Scaling of Differential Equations

Scaling of Differential Equations

by Hans Petter Langtangen, Geir K. Pedersen

Paperback(1st ed. 2016)

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Overview

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.

Product Details

ISBN-13: 9783319327259
Publisher: Springer International Publishing
Publication date: 06/16/2016
Series: Simula SpringerBriefs on Computing , #2
Edition description: 1st ed. 2016
Pages: 138
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

Preface.- 1 Dimensions and Units.- 2 Ordinary Differential Equations Models.- 3 Basic Partial Differential Equations Models.- Advanced Partial Differential Equations Models.- References.- Index.

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