ROE-Scheme Physics-Augmented Graph Neural Networks in Solving Eulerian and Laminar Flow Incompressible NS Equations

SONG Shangxiao; JIANG Longxiang; WANG Liyuan; CHU Xinkun; ZHANG Hao

doi:10.21656/1000-0887.450098

Volume 46 Issue 1

Jan. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(1): 55-71

SONG Shangxiao, JIANG Longxiang, WANG Liyuan, CHU Xinkun, ZHANG Hao. ROE-Scheme Physics-Augmented Graph Neural Networks in Solving Eulerian and Laminar Flow Incompressible NS Equations[J]. Applied Mathematics and Mechanics, 2025, 46(1): 55-71. doi: 10.21656/1000-0887.450098

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ROE-Scheme Physics-Augmented Graph Neural Networks in Solving Eulerian and Laminar Flow Incompressible NS Equations

doi: 10.21656/1000-0887.450098

Institute of Computer Applications, China Academy of Engineering Physics, Mianyang, Sichuan 621900, P.R.China

Received Date: 2024-04-15
Rev Recd Date: 2024-07-08
Publish Date: 2025-01-01

Abstract

Abstract

In recent years, the deep learning method incorporating physical information provided a new idea for solving partial differential equations. However, most of the studies so far has low computational accuracy and poor time extrapolation for problems with discontinuities in the solution space. To address the above 2 problems, the ROE-PIGNN model was proposed for fusing equations or data information with the graph neural networks and the ROE scheme in computational fluid dynamics. Numerical experiments show that, the model achieves a computational accuracy comparable to that of the ROE scheme in solving the shock tube problem controlled by the Eulerian equation, and has the ability of extrapolation over a certain time range. Finally, the 2D cylindrical bypass flow traditional problem controlled by the Navier-Stokes (NS) equations was solved. The experimental results show that, the model can predict the subsequent periodic flow and reproduce the flow structure more accurately at some key positions, with an error reduction of 60% compared to the purely data-driven approach.
- deep learning,
- graph neural network,
- ROE scheme,
- Eulerian equation,
- NS equation

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References

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