that can be used to solve many different flow problems. This is accompanied
by a collection of prepared and solved test cases that are suitable to learn
how to use such tools most effectively. Experience with this tool will be valuable to anyone who has never used such tools before, as the major issues are
common to most of them. Suggestions are also given for parameter variation,
error estimation, grid quality assessment, and efficiency improvement.
The finite volume method is favored in this book, although finite difference
methods are described in what we hope is sufficient detail. Finite element
methods are not covered in detail as a number of books on that subject
already exist.
We have tried t o describe the basic ideas of each topic in such a way
that they can be understood by the reader; where possible, we have avoided
lengthy mathematical analysis. Usually a general description of an idea or
method is followed by a more detailed description (including the necessary
equations) of one or two numerical schemes representative of the better methods of the type; other possible approaches and extensions are briefly described. We have tried to emphasize common elements of methods rather
than their differences.
There is a vast literature devoted to numerical methods for fluid mechanics. Even if we restrict our attention to incompressible flows, it would be
impossible to cover everything in a single work. Doing so would create confusion for the reader. We have therefore covered only the methods that we
have found valuable and that are commonly used in industry in this book.
References to other methods are given, however.
We have placed considerable emphasis on the need to estimate numerical
errors; almost all examples in this book are accompanied with error analysis.
Although it is possible for a qualitatively incorrect solution of a problem to
look reasonable (it may even be a good solution of another problem), the
consequences of accepting it may be severe. On the other hand, sometimes a
relatively poor solution can be of value if treated with care. Industrial users
of commercial codes need to learn to judge the quality of the results before
believing them; we hope that this book will contribute to the awareness that
numerical solutions are always approximate.
We have tried to cover a cross-section of modern approaches, including direct and large eddy simulation of turbulence, multigrid methods and parallel
computing, methods for moving grids and free surface flows, etc. Obviously,
we could not cover all these topics in detail, but we hope that the information contained herein will provide the reader with a general knowledge of the
subject; those interested in a more detailed study of a particular topic will
find recommendations for further reading.
While we have invested every effort to avoid typing, spelling and other
errors, no doubt some remain to be found by readers. We will appreciate
your notifying us of any mistakes you might find, as well as your comments
and suggestions for improvement of future editions of the book. For that
by a collection of prepared and solved test cases that are suitable to learn
how to use such tools most effectively. Experience with this tool will be valuable to anyone who has never used such tools before, as the major issues are
common to most of them. Suggestions are also given for parameter variation,
error estimation, grid quality assessment, and efficiency improvement.
The finite volume method is favored in this book, although finite difference
methods are described in what we hope is sufficient detail. Finite element
methods are not covered in detail as a number of books on that subject
already exist.
We have tried t o describe the basic ideas of each topic in such a way
that they can be understood by the reader; where possible, we have avoided
lengthy mathematical analysis. Usually a general description of an idea or
method is followed by a more detailed description (including the necessary
equations) of one or two numerical schemes representative of the better methods of the type; other possible approaches and extensions are briefly described. We have tried to emphasize common elements of methods rather
than their differences.
There is a vast literature devoted to numerical methods for fluid mechanics. Even if we restrict our attention to incompressible flows, it would be
impossible to cover everything in a single work. Doing so would create confusion for the reader. We have therefore covered only the methods that we
have found valuable and that are commonly used in industry in this book.
References to other methods are given, however.
We have placed considerable emphasis on the need to estimate numerical
errors; almost all examples in this book are accompanied with error analysis.
Although it is possible for a qualitatively incorrect solution of a problem to
look reasonable (it may even be a good solution of another problem), the
consequences of accepting it may be severe. On the other hand, sometimes a
relatively poor solution can be of value if treated with care. Industrial users
of commercial codes need to learn to judge the quality of the results before
believing them; we hope that this book will contribute to the awareness that
numerical solutions are always approximate.
We have tried to cover a cross-section of modern approaches, including direct and large eddy simulation of turbulence, multigrid methods and parallel
computing, methods for moving grids and free surface flows, etc. Obviously,
we could not cover all these topics in detail, but we hope that the information contained herein will provide the reader with a general knowledge of the
subject; those interested in a more detailed study of a particular topic will
find recommendations for further reading.
While we have invested every effort to avoid typing, spelling and other
errors, no doubt some remain to be found by readers. We will appreciate
your notifying us of any mistakes you might find, as well as your comments
and suggestions for improvement of future editions of the book. For that