A 3-D free curved surface of a Pelton bucket was discretized into the 51x51 = 2,601 nodes of boundary fitted grid (BFG) for the CFD. The non-orthogonal curvilinear local frames were introduced with the natural basis vector g for the respective nodes of BFG. The natural basis vector g and its partial derivatives ∂g/∂P at each node were computed based on the differential geometry. As a result, the strong effect of the singular shape of the cutout, especially of its end-wall, on the Pelton bucket was numerically clarified and managed by the differential geometry. After the whole curved surface was approximated by the 50x50 = 2,500 local flat panels tangent to each node, the local surface area ΔS and the Gaussian curvature κ in each panel were investigated to assess the quality of the BFG.
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