Grid spacing control with variation diminishing splines

Abstract

Methods used to specify and control two and three dimensional grids on which numerical solutions of partial differential equations may be obtained were studied. While initially focusing on grid generation, the research will evolve into a consideration of the interaction of grid generation with the solution of a partial differential equation. The multisurface method of grid generation was used to continuously patch a grid onto an existing grid. In the resulting grid the elements of the Jacobian matrix must be continuous across the boundary between the original grid and the patched grid. Programs were written which accept as input the coordinates of the original grid and the desired new boundary, and then use the three-surface or four-surface version of the multisurface method to extend the original grid out to a new boundary.