An artificial viscosity augmented physics-informed neural network for incompressible flow

Yichuan HE, Zhicheng WANG, Hui XIANG, Xiaomo JIANG, Dawei TANG

doi:10.1007/s10483-023-2993-9

Applied Mathematics and Mechanics >

2023 , Vol. 44 >Issue 7: 1101 - 1110

DOI: https://doi.org/10.1007/s10483-023-2993-9

Articles

An artificial viscosity augmented physics-informed neural network for incompressible flow

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1. Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, Liaoning Province, China;
2. Baidu. com Times Technology(Beijing) Co., Ltd., Beijing 100080, China

Received date: 2022-11-12

Revised date: 2023-03-29

Online published: 2023-07-05

Supported by

the Fundamental Research Funds for the Central Universities of China (No. DUT21RC(3)063), the National Natural Science Foundation of China (No. 51720105007), and the Baidu Foundation (No. ghfund202202014542)

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Abstract

Physics-informed neural networks (PINNs) are proved methods that are effective in solving some strongly nonlinear partial differential equations (PDEs), e.g., Navier-Stokes equations, with a small amount of boundary or interior data. However, the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported. The present paper proposes an artificial viscosity (AV)-based PINN for solving the forward and inverse flow problems. Specifically, the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics (CFD) to stabilize the simulation of flow at high Reynolds numbers. The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1 000 and the inverse problem derived from two-dimensional film boiling. The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.

Key words： physics-informed neural network (PINN); artificial viscosity (AV); cavity driven flow; high Reynolds number

Cite this article

Yichuan HE, Zhicheng WANG, Hui XIANG, Xiaomo JIANG, Dawei TANG . An artificial viscosity augmented physics-informed neural network for incompressible flow[J]. Applied Mathematics and Mechanics, 2023 , 44(7) : 1101 -1110 . DOI: 10.1007/s10483-023-2993-9

References

[1] QIANG, L. I., YU, G. U., and WANG, H. The influence of temperature on flow-induced forces on quartzcrystal-microbalance sensors in a Chinese liquor identification electronic-nose:three-dimensional computational fluid dynamics simulation and analysis. Applied Mathematics and Mechanics (English Edition), 40(9), 1301-1312(2019) https://doi.org/10.1007/s10483-019-2512-9
[2] LÓPEZ, A., NICHOLLS, W., STICHLAND, M. T., and DEMPSTER, W. M. CFD study of jet impingement test erosion using Ansys Fluent and OpenFOAM. Computer Physics Communications, 197, 88-95(2015)
[3] JORDAN, M. I. and MITCHELL, T. M. Machine learning:trends, perspectives, and prospects. Science, 349(6245), 255-260(2015)
[4] KARNIADAKIS, G. E., KEVEREKIDIS, I. G., LU, L., PERDIKARIS, P., WANG, S. F., and YANG, L. Physics-informed machine learning. Nature Reviews Physics, 3(6), 422-440(2021)
[5] LECUN, Y., BENGIO, Y., and HINTON, G. Deep learning. nature, 521(7553), 436-444(2015)
[6] RAISSI, M., PERDIKARIS, P., and KARNIADAKIS, G. E. Physics-informed neural networks:a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707(2019)
[7] RAISSI, M., YAZDANI, A., and KARNIADAKIS, G. E. Hidden fluid mechanics:learning velocity and pressure fields from flow visualizations. Science, 367(6481), 1026-1030(2020)
[8] JIN, X. W., CAI, S. C., LI, H., and KARNIADAKIS, G. E. NSFnets (Navier-Stokes flow nets):physics-informed neural networks for the incompressible Navier-Stokes equations. Journal of Computational Physics, 426, 109951(2021)
[9] CAI, S. Z., WANG, Z. C., FUEST, F., JIN, J. Y., CALLUM, G., and KARNIADAKIS, G. E. Flow over an espresso cup:inferring 3-D velocity and pressure fields from tomographic background oriented schlieren via physics-informed neural networks. Journal of Computational Physics, 915, A102(2021)
[10] SUN, L. N., GAO, H., PAN, S. W., and WANG, J. X. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Computer Methods in Applied Mechanics and Engineering, 361, 112732(2020)
[11] RAO, C. P., SUN, H., and LIU, Y. Physics-informed deep learning for incompressible laminar flows. Theoretical and Applied Mechanics Letters, 10(3), 207-212(2020)
[12] MCCLENNY, L. and BRAGA-NETO, U. Self-adaptive physics-informed neural networks using a soft attention mechanism. arXiv Preprint, arXiv:2009.04544(2020) https://doi.org/10.48550/arXiv.2009.04544
[13] BOTELLA, O. and PEYRET, R. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids, 27(4), 421-433(1998)
[14] BISWAS, S. and KALITA, J. C. Topology of corner vortices in the lid-driven cavity flow:2D vis a vis 3D. Archive of Applied Mechanics, 90(3), 2201-2216(2020)
[15] JAGTAP, A. D., KHARAZMI, E., and KARNIADAKIS, G. E. Conservative physics-informed neural networks on discrete domains for conservation laws:applications to forward and inverse problems. Computer Methods in Applied Mechanics and Engineering, 365, 113028(2020)
[16] BAI, X., WANG, Y., and ZHANG, W. Applying physics informed neural network for flow data assimilation. Journal of Hydrodynamics, 32(6), 1050-1058(2020)
[17] CHIU, P. H., WONG, J. C., OOI, C., DAO, M. H., and ONG, Y. S. CAN-PINN:a fast physics-informed neural network based on coupled automatic numerical differentiation method. Computer Methods in Applied Mechanics and Engineering, 395, 114909(2022)
[18] WANG, Z., TRIANTAFYLLOU, M. S., CONSTANTINIDES, Y., and KARNIADAKIS, G. E. An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe. Journal of Fluid Mechanics, 859, 691-730(2019)
[19] CHEN, X. H., CHEN, R. L., WAN, Q., XU, R., and LIU, J. An improved data-free surrogate model for solving partial differential equations using deep neural networks. Scientific Reports, 11, 19507(2021)
[20] WANG, Z., ZHENG, X., CHRYSSOSTOMIDIS, C., and KARNIADAKIS, G. E. A phase-field method for boiling heat transfer. Journal of Computational Physics, 435, 110239(2021)

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