Scaling of Differential Equations 2016 Edition Contributor(s): Langtangen, Hans Petter (Author), Pedersen, Geir K. (Author) |
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ISBN: 3319327259 ISBN-13: 9783319327259 Publisher: Springer
Binding Type: Paperback - See All Available Formats & Editions Published: June 2016 Click for more in this series: Simula Springerbriefs on Computing |
Additional Information |
BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Applied - Computers | Computer Science |
Dewey: 003.3 |
Series: Simula Springerbriefs on Computing |
Physical Information: 0.33" H x 6.14" W x 9.21" L (0.50 lbs) 138 pages |
Features: Illustrated |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |
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