Hans Petter Langtangen, Geir K. Pedersen

Scaling of Differential Equations

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Simula SpringerBriefs on Computing 2
• Verlag: Simula Research Laboratory / Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-32725-9
• 1st ed. 2016
• Seitenzahl: 152
• Erscheinungstermin: 24. Juni 2016
• Englisch
• Abmessung: 235mm x 155mm x 9mm
• Gewicht: 242g
• ISBN-13: 9783319327259
• ISBN-10: 3319327259
• Artikelnr.: 44711542

Autorenporträt

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.     

Inhaltsangabe

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