A detailed knowledge of the fluid flow and the mixing processes in gas turbine combustion chambers is an important prerequisite for the development of fuel and emission efficient gas turbine combustion chambers. The usage of computational fluid dynamics is a valuable development tool, provided that the results are sufficiently exact and can be achieved with an acceptable speed. The usage of non-linear eddy-viscosity turbulence models for the calculation of complex turbulent flows under conditions which are typical for combustion chambers is the focal point of this work. This class of turbulence models was developed in order to combine the advantages of linear eddy-viscosity models (numerical robustness, speed of calculation) with those of Reynolds Stress turbulence models (accuracy in complex flows). After the presentation of the governing equations of fluid flow and possible methods for the calculation of turbulent fluid flows the statistical method as well as various methods for the modeling of turbulence within the framework of the statistical approach is described in more detail. The turbulence models are classified as being algebraic or differential. It is shown that within both classes there are linear and non-linear turbulence models. Examples of all four types of turbulence models are shown which are of particular interest for the calculation of turbulent flows within combustion chambers. Then it is demonstrated why the turbulent flow within gas turbine combustion chambers is especially demanding with respect to turbulence modeling. The numerical scheme is described which is employed for this work as well as the implementation of the non-linear algebraic turbulence model of cubic order. With the help of an analysis it is demonstrated that the lack of numerical robustness of this turbulence model can be attributed to the calibration of the model coefficients. The importance of the calibration is shown with the help of a turbulent flow through a channel with a quadratic cross section. The flow configurations which are most relevant in combustion chambers, the swirl flow and the flow injection into a cross flow, are identified and described in more detail. Examples of well documented experiments for both flow configurations are chosen and this data is compared with the flow calculation results of the turbulence models which are used for this work. Finally the flow configuration of a secondary flow injection into a swirling cross flow is calculated and the numerical results are compared with experimental data. From the results it can be concluded that for this demanding case the more complex turbulence models are not capable of achieving better results than simpler turbulence models. The theoretical superiority of advanced turbulence models is diminished by a lack of numerical robustness. In the course of this work it has turned out that the so called quasi-linear turbulence model is a practicable compromise between accuracy and numerical robustness.