No comparable book exists
Scaling is a classical topic in applied mathematics, but here strongly connected to numerical simulations
The book contains a wide range of examples, of differing complexity, from many different scientific fields
Includes supplementary material: sn.pub/extras
Part of the book series: Simula SpringerBriefs on Computing (SBRIEFSC, volume 2)
Table of contents (4 chapters)
About this book
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models.
Scaling (or non-dimensionalization) is a
mathematical technique that greatly simplifies the setting of input parameters in
numerical simulations. Moreover, scaling enhances the understanding of how
different physical processes interact in a differential equation model.
Compared to the existing literature, where the topic of scaling is frequently
encountered, but very often in only a brief and shallow setting, the present
book gives much more thorough explanations of how to reason about finding the
right scales. This process is highly problem dependent, and therefore the book
features a lot of worked examples, from very simple ODEs to systems of PDEs,
especially from fluid mechanics.
The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically.
This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
- ordinary differential equations
- partial differential equations
- dimensionless numbers
- fluid mechanics
- multiphysics models
Authors and Affiliations
Center for Biomedical Computing, Simula Research Laboratory, Fornebu, Norway
Hans Petter Langtangen
Department of Mathematics, University of Oslo, Oslo, Norway
Geir K. Pedersen
About the authors
Hans Petter Langtangen is a professor of computer science at the University of Oslo. He has formerly been a professor of mechanics and is now the director of a Norwegian Center of Excellence: "Center for Biomedical Computing", at Simula Research Laboratory. Langtangen has published over 100 scientific publications and written several books, including papers and the bestseller TCSE 6 "A Primer on Scientific Programming with Python", now in its 5th edition. He has also developed open source and commercial software systems for computational sciences.
Geir K. Pedersen is a professor of mechanics at the
Department of Mathematics, University of Oslo. He has a life-long experience in
fluid dynamics and mathematical modeling. Pedersen has published articles on
wave theory, numerical modeling, perturbation techniques, tsunamis,
hydrodynamic stability and experimental fluid dynamics.
Book Title: Scaling of Differential Equations
Authors: Hans Petter Langtangen, Geir K. Pedersen
Series Title: Simula SpringerBriefs on Computing
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and the Author(s) 2016
License: CC BY-NC
Softcover ISBN: 978-3-319-32725-9Published: 24 June 2016
eBook ISBN: 978-3-319-32726-6Published: 15 June 2016
Series ISSN: 2512-1677
Series E-ISSN: 2512-1685
Edition Number: 1
Number of Pages: XIII, 138
Number of Illustrations: 22 b/w illustrations
Topics: Differential Equations, Mathematical Modeling and Industrial Mathematics, Computational Science and Engineering, Computer Modelling