Scaling of Differential Equations by Hans Petter Langtangen

Scaling of Differential Equations by Hans Petter Langtangen

by Hans Petter Langtangen (Author), Geir K. Pedersen (Author)

ISBN-13: 9783319327259

ISBN-10: 3319327259

Publisher : Springer; 1st ed. 2016 edition (June 15, 2016)

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.