**by Hans Petter Langtangen, Geir K. Pedersen**

DescriptionDetailsHashtagsReport an issue ### Book 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. ### Book Details

### Related Books

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.

This open book is licensed under a Creative Commons License (CC BY-NC). You can download Scaling of Differential Equations ebook for free in PDF format (6.4 MB).

Subject

Science and Mathematics

Publisher

Springer

Published

2016

Pages

149

Edition

1

Language

English

ISBN13

9783319327259

ISBN10

3319327259

ISBN13 Digital

9783319327266

ISBN10 Digital

3319327267

PDF Size

6.4 MB

License

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