A method of two and three dimensional orthogonal grid generations with control of spacing by using the covariant Laplace equation is presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries while maintaining good orthogonality in the whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformations of an approximate conformal mapping and an auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length and orthogonal correction is performed in the auxiliary domain. It is concluded that the methodology can successfully generate well-controlled orthogonal grids around aerodynamic bodies such as airfoils, wing-body shapes and airplanes including wing-fuselage-tail wing, etc.
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