Searching fundamental information in ordinary differential equations. Nondimensionalization technique

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of th...

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Bibliographic Details
Published in:PloS one 2017-10, Vol.12 (10), p.e0185477-e0185477
Main Authors: Sánchez Pérez, J F, Conesa, M, Alhama, I, Alhama, F, Cánovas, M
Format: Article
Language:English
Subjects:
Analysis
Differential equations
Dimensional analysis
Engineering
Engineering and Technology
Fluids
Heat transfer
Mathematical models
Mechanics
Methods
Models, Theoretical
Ordinary differential equations
Partial differential equations
Physical Sciences
Research and Analysis Methods
Reynolds number
Simulation
Variables
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Summary:Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0185477