rate and exhaust emissions. Additionally, the model is compared to more detailed 3D combustion simulations for three selected operating points. The comparison shows the model is able to capture turbulence effects and local temperature and mixture distribution. Overall, the 0D model has proven its predictive capability and can be assigned to engine map simulation problems.