https://doi.org/10.1140/epjp/s13360-023-04225-5
Regular Article
Novel prediction of fluid forces on obstacle in a periodic flow regime using hybrid FEM-ANN simulations
1
Department of Mathematics, Air University, PAF Complex E-9, 44000, Islamabad, Pakistan
2
Faculty of Materials and Manufacturing, College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, China
3
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952, Al-Majmaah, Saudi Arabia
Received:
12
March
2023
Accepted:
23
June
2023
Published online:
23
August
2023
A lot of computational resources are required for time-dependent CFD simulations for the accurate prediction of the quantities of interest. To circumvent such difficulties, an artificial neural network (ANN) has been coupled with CFD simulations. Training and validation datasets have been generated by CFD and then are fed through ANN with optimal number of neurons and inner layers. A well-known benchmark problem for incompressible flows, namely, the flow around cylinder has been considered for the hybrid CFD network. The mathematical formulations are based on nonstationary Navier–Stokes equations incorporating the viscosity through power-law fluid constitutive model. The underlying ANN model consists of 3 input layers, 2 output layers, and 10 hidden layers. The network has been trained through one of the most efficient backpropagation algorithms, namely, Levenberg–Marquardt (LM) algorithm that provides second-order training speed. The obtained finite element results for drag and lift coefficients have been validated with the ANN predicted values through statistical measures represented by mean square error (MSE) and the coefficient of determination (R). For all cases, we have obtained a higher predictivity for drag coefficient 
and lift coefficient 
as MSE values approached zero and R values found to be close to unity. The agreement between the CFD results and the data predicted from ANN determined via the correlations is within less than ± 5% errors. It is concluded that ANNs may help to reduce the computing time and other resources required for time-dependent simulations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
