LES is expected to become a powerful tool for turbulent flow calculations of practical interest in the near future. The paper is concerned with the development and first applications of a finite-volume method based on curvilinear body-fitted grids suitable to simulate flows in or around complex geometries. Two different subgrid-scale models are implemented and tested. Because the near-wall region cannot be resolved for high-Reynolds-number flows, two different wall function approaches are applied. The turbulent flow through a straight duct at two different Reynolds numbers (Re = 4410/56690) and a 180 degree bend (Re = 56690) is investigated. While for the low-Reynolds-number flow the results are in close agreement with DNS and other LES data, the higher Reynolds number computations are not yet satisfactory when compared with available measurements. However, the main features of the flows like Prandtl's secondary motion of first and second kind are reasonably predicted by LES.