Scaling of Differential Equations
(Sprache: Englisch)
The book serves both as a reference forvarious scaled models with corresponding dimensionless numbers, and as aresource for learning the art of scaling. A special feature of the book is the emphasis on how to create softwarefor scaled models, based on...
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Klappentext zu „Scaling of Differential Equations “
The book serves both as a reference forvarious scaled models with corresponding dimensionless numbers, and as aresource for learning the art of scaling. A special feature of the book is the emphasis on how to create softwarefor scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is amathematical technique that greatly simplifies the setting of input parameters innumerical simulations. Moreover, scaling enhances the understanding of howdifferent physical processes interact in a differential equation model.Compared to the existing literature, where the topic of scaling is frequentlyencountered, but very often in only a brief and shallow setting, the presentbook gives much more thorough explanations of how to reason about finding theright scales. This process is highly problem dependent, and therefore the bookfeatures a lot of worked examples, from very simple ODEs to systems of PDEs,especially from fluid mechanics.
The text is easily accessible andexample-driven. The first part on ODEs fits even a lower undergraduate level,while the most advanced multiphysics fluid mechanics examples target thegraduate level. The scientific literature is full of scaled models, but in mostof the cases, the scales are just stated without thorough mathematicalreasoning. This book explains how the scales are found mathematically.
This book will be a valuable read for anyonedoing numerical simulations based on ordinary or partial differential equations.
Inhaltsverzeichnis zu „Scaling of Differential Equations “
Preface.- 1 Dimensions and Units.- 2 Ordinary Differential Equations Models.- 3 Basic Partial Differential Equations Models.- Advanced Partial Differential Equations Models.- References.- Index.
Autoren-Porträt von Hans Petter Langtangen, Geir K. Pedersen
Hans Petter Langtangen is a professor ofcomputer science at the University of Oslo. He has formerly been a professor ofmechanics 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 severalbooks, including papers and the bestseller TCSE 6 "A Primer on ScientificProgramming with Python", now in its 5th edition. He has also developedopen source and commercial software systems for computational sciences. Geir K. Pedersen is a professor of mechanics at theDepartment of Mathematics, University of Oslo. He has a life-long experience influid dynamics and mathematical modeling. Pedersen has published articles onwave theory, numerical modeling, perturbation techniques, tsunamis,hydrodynamic stability and experimental fluid dynamics.
Bibliographische Angaben
- Autoren: Hans Petter Langtangen , Geir K. Pedersen
- 2016, 1st ed. 2016, XIII, 138 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3319327259
- ISBN-13: 9783319327259
- Erscheinungsdatum: 24.06.2016
Sprache:
Englisch
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