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Fractional Calculus and Applied Analysis

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Volume 22, Issue 6


Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network

Pavan Pranjivan Mehta / Guofei Pang / Fangying Song / George Em Karniadakis
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0086


The first fractional model for Reynolds stresses in wall-bounded turbulent flows was proposed by Wen Chen [2]. Here, we extend this formulation by allowing the fractional order α(y) of the model to vary with the distance from the wall (y) for turbulent Couette flow. Using available direct numerical simulation (DNS) data, we formulate an inverse problem for α(y) and design a physics-informed neural network (PINN) to obtain the fractional order. Surprisingly, we found a universal scaling law for α(y+), where y+ is the non-dimensional distance from the wall in wall units. Therefore, we obtain a variable-order fractional model that can be used at any Reynolds number to predict the mean velocity profile and Reynolds stresses with accuracy better than 1%.

MSC 2010: Primary 76F40; 65N21; Secondary 68T20

Key Words and Phrases: turbulence; Reynolds-averaged Navier-Stokes (RANS) equations; fractional calculus; physics-informed neural networks (PINNS); machine learning

This paper is dedicated to the memory of the late Professor Wen Chen


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About the article

Received: 2019-08-15

Published Online: 2019-12-31

Published in Print: 2019-12-18

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1675–1688, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0086.

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