Parabolic Equation Method of Grid Generation for Enclosed Regions

Liou, Yuan Chang; Jeng, Yih

doi:10.1080/10407799608914983

Cited by 1 publication

(2 citation statements)

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“…The resulting grid system generated by the nonlinear modi ed Thomas and Middlecoffmethod [Eqs. (21), (29), and (30)] is shown in Fig. 11, where all of the data are the same as those of Fig.…”

Section: Nonlinear Grid Systemmentioning

confidence: 97%

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

Jeng

Kuo

2000

AIAA Journal

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The Thompson method of explicitly evaluating control function of the elliptic grid solver is employed to improve local grid quality around convex and concave boundaries. The curvature correction is principally added to the grid lines around a boundary and is quickly attenuated as the grid points move inward. The algebraic advancing front method is employed to estimate two levels of orthogonal grids for evaluating the control functions at the boundary. If the grid equation based on the Cauchy-Riemann relation with » and´as independent variables is employed, numerical examinations show that a lengthy trial-and-error procedure is required to get a satisfactory grid distribution. In contrast, the method based on the Cauchy-Riemann relation with x and y as independent variables, which bene ts from the maximum principle, not only removes the undesired grid clustering and diluting easily but also effectively improves overall grid smoothness and slightly enhances boundary grid orthogonality. Nomenclature a 1 , b 1 , c 1 , d 1 = user-speci ed parameters; see Eq. (9) a 2 , b 2 , c 2 , d 2 = user-speci ed parameters; see Eq. (9) f = 1/ r the curvature i, j, k = unit vectors in the x, y, z directions, respectively J = Jacobian; see Eq. (2) m = modi cation factor of u , w ; Eq. (28) P, Q = control function of Eq. (3) R 1 , R 2 = functions of Eqs. (5b) and (23-25) r = radius of curvature s = arc length x, y = coordinates on the physical domain a , b , c = functions de ned in Eq. (2) h = grid angle j = curvature; Eq. (14) m = · 1 2 , parameter of Eq. (17) n , g = coordinates on the computational domain u , w = control functions; Eq. (4) x , x 1 = user-speci ed parameters; see Eq. (16)Subscripts i, j = grid indices along n , g direction, respectively o = variables on boundary n , g = partial derivatives, x n = @x / @n , x g = @x / @g , . . .

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Section: Nonlinear Grid Systemmentioning

confidence: 97%

“…21 All of these methods are principally designed to simulate the elliptic equation method. To eliminate undesired grid clustering and diluting around sharp corners along a boundary, these methods include enhancements involving user-speci ed parameters.…”

Section: Introductionmentioning

confidence: 99%