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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.
List 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.
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.
Summary
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.
