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Scaling of differential equations

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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Detail Information
Series Title
-
Call Number
515.35 LAN s
Publisher
Cham, Switzerland : Springer Open.,
Collation
xiii, 138p. : ill.
Language
English
ISBN/ISSN
9783319327266
Classification
515.35
Content Type
-
Media Type
-
Carrier Type
-
Edition
-
Subject(s)
Computer Science
Computer simulation
Computer science--Mathematics
Differential equations
Differential equations, Partial
Multiscale modeling
Differential equations--Numerical solutions
Mathematical models
Specific Detail Info
-
Statement of Responsibility
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