ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

宋尚校; 姜龙祥; 王丽媛; 褚新坤; 张浩

doi:10.21656/1000-0887.450098

ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

doi: 10.21656/1000-0887.450098

中国工程物理研究院计算机应用研究所，四川绵阳 621900

详细信息

作者简介:
宋尚校（1996—），男，助理工程师，硕士（E-mail: sshangxiao@126.com）;张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

通讯作者:
张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

中图分类号: O29|O351
计量
- 文章访问数: 13
- HTML全文浏览量: 1
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-15
- 修回日期: 2024-07-08

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

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

摘要

摘要: 近年来，融合物理信息的深度学习方法为偏微分方程的求解提供了一个新的思路.然而，到目前为止，大多数工作在解空间存在间断的问题上的计算精度不高，时间外推能力差.针对以上两个问题，该文提出了使用图神经网络结合流体计算领域的ROE格式融合方程或数据信息的模型——ROEPIGNN.数值实验表明，该模型在求解由Euler方程控制的激波管问题时，可达到与传统ROE格式相当的计算精度，并具备一定时间范围的外推能力.最后，对由NavierStokes(NS)方程控制的二维圆柱绕流问题进行了求解，实验结果表明：模型可以预测后续的周期性流动，并实现对部分关键位置流动结构的更精确的复现，相比纯数据驱动，误差降低了60%.
- 深度学习 /
- 图神经网络 /
- ROE格式 /
- Euler方程 /
- NS方程
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

HTML全文

参考文献(35)

RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J].Journal of Computational Physics,2019,378: 686-707.

[2]KARNIADAKIS G E, KEVREKIDIS I G, LU L, et al. Physics-informed machine learning[J].Nature Reviews Physics,2021,3: 422-440.

[3]王江, 陈文. 基于组合神经网络的时间分数阶扩散方程计算方法[J]. 应用数学和力学, 2019,40(7): 741-750.(WANG Jiang, CHEN Wen. A combined artificial neural network method for solving time fractional diffusion equations[J].Applied Mathematics and Mechanics,2019,40(7): 741-750.(in Chinese))

[4]林云云, 郑素佩, 封建湖, 等. 间断问题扩散正则化的PINN反问题求解算法[J]. 应用数学和力学, 2023,44(1): 112-122.(LIN Yunyun, ZHENG Supei, FENG Jianhu, et al. Diffusive regularization inverse PINN solutions to discontinuous problems[J].Applied Mathematics and Mechanics,2023,44(1): 112-122.(in Chinese))

[5]DAFERMOS C M.Hyperbolic Conservation Laws in Continuum Physics[M]. Berlin: Springer, 2016.

[6]MAO Z, JAGTAP A D, KARNIADAKIS G E. Physics-informed neural networks for high-speed flows[J].Computer Methods in Applied Mechanics and Engineering,2020,360: 112789.

[7]LEVEQUE R J.Finite-Volume Methods for Hyperbolic Problems[M]. Cambridge: Cambridge University Press, 2002.

[8]GODLEWSKI E, RAVIART P A.Numerical Approximation of Hyperbolic Systems of Conservation Laws[M]. New York: Springer, 1996.

[9]COCKBURN B, KARNIADAKIS G E, SHU C W.Discontinuous Galerkin Methods[M]. Berlin: Springer, 2000.

[10]MAGIERA J, RAY D, HESTHAVEN J S, et al. Constraint-aware neural networks for Riemann problems[J].Journal of Computational Physics,2020,409: 109345.

[11]SCHWANDER L, RAY D, HESTHAVEN J S. Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks[J].Journal of Computational Physics,2021,431: 110144.

[12]BEZGIN D A, SCHMIDT S J, ADAMS N A. A data-driven physics-informed finite-volume scheme for nonclassical undercompressive shocks[J]. Journal of Computational Physics,2021,437: 110324.

[13]BEZGIN D A, SCHMIDT S J, ADAMS N A. WENO3-NN: a maximum-order three-point data-driven weighted essentially non-oscillatory scheme[J]. Journal of Computational Physics,2022,452: 110920.

[14]LIU L, LIU S, XIE H, et al. Discontinuity computing using physics-informed neural networks[J].Journal of Scientific Computing,2024,98: 22.

[15]CAO W, SONG J, ZHANG W. A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation[J].Physics of Fluids,2024,36(2): 027134.

[16]HUANG H, LIU Y, YANG V. Neural networks with inputs based on domain of dependence and A converging sequence for solving conservation laws, part Ⅰ: 1D Riemann problems[J/OL]. 2021[2024-07-08]. https://arxiv.org/abs/2109.09316.

