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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.
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