By Peter M. Neumann
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The use of smoothed control functions evaluated from the algebraic grid produces a smooth grid that retains essentially the spacing of the algebraic grid. The elliptic generation system can be solved by point SOR iteration using a field of locally optimum acceleration parameters. These optimum parameters make the solution robust and capable of convergence with strong control functions. ©1999 CRC Press LLC Control functions can also be evaluated on the boundaries using the specified boundary point distribution in the generation system, with certain necessary assumptions (orthogonality at the boundary) to eliminate some terms, and then can be interpolated from the boundaries in this manner.
9) which, in fact, does arise from a variational form (Warsi and Thompson ). 9. 4 Unstructured Grids Unstructured grid generation has its roots in the finite element world of structures modeling. The real introduction to the CFD community came in the 1980s primarily from Baker, Weatherill, and Lohner. Unstructured grids have inherent simplicity of construction in that, by definition, no structure is required. Also it is not inherently necessary to communicate the actual topology of the configuration to the grid generator.
A second-order elliptic generation system allows either the point locations on the boundary or the coordinate line slope at the boundary to be specified, but not both. It is possible, however, to iteratively adjust the control functions in the generation system until not only a specified line slope but also the spacing of the first coordinate surface off the boundary is achieved, with the point locations on the boundary specified. These relations can be applied on each successive coordinate surface off the boundary, with the off-surface spacing determined by a hyperbolic sine distribution from the spacing specified at the boundary.