[17]ROE P L. Approximate Riemann solvers, parameter vectors, and difference schemes[J].Journal of Computational Physics,1981,43(2):357-372.

[18]GODUNOV S K. A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations[J].Mathematics of the USSR-Sbornik,1959,47: 271-306.

[19]VAN LEER B.Towards the Ultimate Conservative Difference Scheme I. The Quest of Monotonicity[M]. Berlin: Heidelberg, 1973.

[20]VAN LEER B. Towards the ultimate conservative difference scheme[J].Journal of Computational Physics,1997,135(2): 229-248.

[21]HARTEN A, ENGQUIST B, OSHER S, et al. Uniformly high order accurate essentially non-oscillatory schemes, Ⅲ[J].Journal of Computational Physics,1997,131(1): 3-47.

[22]LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J].Journal of Computational Physics,1994,115(1): 200-212.

[23]LIU Y, SHU C W, TADMOR E, et al. Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction[J].SIAM Journal on Numerical Analysis,2007,45(6): 2442-2467.

[24]LIU Y, SHU C W, TADMOR E, et al. Non-oscillatory hierarchical reconstruction for central and finite volume schemes[J].Communications in Computational Physics,2007,2(5): 933-963.

[25]XU Z, LIU Y, SHU C W. Hierarchical reconstruction for discontinuous Galerkin methods on unstructured grids with a WENO-type linear reconstruction and partial neighboring cells[J].Journal of Computational Physics,2009,228(6): 2194-2212.

[26]YANG V. Modeling of supercritical vaporization, mixing, and combustion processes in liquid-fueled propulsion systems[J].Proceedings of the Combustion Institute,2000,28(1): 925-942.

[27]WANG X, YANG V. Supercritical mixing and combustion of liquid-oxygen/kerosene bi-swirl injectors[J].Journal of Propulsion and Power,2016,33(2): 316-322.

[28]UNNIKRISHNAN U, HUO H, WANG X, et al. Subgrid scale modeling considerations for large eddy simulation of supercritical turbulent mixing and combustion[J].Physics of Fluids,2021,33(7): 075112.

[29]TEYSSIER R, COMMERON B. Numerical methods for simulating star formation[J].Frontiers in Astronomy and Space Sciences,2019,6: 51.

[30]BAR-SINAI Y, HOYER S, HICKEY J, et al. Learning data-driven discretizations for partial differential equations[J].Proceedings of the National Academy of Sciences of the United States of America,2019,116(31): 15344-15349.

[31]高普阳, 赵子桐, 杨扬. 基于卷积神经网络模型数值求解双曲型偏微分方程的研究[J]. 应用数学和力学, 2021,42(9): 932-947.(GAO Puyang, ZHAO Zitong, YANG Yang. Study on numerical solutions to hyperbolic partial differential equations based on the convolutional neural network model[J].Applied Mathematics and Mechanics,2021,42(9): 932-947.(in Chinese))

[32]JIANG L, WANG L, CHU X, et al. PhyGNNet: solving spatiotemporal PDEs with physics-informed graph neural network[C］//Proceedings of the 2023 2nd Asia Conference on Algorithms, Computing and Machine Learning. Shanghai: ACM, 2023: 143-147.

[33]ZHANG H, JIANG L, CHU X, et al. Combining physics-informed graph neural network and finite difference for solving forward and inverse spatiotemporal PDEs[J/OL]. 2024[2024-07-08]. https://arxiv.org/abs/2405.20000.

[34]GILMER J, SCHOENHOLZ S S, RILEY P F, et al. Neural message passing for quantum chemistry[J/OL]. 2017[2024-07-08]. https://arxiv.org/abs/1704.01212v2.

[35]SANCHEZ-GONZALEZ A, GODWIN J, PFAFF T, et al. Learning to simulate complex physics with graph networks[C］//Proceedings of the 37th International Conference on Machine Learning. 2020: 8459-468.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 13
HTML全文浏览量: 1
PDF下载量: 1
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

doi: 10.21656/1000-0887.450098

作者简介:
宋尚校（1996—），男，助理工程师，硕士（E-mail: sshangxiao@126.com）;张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

通讯作者:
张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

计量

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

计量

目录

留言板

ROE格式的物理增强图神经网络求解Euler与层流不可压NS方程

doi: 10.21656/1000-0887.450098

作者简介: 宋尚校（1996—），男， 助理工程师，硕士（E-mail: sshangxiao@126.com）;张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

通讯作者: 张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

计量

出版历程

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

计量

出版历程

目录

作者简介:
宋尚校（1996—），男，助理工程师，硕士（E-mail: sshangxiao@126.com）;张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.

通讯作者:
张浩（1981—），男，副研究员，博士（通讯作者. E-mail: linusec@163.com）.