A synopsis of elliptic PDE models for grid generation

摘要

This paper is devoted to an analytical comparison of the various elliptic partial-differential-equation (PDE) models which are in current use for grid generation. These comparisons, particularly between the equations from the Laplace-Poisson system and the equations from a Gaussian approach, have yielded useful expressions connecting the 3D Laplacians and the surface Beltramians. This effort specifically been successful when the transverse coordinate leaving the surface is orthogonal to the surface. Equations which are derivable from Cartesian-type Poisson and those obtained by using the variational priciple in surface coordinates have also been considered.