Direct Design Solution of the Elliptic Grid Generation Equations

Abstract

Thompson et al. proposed a set of elliptic equations for generating smooth, structured, boundary-fitted grids. This equation set defines an inverse problem. The solution is usually obtained by first inverting the equations to convert from the inverse problem to a direct problem. The present article shows that the original equations can be discretized and solved in the physical domain, avoiding the inversion. This new method is applied to solve several 1-D and 2-D problems, and is extendible to three dimensions.

The implementation complexity and the computational cost of the new approach are both higher than under the usual approach. The new method, however, can map unstructured meshes as well, and may provide a building block for new grid generation methods in the future.

This research was supported by a Discovery Grant to G. D. Raithby from the Natural Sciences and Engineering Research Council of Canada. The authors are grateful to Gordon Stubley and Bruce Simpson, both faculty at the University of Waterloo, for helpful discussions.