Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F19%3A10242723" target="_blank" >RIV/61989100:27740/19:10242723 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2079-3197/7/3/48" target="_blank" >https://www.mdpi.com/2079-3197/7/3/48</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/computation7030048" target="_blank" >10.3390/computation7030048</a>

Result language
angličtina
Original language name
Colebrook's Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression
Original language description
The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and Wright omega functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Pade approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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