Preface
Due to the enormous progress in computer technology and numerical methods
that have been achieved in recent years, the use of numerical simulation methods
in industry gains more and more importance. In particular, this applies
to all engineering disciplines. Numerical computations in many cases offer a
cost effective and, therefore, very attractive possibility for the investigation
and optimization of products and processes.
Besides the need for developers of corresponding software, there is a strong
– and still rapidly growing – demand for qualified specialists who are able to
efficiently apply numerical simulation tools to complex industrial problems.
The successful and efficient application of such tools requires certain basic
knowledge about the underlying numerical methodologies and their possibilities
with respect to specific applications. The major concern of this book is
the impartation of this knowledge in a comprehensive way.
The text gives a practice oriented introduction in modern numerical methods
as they typically are applied in engineering disciplines like mechanical,
chemical, or civil engineering. In corresponding applications the by far most
frequent tasks are related to problems from heat transfer, structural mechanics,
and fluid mechanics, which, therefore, constitute a thematical focus of the
text.
The topic must be seen as a strongly interdisciplinary field in which aspects
of numerical mathematics, natural sciences, computer science, and the corresponding
engineering area are simultaneously important. As a consequence,
usually the necessary information is distributed in different textbooks from
the individual disciplines. In the present text the subject matter is presented
in a comprehensive multidisciplinary way, where aspects from the different
fields are treated insofar as it is necessary for general understanding.
Following this concept, the text covers the basics of modeling, discretization,
and solution algorithms, whereas an attempt is always made to establish
the relationships to the engineering relevant application areas mentioned
above. Overarching aspects of the different numerical techniques are emphasized
and questions related to accuracy, efficiency, and cost effectiveness, which
VI Preface
are most relevant for the practical application, are discussed. The following
subjects are addressed in detail:
Modelling: simple field problems, heat transfer, structural mechanics, fluid
mechanics.
Discretization: connection to CAD, numerical grids, finite-volume methods,
finite-element methods, time discretization, properties of discrete systems.
Solution algorithms: linear systems, non-linear systems, coupling of variables,
adaptivity, multi-grid methods, parallelization.
Special applications: finite-element methods for elasto-mechanical problems,
finite-volume methods for incompressible flows, simulation of turbulent
flows.
The topics are presented in an introductory manner, such that besides basic
mathematical standard knowledge in analysis and linear algebra no further
prerequisites are necessary. For possible continuative studies hints for corresponding
literature with reference to the respective chapter are given.
Important aspects are illustrated by means of application examples. Many
exemplary computations done “by hand” help to follow and understand the
numerical methods. The exercises for each chapter give the possibility of reviewing
the essentials of the methods. Solutions are provided on the web page
www.fnb.tu-darmstadt.de/ceinm/. The book is suitable either for self-study or
as an accompanying textbook for corresponding lectures. It can be useful for
students of engineering disciplines, but also for computational engineers in
industrial practice. Many of the methods presented are integrated in the flow
simulation code FASTEST, which is available from the author.
The text evolved on the basis of several lecture notes for different courses
at the Department of Numerical Methods in Mechanical Engineering at Darmstadt
University of Technology. It closely follows the German book Numerik
im Maschinenbau (Springer, 1999) by the author, but includes several modifications
and extensions.
The author would like to thank all members of the department who have
supported the preparation of the manuscript. Special thanks are addressed to
Patrick Bontoux and the MSNM-GP group of CNRS at Marseille for the warm
hospitality at the institute during several visits which helped a lot in completing
the text in time. Sincere thanks are given to Rekik Alehegn Mekonnen
for proofreading the English text. Last but not least the author would like to
thank the Springer-Verlag for the very pleasant cooperation.
