Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

Sorenson, Reese L.

doi:10.1016/0096-3003(82)90213-2

“…'Automatic' control functions were calculated on the basis of finite difference approximations to the metric coefficients, as given in Equations (27) and (28). The grids shown in Figure 10(c) and (d) were computed by using the present method only, according to Equation (29). Figures 11 and 12 show monitor point data for the results of Figure 10.…”

Section: Discussionmentioning

confidence: 99%

“…Interior source terms (control functions) are interpolated from the six sets of boundary values weighted according to the Jacobian g. Figure 4(c) shows a Dirichlet -Laplace system. Figure 4(d) demonstrates the use of automatic control functions according to Equation (29) to obtain boundary orthogonality. The same end may also be achieved by varying reference values.…”

Section: Control Functionsmentioning

confidence: 99%

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A finite volume method for numerical grid generation

Beale

¹

1999

Int. J. Numer. Meth. Fluids

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A novel method to generate body‐fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables ξ, η and ζ is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re‐zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid‐correction procedure. The scalar variables are re‐mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet–Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local‐boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point‐by‐point and whole‐field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright © 1999 National Research Council of Canada.

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“…'Automatic' control functions were calculated on the basis of finite difference approximations to the metric coefficients, as given in Equations (27) and (28). The grids shown in Figure 10(c) and (d) were computed by using the present method only, according to Equation (29). Figures 11 and 12 show monitor point data for the results of Figure 10.…”

Section: Discussionmentioning

confidence: 99%

“…Benchmark problems: (a) and (b) H-and O-grids with 'automatic' control functions computed from metric coefficients according to Equations(27) and(28): identical grids were generated by using both present and inverse methods; (c) and (d): control functions prescribed from missing source terms according to Equation(29), present method only.…”

mentioning

confidence: 99%

A finite volume method for numerical grid generation

Beale

¹

1999

Int. J. Numer. Meth. Fluids

0

View full text Add to dashboard Cite

A novel method to generate body‐fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables ξ, η and ζ is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re‐zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid‐correction procedure. The scalar variables are re‐mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet–Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local‐boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point‐by‐point and whole‐field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright © 1999 National Research Council of Canada.

show abstract