TY  - BOOK
AU  - Langtangen, Hans Petter
AU  - Pedersen, Geir K.
AB  - 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.
DO  - 10.1007/978-3-319-32726-6
ID  - OAPEN ID: ONIX_20201113_9783319327266_3
KW  - Ordinary Differential Equations
KW  - Partial Differential Equations
KW  - Mathematical Modeling and Industrial Mathematics
KW  - Computational Science and Engineering
KW  - Simulation and Modeling
KW  - Analysis
KW  - Computer Science
KW  - scaling
KW  - non-dimensionalization
KW  - dimensionless numbers
KW  - fluid mechanics
KW  - multiphysics models
KW  - Differential calculus & equations
KW  - Mathematical modelling
KW  - Maths for engineers
KW  - Maths for scientists
KW  - Computer modelling & simulation
L1  - https://library.oapen.org/bitstream/id/ce24a851-aa41-4c4a-9df0-4b2011a3f067/2016_Book_ScalingOfDifferentialEquations.pdf
LA  - English
LK  - https://library.oapen.org/handle/20.500.12657/42897
PB  - Springer Nature
PY  - 2016
TI  - Scaling of Differential Equationsnull
ER  - 
