Development of Elliptic and Hyperbolic Grid Generation

It has been found that partial differential equations (PDE's) could be used to efficiently generate high quality structured grids. The grid discretizes the physical domain to computational domain, typically an array data structure in Fortran. This study concentrates on elliptic and hyperbolic methods for structured grid generation. The elliptic method uses the Laplace equations to transfonn the physical domain to computational domain and finite difference to generate the grids. Whereas, the hyperbolic method uses orthogonal relations to solve the PDE's, a marching scheme to create the grids and then cubic spline interpolations to smoothen grid lines at the boundaries. C-type and O-type elliptic and hyperbolic grids have been generated for an airfoil and smooth boundary conditions were obtained in the elliptic method but not by the hyperbolic method.

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