are responsible for point spacing within D. Transforming above equations in computational space yields a set of two elliptic PDEs of the form, where These systems of equations are solved in the computational plane on uniformly spaced grid which provides us with the co-ordinates of each point in physical space. The advantage of using elliptic PDEs is the solution linked to them is smooth and the resulting grid is smooth. But, specification of P and Q becomes a difficult task thus adding it to its disadvantages. Moreover, the grid has to be computed after each time step which adds up to computational time. Hyperbolic schemes This grid generation scheme is generally applicable to problems with open domains consistent with the type of PDE describing the physical problem. The advantage associated with hyperbolic PDEs is that the governing equations need to be solved only once for generating grid. The initial point distribution along with the approximate boundary conditions forms the required input and the solution is the then marched outward. Steger and Sorenson (1980) proposed a volume orthogonality method that uses Hyperbolic PDEs for mesh generation. For a 2-D problem, Considering computational space to be given by , the inverse of the Jacobian is given by, where represents the area in physical space for a given area in computational space. The second equation links the orthogonality of grid lines at the boundary in physical space which can be written as For and surfaces to be perpendicular the equation becomes The problem associated with such system of equations is the specification of . Poor selection of may lead to shock and discontinuous propagation of this information throughout the mesh. While mesh being orthogonal is generated very rapidly which comes out as an advantage with this method. Parabolic schemes The solving technique is similar to that of hyperbolic PDEs by advancing the solution away from the initial data surface satisfying the boundary conditions at the end. Nakamura (1982) and Edwards (1985) developed the basic ideas for parabolic grid generation. The idea uses either of Laplace or the Poisson's equation and especially treating the parts which controls elliptic behavior. The initial values are given as the coordinates of the point along the surface and the advancing the solutions to the outer surface of the object satisfying the boundary conditions along edges. The control of the grid spacing has not been suggested until now. Nakamura