Overview

Historically, the process of modifying an initial mesh through the application of an elliptic equation system is termed mesh generation. This book chooses to make the distinction between methods that generate a mesh where none existed previously (mesh generation), and methods that improve an existing mesh (mesh enhancement). This distinction is necessary to define the scope of this book, as only selected elliptic methods that improve an existing mesh are discussed.

The elliptic approaches studied here are, technically, not mesh generators, but are node redistribution methods. They are mesh enhancement systems as they make improvements to an existing mesh. Methods such as Delaunay triangulation and transfinite interpolation (see Section 1.3.4) are mesh generators, since they create an initial mesh where none existed previously. Further, meshes resulting from mesh generation methods are viewed as initial conditions for the elliptic methods described in this chapter and in the rest of this book. The terms mesh generation and mesh enhancement, however, may generally be viewed as synonyms when employing elliptic equation systems.

In this chapter, derivation of various elliptic mesh enhancement systems is provided, based on the requirement that the grid lines form an isothermal coordinate system on a two-dimensional surface. The existing elliptic grid generators are shown to be special cases of this, more general, framework. By introducing a harmonic coordinate system, a generalization to three dimensions is also indicated.

Adaptive mesh enhancement is an important tool for the efficient solution of a large number of problems in computational fluid...