ques in numerical heat transfer the content should be of use and interest to a
large sector of the research community.
The packaging is good, with typeset text
and professionally produced illustrations, giving the book a solid and respectable image, very important in what
could become a useful reference work.
Ft. Voller
Numerical grid generation-foundations and applications
J. F. Thompton, S. Warsi and
C. W. Mastin
North Holland, Amsterdam, 1985,
483 pp. 150Dfl
This book tackles a subject of growing
importance for those involved in scientific and engineering computation. As its
title indicates, the book aims to provide
the mathematical foundations of the
numerical generation of meshes and so
it is not a trivial read. Having said this,
the book and the subject will be attractive to applied mathematicians because
it involves a number of classic topics,
including vector and tensor analysis,
complex analysis, elements of applied
functional analysis, as well as numerical
analysis.
The objective of the book is to describe the techniques used to generate
meshes to approximate complex regions
within which the behaviour of a variable
is governed by an appropriate partial
differential equation. There are a
number of ways in which meshes can be
generated to cover a region. The methods with which this book is concerned
are those associated with the mapping
of a uniform mesh on a simple rectangular shape onto the complex irregular
integration domain. Such an approach
provides a means of achieving meshes
which fits the integration domain very
precisely. The net result of this is that
the governing equations then have to be
expressed and solved in curvilinear coordinates. The reason for taking this route
is obvious, of course, but whilst one
gains accuracy of representation of the
region, there is a heavy cost associated
with the solution procedure. Certainly
the move from regular to irregular
meshes has nontrivial implications for
the finite domain method.
The book develops the approach in
a fairly readable way, covering simply
and multiply-connected, as well as composite, regions. Also mentioned are
overlaid grids, but I have to say that,
although the ability to generate such distributions may be helpful, their utility
must surely be rare and rather restricted.
The mathematics becomes interesting in
chapter 3 when transformation relations
are considered. Here, the vector and
tensor analysis is far from trivial and
requires very careful study before the
subsequent chapters can be sensibly
dealt with.
The fourth chapter is concerned with
numerical implementation of the transformed equations on a regular grid. The
numerical formulation considered is
based upon finite difference methods but
foeusses upon the finite or control
volume approach to ensure conservation. The only equation considered is
that describing generalized convectiondiffusion and then by example to illustrate the effects of the transformation.
Of course, the actual integration takes
place over the transformed (i.e. regular)
grid so the numerical approximations
are rather straightforward. The chapter
does, however, contain some helpful
details on coping with interfaces
between subregions of the finite volume
approach. The discussion on numerical
approximation is completed by a section
on truncation error, which I did not find
particularly enlightening.
The question of how to actually locate
the nodal points in the physical region
from a transformation of those regular
nodes in the rectangular integration
domain is divided into elliptic, parabolic
and hyperbolic generation systems. In
elliptic systems, the source term of the
Poisson equation can be used to
influence the variation of the density of
grid cells in a region. A detailed discussion follows of how to determine the grid
density distribution for any particular
region; this includes the particular problems that three-dimensional regions
bring. The subject is completed by a survey of algebraic grid generation systems.
The book concludes with three
chapters on special topics: orthogonal
systems, conformal mapping, and adaptive grids. I found each interesting and
helpful in its own way, but was particularly grateful for one of the appendices
which provided a program, together
with a guide through it.
I enjoyed reading the book and certainly feel that justice has been done to
a ditt~cult subject. I would have been
interested, however, to see how such
grid distribution techniques actually
contribute to the accurate solution of an
important partial differential equation
(representing
convection-diffusion,
say). I suspect this book will become a
useful reference text for some years to
come.
M. Cross
Computer-aided engineering--heat
transfer and fluid flow
A. D. Gosman, B. E. Launder and G.
J. Reece
Ellis Horwood, Chichester, 1985, 179
pp., £18.50
This document, in the form of a ringbound booklet, provides a guide to a
462 Appl. Math. Modelling, 1986, Vol. 10, December
general computer program. TEACH-C,
used to stimulate heat conduction and
species diffusion. The book is intended
to strengthen the traditional methods of
teaching heat transfer and fluid mechanics at undergraduate and postgraduate
level by the more effective use of the
computer in an instructional mode.
Furthermore, it describes the physical
and mathematical model on which the
program is based.
The presentation format, layout,
cover design, and the size of the book
are pleasing for both students and
teachers. The program TEACH-C is
applicable to heat conduction (or species
diffusion) problems which are transient
or in the steady state, plane or axisymmetric, with uniform or variable thermal
conductivity and with distributed heat
sources.
In the field of fluid mechanics it can
be used to calculate irrotationaI flows,
flows in porous media and lubricant
films. Although limited in applicability
for real world problems, it should prove
useful to students who, after learning
how to adapt it to solve various problems, will be ready to use one of the
more complicated packages available for
the simultaneous solution of both fluid
flow and heat transfer phenomena.
Section 1 of the book provides an
introduction, by outlining the capabilities of TEACH-C, discussing the layout
of the user guide to the program and
by making suggestions on how to use it
in a computer-aided learning course.
Section 2 is devoted to the description
of the differential equation solved by the
program and to the derivation and solution of the finite difference equations,
to which the original equation is transformed. The presentation is clear and
covers all relevant topics such as computational grid treatment of boundary conditions, solution of difference equations,
convergence, stability, and accuracy. I
found this section the most satisfying in
the book.
Section 3 describes the computer program, starting with its capabilities and
limitations. The overall structure of the
program is then described and the most
important FORTRAN symbols defined.
Attention is then turned to describing
the problem solved by the basic
TEACH-C, e.g. a transient 2D conduction problem. Using this example, the
authors describe the various subroutines
and their operations. The section ends
with suggestions for preparation and
operation of the program. Closing
remarks, references (albeit limited) and
algebraic notation conclude the main
part of the text. The appendices provide
four problems:
• unsteady 1D conduction processes
• 2D conduction processes
• potential flow
• fully-developed flow in noncircular
ducts