Computations are performed to simulate a discrete hole film cooling how over an experimental test geometry representative of the leading edge of turbine blades. A multiblock pressure correction algorithm is used for the computations, and both low-Reynolds number and wall function k-epsilon models are used for turbulence closure. The flow through the coolant ducts, from the plenum to the blade surface, is resolved as a part of the computation by specifying the coolant mass flux in the plenum. A systematic grid refinement study is conducted with the finest grid consisting of approximately one million points. Next, the flowfield is examined; key physical mechanisms resulting from the interactions between the cooling jets and the freestream are identified and their effect on the thermal field is compared with the experimentally observed thermal field. Finally, a study of geometric parametric variation is conducted to optimize the film cooling design. Nine different combinations of two parameters, namely, the relative stagger and the relative angle between the two rows of cooling holes are investigated for their effect on heat transfer on the blade surface.