Using covariant Laplace equations as grid generating equations, generate orthogonal grid system in 2, 3 The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and an auxiliary orthogonal mapping to have linear and uncoupled equations. Conformal transformation and the solution of potential flows are used to fulfill the requirements for the appropriate boundary conditions.
Control of Grid spacing is based on the concept of reference arc length, and orthogonal correction is performed in the auxiliary domain using Cauchy-Riemann equation.
It is concluded that the methodology can successfully generate orthogonal grids with control of spacing around aerodynamic bodies such as 2D O,H,C type airfoil grids, RAE wingbody and generic airplane including wing-fuselage-tail wing in a very short time.
