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.
