Two Modified Versions of Hsu-Lee's Elliptic Solver of Grid Generation

Adaptive Grid Generation by Elliptic Equations With Grid Control at All of the Boundaries

“…The present investigation combines the adaptive grid procedure of Anderson [I61 with our previously developed boundary grid control method [15]. For the sake of clarity, both the adaptive grid and boundary grid control methods are first restated.…”

Parabolic Equation Method of Grid Generation for Enclosed Regions

“…(8). For the grid level next to the left and right boundaries U = 1 0 and i m ) , the weighting function takes the form (9) In other words, unknown grids next to the bottom-top boundary pair and next to the left-right boundary pair are estimated separately. At the four comer points, direct averaging gives a unique definition of the grid point.…”

“…On the merit side, the hyperbolic equation method employs the , weighting function, Eqs. (3b), + angle measured from Y" to' (6), (8), (9) angle measured frorn F" to r • orthogonal condition as the governing equation, which has a much stronger driving force to provide grid orthogonality over the entire domain than the parabolic equation method. As to the demerit side, the characteristic waves of the hyperbolic equation method might cause grid oscillation around sharp comers and boundaries perpendicular to the marching direction.…”

“…The second method involves solving elliptical, parabolic, or hyperbolic partial differential equations, among which the elliptical equation method is the most popular. The elliptical equation method [1][2][3][4][5][6][7][8][9][10][11] can preserve grid orthogonality around boundaries and grid smoothness over the entire domain but generally requires much more computing time than other methods. Equations of the parabolic equation method are obtained by modifying proper terms from the grid equations of the elliptical equation method [12][13][14][15][16][17].…”

Two-Dimensional Elliptic Grid Solver Using Boundary Grid Control and Curvature Correction

“…Jeng and Liou employed the two-dimensional trans nite interpolation formula for the control function. 16,17 In 1980 Thomas and Middlecoff proposed a direct method for grid control on boundaries. 18 They rewrote the grid equations and noted that for two-dimensional grid systems one control function is closely related to the grid size distribution along one family of grid lines, and the other control function is related to the grid size distribution along another family.…”