Transport phenomena problems that occur in engineering and physics are
often multi-dimensional and multi-phase in character. When taking
recourse to numerical methods the spectral method is particularly useful
and efficient.
The book is meant principally to train students and non-specialists to
use the spectral method for solving problems that model fluid flow in
closed geometries with heat or mass transfer. To this aim the reader
should bring a working knowledge of fluid mechanics and heat transfer
and should be readily conversant with simple concepts of linear algebra
including spectral decomposition of matrices as well as solvability
conditions for inhomogeneous problems.
The book is neither meant to supply a ready-to-use program that is
all-purpose nor to go through all manners of mathematical proofs. The
focus in this tutorial is on the use of the spectral methods for space
discretization, because this is where most of the difficulty lies. While
time dependent problems are also of great interest, time marching
procedures are dealt with by briefly introducing and providing a simple,
direct, and efficient method.
Many examples are provided in the text as well as numerous exercises for
each chapter. Several of the examples are attended by subtle points
which the reader will face while working them out. Some of these points
are deliberated upon in endnotes to the various chapters, others are
touched upon in the book itself.