By W. J. Thron

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**Extra info for Analytic Theory of Continued Fractions II**

**Sample text**

8. In general, this approach results in good spatial discretization in the interior of the domain, although in the vicinity of boundaries the grid quality can be poor. 3 Point Creation Driven by the Boundary Point Distribution For grid generation purposes, the domain is defined by points on the geometrical boundaries. It will be assumed that this point distribution reflects appropriate geometrical features, such as variation in boundary curvature and gradient. Ideally, any method for automatic point generation should ensure that the boundary point distribution is extended into the domain in a smooth manner.

These overlaid grids also require interpolation to transfer data between grids, and that subject is the principal focus of effort in regard to the use of this type of composite grid. The hybrid structured–unstructured grids avoid this interpolation by replacing the overlaid region with an unstructured grid connecting logically rectangular structured component grids. This can require modification of solution codes, however. 2 Block-Structured Grids Block-structured grids opened the door to real-world CFD in the late 1980s, and many real applications are still based on these grids (see Chapters 12 and 13).

The proceedings of the several international conferences on grid generation (Thompson [1982], Hauser and Taylor [1986], Sengupta, et al. [1988], Arcilla, et al. [1991], Eiseman, et al. [1994], Soni et al. [1996]) as well as those of the NASA conferences (Smith [1980], Smith [1992], Choo [1995]) provide numerous illustrations of application to CFD and some other fields. A recent comprehensive text is Carey [1997]. 2 Mesh Generation Considerations The generated mesh must be sufficiently dense that the numerical approximation is an accurate one, but it cannot be so dense that the solution is impractical to obtain.