Note on the Mathematical Formulation of the Problem of Numerical Coordinate Generation

摘要

A set of second order partial differential equations for the generation of three-dimensional grids around and between arbitrary shaped bodies has been proposed. These equations basically depend on the Gauss equations for a surface and have been structured in such a way that an automatic connection is established between the succeeding generated surfaces. The vanishing of the Riemann curvature tensor has been used to isolate those fundamental equations which every coordinate system in either two- or three-dimensional Euclidean space must satisfy.(Author)