A non-orthogonal curvilinear coordinate system has been introduced in this paper to overcome the difficulties of indeterminate boundaries in computational domain in inverse and hybrid problems. A universal method for direct, inverse, and hybrid problems has been established by using a discrete unified mathematic model. Three dimensional finite element technigue and finite volume method were used accordingly. The unified method contains the threedimensional analysis of direct problem, the full three dimensional design of the blade, and the partial modification for the blade.