A method of three-dimensional grid generation for general three-dimensional arbitrary shapes by using the covariant Laplace equation is presented. The method is based on the concept of decomposition of the global three-dimensional transformation into consecutive mappings of a quasi-conformal mapping and an auxiliary mapping to have linear and uncoupled equations. The linearization of the generating equations is implemented by introducing a preliminary step. This preliminary step corresponds to a quasi-conformal map and is based on the boundary element method(BEM). The boundary conditions must be specified in a manner consistent with the auxiliary domain to ensure that the resulting grid remains nearly orthogonal. So, the boundary element method is introduced to apply a proper boundary conditions and is used to determine the boundary point distributions.
The present method can generate nearly orthogonal grids for arbitrary shapes without considering complex mathematical techniques. The proposed method is applied to several three-dimensional geometries to generate nearly orthogonal grid systems and shows good capability to generate orthogonal grids on the boundary. Lastly, the flowfield for a RAE wing-fuselarge is calculated with the generated grid to verify the present grid method. The compressible Euler equations are solved using a central-differenced finite volume scheme and the DADI(Diagonalized Alternating Direction Implicit) time integration method.
