Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F18%3A10240156" target="_blank" >RIV/61989100:27740/18:10240156 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-9717/6/8/130" target="_blank" >https://www.mdpi.com/2227-9717/6/8/130</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/pr6080130" target="_blank" >10.3390/pr6080130</a>

Result language

angličtina

Original language name

Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Original language description

The Colebrook equation is implicitly given in respect to the unknown flow friction factor lambda; lambda = zeta(Re, epsilon*, lambda) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Dzunic-Petkovic-Petkovic; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Czech name

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Czech description

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Type

J_imp - 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

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Continuities

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Processes

ISSN

2227-9717

e-ISSN

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Volume of the periodical

6

Issue of the periodical within the volume

8

Country of publishing house

CH - SWITZERLAND

Number of pages

17

Pages from-to

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UT code for WoS article

000443615900034

EID of the result in the Scopus database

2-s2.0-85051805790