Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F20%3A10244887" target="_blank" >RIV/61989100:27740/20:10244887 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/math8010026" target="_blank" >https://doi.org/10.3390/math8010026</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math8010026" target="_blank" >10.3390/math8010026</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Popis výsledku v původním jazyce

The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Pade approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.

Název v anglickém jazyce

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Popis výsledku anglicky

The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Pade approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

8

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

8

Strana od-do

—

Kód UT WoS článku

000515730100105

EID výsledku v databázi Scopus

2-s2.0-85079618293