In this paper, a numerical method for generating structured grids which are adapted to the curved edges of quadrilateral patches, lying in surfaces of arbitrary shape, is presented. The surface geometry is provided using an unstructured set of grid points, their coordinates and connectivity being the data of the calculation. The structured grid is defined by introducing a convenient set of two parametric coordinates, which satisfy the surface Laplace equation. These equations are solved in the physical domain using the finite element technique, and provide the parametric values over the primitive unstructured grid nodes. The curvilinear coordinate lines, which coincide with the structured grid lines, are defined by searching for the solution contours inside the surface patch. The generation of a high quality structured grid is finally accomplished through a structured-to-structured grid transformer which improves the grid characteristics, such as orthogonality, smoothness and achieves the grid lines clustering, as required by the user. The proposed method has been successfully applied in a number of cases of industrial interest and several practical applications are illustrated herein.

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