A Non-iterative Scheme for Orthogonal Grid Generation with Control Function and Specified Boundary Correspondence on Three Sides

Simulation of non-hydrostatic, density-stratified flow in irregular domains

“…By prescribing the distribution of boundary points, the spatial distribution of the grid resolution can be controlled. Although specification of boundary correspondence on two sides was found to be adequate for purposes here, Oh and Kang [3] have shown that correspondence can be specified on up to three sides. Because we only require the grid generation to be done once, prior to the flow simulations, the implementation of the covariant Laplace technique employs accurate numerical techniques wherever possible.…”

Nearly Orthogonal Two-Dimensional Grid Generation with Aspect Ratio Control

“…In the second method, used by Duraiswami and Prosperetti [16], Kang and Leal [14], and Oh and Kang [15], the main problem is to define an admissible function for f . 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).…”

“…Similar observations as for domain A can be deduced. Domain C is used by Oh and Kang [15]. Grids obtained with both specified boundaries and with sliding (Neumann-Dirichlet) boundaries on the bottom are shown in Figs.…”

“…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.…”

“…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.…”