Two Dimensional Multi-Block Grid Optimisation by Variational Techniques
A method for generating optimal two dimensional structured grids based on a method developed by Kennon and Dulikravitch is described. The global quality of the grid is calculated as a linear weight of the sum of the local orthogonality and smoothness measures. A conjugate gradient method is used to optimise the quality function by varying the distribution of grid points. Special consideration is given at the boundaries to ensure that the grid points can move freely along the boundary to optimise the local quality measures. Results are presented for some basic test cases.
The basic algorithm is extended to a two dimensional Multi-Block structure. Connectivity across internal block boundaries is resolved to ensure that orthogonality and smoothness are retained between blocks. Results are given that illustrate the applicability of the method.
Both versions of the code can readily be extended to three dimensions with the minimum of extra effort.
Unable to display preview. Download preview PDF.
- Anderson, D.A., ’Computational Fluid Mechanics and Heat Transter’ , ISBI 0-89116-471-6 , 1984Google Scholar
- Borne, A.F.E ., ’Sub-Task 4.3, Adaptive Mesh Generation within a 2D Computational Fluid Dynamic Environment using Optimisation Techniques ’, JS12016, March 1992.Google Scholar
- Carcaillet, R., ’Generation and Optimisation of flow-adaptive computational grids’, Msc . Thesis University of Texas at Austin, 1986 .Google Scholar
- Kennon, S.R. and Dulikravitch, G.S., ’Gener at i on of Computational Grids using Optimisation’ , AIAA J., 24, 1069-1073, July 1986.Google Scholar
- Pierre, D.A. , ’Optimisation Theory and Applications’, ISBI 0-486-66206-X, 1986.Google Scholar
- de Boor, C. ’Bi cubi c spline interpolation’, J . Math. Phys., 41, 212-218, 1962.Google Scholar
- Lancaster , P., ’Curve and Surface Fitting : An Introduction’, ISBI 0-12-436061-0 , 1986.Google Scholar