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dc.contributor.authorLangtangen, Hans Petter
dc.contributor.authorPedersen, Geir K.
dc.date.accessioned2020-11-13T13:34:15Z
dc.date.available2020-11-13T13:34:15Z
dc.date.issued2016
dc.identifierONIX_20201113_9783319327266_3
dc.identifier.urihttps://library.oapen.org/handle/20.500.12657/42897
dc.description.abstractThe 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.
dc.languageEnglish
dc.relation.ispartofseriesSimula SpringerBriefs on Computing
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PB Mathematics::PBK Calculus & mathematical analysis::PBKJ Differential calculus & equations
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PD Science: general issues::PDE Maths for scientists
dc.subject.classificationbic Book Industry Communication::U Computing & information technology::UY Computer science::UYM Computer modelling & simulation
dc.subject.otherOrdinary Differential Equations
dc.subject.otherPartial Differential Equations
dc.subject.otherMathematical Modeling and Industrial Mathematics
dc.subject.otherComputational Science and Engineering
dc.subject.otherSimulation and Modeling
dc.subject.otherAnalysis
dc.subject.otherComputer Science
dc.subject.otherscaling
dc.subject.othernon-dimensionalization
dc.subject.otherdimensionless numbers
dc.subject.otherfluid mechanics
dc.subject.othermultiphysics models
dc.subject.otherDifferential calculus & equations
dc.subject.otherMathematical modelling
dc.subject.otherMaths for engineers
dc.subject.otherMaths for scientists
dc.subject.otherComputer modelling & simulation
dc.titleScaling of Differential Equations
dc.typebook
oapen.identifier.doi10.1007/978-3-319-32726-6
oapen.relation.isPublishedBy6c6992af-b843-4f46-859c-f6e9998e40d5
oapen.imprintSpringer International Publishing
oapen.series.number2
oapen.pages138


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