EAN: 9783319327259

SCALING OF DIFFERENTIAL EQUATIONS - HANS PETTER...

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.

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