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

doi:10.1007/s10483-023-2993-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (7): 1101-1110.doi: https://doi.org/10.1007/s10483-023-2993-9

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

Yichuan HE¹, Zhicheng WANG¹, Hui XIANG², Xiaomo JIANG¹, Dawei TANG¹

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:2022-11-12 Revised:2023-03-29 Online:2023-07-01 Published:2023-07-05
Contact: Zhicheng WANG, E-mail:zhicheng_wang@dlut.edu.cn; Dawei TANG, E-mail:dwtang@dlut.edu.cn
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)

Abstract

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

2010 MSC Number:

68T01

Yichuan HE, Zhicheng WANG, Hui XIANG, Xiaomo JIANG, Dawei TANG. An artificial viscosity augmented physics-informed neural network for incompressible flow. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1101-1110.

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

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