Physical Sciences and Mathematics Commons^™

Algebraic Grid Generation Using Tensor Product B-Splines, Bonita Valerie Saunders

Mathematics & Statistics Theses & Dissertations

In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.

Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.

The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the …