The application of the Chebyshev-spectral method in transport phenomena
The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flows 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. This book presents topics that guide the reader through various stages of the Chebyshev-spectral method to solve transport problems. It relies on a knowledge at an undergraduate level in transport phenomena, some linear algebra as well as applied differential equations. The book is written for the typical graduate student in engineering, or even for the physicist, that enjoys working with pencil and paper, and who wishes to use common software such as \texttt{MATLAB}, \texttt{MATHEMATICA}, or \texttt{MAPLE}. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all mathematical proofs. The focus in this tutorial is on the use of spectral methods for space discretization, because this is where most of the difficulties lie. 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 on in endnotes to various chapters, others are touched upon in the book itself.
scientific article; zbMATH DE number 6115303
scientific article