| Summary: | 碩士 === 國立成功大學 === 航空太空工程學系 === 85 ===
The improvement upon the Thomas-Middlecoff elliptic grid solver of direct grid control is proposed such that the grid clustering aroud the convex boundary and grid diluting aroud the concave boundary are effectively eliminated. The main concern is to add the curvature correction to the linear and nonlinear grid equations. The linear equations employ the phycial coordinates as dependent variables. The nonlinear equations, which are orignally linear, employ the coordinates on the computational domain as dependent variables and interchange the independent and dependent variables. The curvature correction is principally added to the grid lines around a boundary and is quickly attentuated as the grid points move inward. Numerical examinations show that both the linear and nonlinear equation methods can ffectively eliminated the undesired grid clustering and diluting. However, the linear equation method requires a lengthy try and error to get a proper correction. On the other hand, the nonlinear equation method, which get benefit from the maximum principle, in addtion to remove the undesired grid clustering and diluting with easy, improve the overall grid smoothness effectively and enhance boundary grid orthogonality slightly. This study adds the curvature correction to the Steger and Sorenson boundary grid control method and no significant effect is found the H-grids. For the C-grid system, the curvature correction is helpful to enhance the convergence of iteration.
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