Page 11 - Basic Structured Grid Generation

x Preface

as smoothness, orthogonality, and grid density can be controlled by the minimization
of an appropriate functional (dependent on the components of a fundamental metric
tensor). Surface grid generation has been considered here in the general context of
harmonic maps. In Chapter 7 time-dependent problems with moving boundaries are
considered. Finally, Chapter 8 provides an introduction to the currently very active area
of unstructured grid generation, presenting the fundamentals of Delaunay triangulation
and advancing front techniques.
Our aim throughout is to provide a straightforward and compact introduction to grid
generation, covering the essential mathematical background (in which, in our view,
tensor calculus forms an important part), while steering a middle course regarding the
level of mathematical difficulty. Mathematical exercises are suggested from time to
time to assist the reader. In addition, the companion website (www.bh.com/companions/
0750650583) provides a series of easy-to-follow, clearly annotated numerical codes,
closely associated with Chapters 4, 5, 6, and 8. The aim has been to show the applica-
tion of the theory to the generation of numerical grids in fairly simple two-dimensional
domains, varying from rectangles, circles and ellipses to more complex geometries,
such as C-grids over an airfoil, and thus to offer the reader a basis for further progress
in this field. Programs involve some of the most frequently used and familiar stable
numerical techniques, such as the Thomas Algorithm for the solution of tridiagonal
matrix equations, the Gauss-Seidel method, the Conjugate Gradient method, Succes-
sive Over Relaxation (SOR), Successive Line Over Relaxation, and the Alternating
Direction Implicit (ADI) method, as well as Transfinite Interpolation and the marching
algorithm (a grid generator for hyperbolic partial differential equations). The program-
ming language is the standard FORTRAN 77/90.
Our objective in this book is to give an introduction to the most important
aspects of grid generation. Our coverage of the literature is rather select-
ive, and by no means complete. For further information and a much wider
range of references, texts such as Carey (1997), Knupp and Steinberg (1993),
Thompson, Warsi, and Mastin (1985), and Liseikin (1999) may be consulted. Unstruc-
tured grid generation is treated in George (1991). A very comprehensive survey of mod-
ern developments, together with a great deal of background information, is provided
by Thompson, Soni, and Weatherill (1999).
The authors would like to express their gratitude to Mr. Thomas Sippel-Dau, LINUX
Service Manager at Imperial College of Science, Technology and Medicine for help
with computer administration.
M. Farrashkhalvat

J.P. Miles