A new adaptive grid generation by elliptic equations with orthogonality at all of the boundaries

Jeng, Yih; Liou, Yuan Chang

doi:10.1007/bf01060211

Cited by 10 publications

(6 citation statements)

References 20 publications

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“…Moreover, Eq. (17) with m = 0.2 is marched upward from the bottom boundary. Although the orthogonal condition is not considered, the maximum principle keeps grids from being seriously distorted so that grid orthogonalityis preservedto a certain extent.Consequently,the curvature correction effectively eliminated the undesired grid clustering and dilution of Fig.…”

Section: Nonlinear Grid Systemmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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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: 99%

Section: Introductionmentioning

confidence: 99%

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

Jeng

Kuo

2000

AIAA Journal

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“…In their adaptive grid scheme for solving elliptic grid equations [9], Jeng and Liou modified the weighting function of Eq. (3) to be…”

Section: Present Extensionmentioning

confidence: 99%

“…It is well known [1][2][3][4][5] that if grid smoothness can be maintained to a certain degree in a structured grid system, grid adaptivity to the variation of physical variables determines the accuracy of solution. At the present, grid smoothing methods that involve the solution of elliptic equations are often applied [4,[6][7][8][9][10]. However, the elliptic equation methods generally require much computing time.…”

Section: Introductionmentioning

confidence: 99%

Revisit to the Modified Multiple One-Dimensional Adaptive Grid Method

Jeng

Lee

1996

Numerical Heat Transfer, Part B: Fundamentals

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The multiple one-dimensional adaptive grid method is repeatedly applied in this work to improve grid adaptivity with constant or incremental adaptive factors. A simple averaging formukJ is also employed to smooth the grid system. Three examples are examined: 0) a steady isotropic heal conduction problem, (]) a steady laminar driven cavity flow, and (3) an inuiscid supersonic flow over a 4% circular bump. Numerical results show that, if the final adaptive factor is moderate, the procedure using a constant adaptive factor works best.On the other hand, if the final adaptive factor is relatively large (i.e., the resulting grid system without the grid smoother involves excess grid skewness), the procedure using the incremental adaptive factor is recommended.

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“…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].…”

Section: Introductionmentioning

confidence: 99%