This thesis deals with the numerical computation of flow properties and the position of the free water surface in turbulent water bodies. For this purpose the well-known and mass-conserving Finite Volume method is applied in three spatial dimensions. In contrast to usual techniques, computation cells are being used which are characterised by an arbitrary number of faces. Due to this, the presence of flows not perpendicular to element faces, which are usually the reason for a reduction in accuracy, can be reduced by a reasonable amount.
In a first step, the capabilities and characteristics of 3D models in use in hydraulic research today are evaluated and subject to comparison.
Afterwards, algorithms for generating computation grids based on polyhedral cells are presented. Subsequently the governing equations for fluid flow and turbulent properties are discretised on these computation cells, and the required boundary conditions are discussed. The resulting equations and grid generation algorithms, as well as some post processing functionality, are implemented into a computer model called RSim-3D. This model is then validated against measurements of four different laboratory experiments before it is applied to a reach of the river Danube in Austria. The discussion of potential future prospects finally concludes the work.