Orthogonal grid generation

A technique is presented for the generation of two-dimensional orthogonal grids which is accurate, rapid, conceptually simple, relatively robust, and general enough to be applicable to a wide range of applications when coupled with modern flow solvers. A novel application of the hinge point transformation is used to map a contour onto a half plane, which is thereby transformed into an open rectangle, where the points added to close the rectangle and grid boundary point locations are specified according to preselected stretchings. Exponential spline interpolation determines the physical plane locations corresponding to the grid boundary point locations on three sides of the rectangle, and physical locations corresponding to the fourth side are obtained by inverting the transformations. A fast Poisson solver is then used to determine the physical location of the interior grid nodes. A method for building complex multiple region grids through the matching of simpler grids at common boundaries is illustrated. Suitable grids can be produced for a wide range of nonperiodic geometries.