On distortion functions for the strong constraint method of numerically generating orthogonal coordinate grids

Nearly Orthogonal Two-Dimensional Grid Generation with Aspect Ratio Control

“…Ascoli et al [11] showed that if f is a special product of the form f (ξ, η) = (ξ ) (η), and if h ξ is specified at one of the boundaries, then an orthogonal mapping does exist between (ξ, η) and (x, y). However, robustness problems can still arise.…”

“…Orthogonal grid generation is the subject of many studies [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. One of the well-known and frequently used ways to obtain orthogonal grids in two dimensions is through conformal mapping.…”

“…Theoretical foundations of elliptic grid generation owe much to the theory of conformal mappings, which preceded it by several decades. In fact, the main impetus for the development of elliptic methods is the lack of versatility in the construction of conformal maps and inability to control the distribution of grid points in the generated grid [1,3,8,11,12,16,20].…”

“…In this method, constraints on the components of the metric tensor of the curvilinear coordinates are used to achieve orthogonality and to control the spacing of coordinate lines. This method has been the subject of many articles [9][10][11][12][13][14][15][16]20]. The main problem in all these methods is determination of the so-called distortion function f which controls the scale factors.…”