This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The flow in a Taylor-Couette system is one of the most explored flows today. The behaviour of the flow is characterized by Reynolds number, radii and aspect ratio. By reducing the gap width the Taylor-Couette system can be used as a simplified bearing model which has one additional feature. To cover flow effects of a real bearing the rotating inner cylinder moves on an offset track. Thus the system is also characterized by a varying annulus. That changes the eccentricity which is also related to the critical Reynolds number for the system. There is a higher Reynolds number for a higher eccentricity. This is used as a benchmark to validate the code. Depending on the eccentric position of the rotating inner cylinder one can notice either Taylor Vortex flow or Couette Flow. After testing the code the gap width will be adjusted to realistic bearing geometries. This second part refers to bearing simulations where the gap width is adjusted to real bearing conditions. In Fact the present system is a simplified bearing, which covers not all details of a real one. It becomes more complex in later stages of the project, where oil feedings and notches are implemented as well as the occurrence of cavitation. Furthermore the offset tracks will be much more complex. The final goal is to develop a 3D simulation tool for hydrodynamic journal bearings that resolves effects like cross flow from the oil feedings and also cavitation. Known methods based on the Reynolds equations fail to predict important flow characteristics in complex bearing geometries due to their two dimensional nature. If sufficiently low local pressure areas occur, cavitation- related damages may appear. So the pressure distribution of the flow is of interest