In this dissertation, Immersed Boundary Method (IBM) is evaluated in ribbed duct geometries to show the potential of simulating complex geometry with a simple structured grid. IBM is first investigated in well-accepted benchmark cases: channel flow and pipe flow with circular cross-section. IBM captures all the flow features with very good accuracy in these two cases. Then a two side ribbed duct geometry is test using IBM at Reynolds number of 20,000 under fully developed assumption. The IBM results agrees well with body conforming grid predictions. A one side ribbed duct geometry is also tested at a bulk Reynolds number of 1.5⨉10⁴. Three cases have been examined for this geometry: a stationary case; a case of positive rotation at a rotation number (Ro=ΩDₕ/U) of 0.3 (destabilizing); and a case of negative rotation at Ro= -0.3 (stabilizing). Time averaged mean, turbulent quantities are presented, together with heat transfer. The overall good agreement between IBM, BCG and experimental results suggests that IBM is a promising method to apply to complex blade geometries. Due to the disadvantage of IBM that it requires large amount of cells to resolve the boundary near the immersed surface, wall modeled LES (WMLES) is evaluated in the final part of this thesis. WMLES is used for simulating turbulent flow in a developing staggered ribbed U-bend duct. Three cases have been tested at a bulk Reynolds number of 10⁵: a stationary case; a positive rotation case at a rotation number Ro=0.2; and a negative rotation case at Ro=-0.2. Coriolis force effects are included in the calculation to evaluate the wall model under the influence of these effects which are known to affect shear layer turbulence production on the leading and trailing sides of the duct. Wall model LES prediction shows good agreement with experimental data.