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可压缩两气体流动的简化神经网络模型

刘子岩 许亮 刘耀峰

刘子岩, 许亮, 刘耀峰. 可压缩两气体流动的简化神经网络模型[J]. 气体物理, 2024, 9(2): 33-42. doi: 10.19527/j.cnki.2096-1642.1089
引用本文: 刘子岩, 许亮, 刘耀峰. 可压缩两气体流动的简化神经网络模型[J]. 气体物理, 2024, 9(2): 33-42. doi: 10.19527/j.cnki.2096-1642.1089
LIU Ziyan, XU Liang, LIU Yaofeng. A Simplified Neural Network Model for Compressible Two-Gas Flows[J]. PHYSICS OF GASES, 2024, 9(2): 33-42. doi: 10.19527/j.cnki.2096-1642.1089
Citation: LIU Ziyan, XU Liang, LIU Yaofeng. A Simplified Neural Network Model for Compressible Two-Gas Flows[J]. PHYSICS OF GASES, 2024, 9(2): 33-42. doi: 10.19527/j.cnki.2096-1642.1089

可压缩两气体流动的简化神经网络模型

doi: 10.19527/j.cnki.2096-1642.1089
基金项目: 

国家自然科学基金 11872351

详细信息
    作者简介:

    刘子岩(1998—)男, 博士, 主要研究方向为机器学习在可压缩多介质流问题中的应用。E-mail: lzy210@buaa.edu.cn

    通讯作者:

    许亮(1982-)男, 研究员, 主要研究方向为可压缩多介质流模拟方法、CFD中机器学习建模方法等。E-mail: xul@buaa.edu.cn

  • 中图分类号: O359

A Simplified Neural Network Model for Compressible Two-Gas Flows

  • 摘要: 实用的虚拟流体方法(practical ghost fluid method, PGFM)利用Riemann问题速度解对可压缩多介质流场界面条件进行建模。基于构造的嵌入物理约束的神经网络模型预测Riemann问题速度解的方式, 给出一种两气体流动的神经网络模型简化方法。首先提出完全气体状态方程下神经网络模型输入特征采样范围从无界域到有界域的转换方法, 改善模型预测不同初始条件下Riemann解的泛化性能。根据该转化方法, 进一步提出一种结构更加简单的神经网络优化方法, 将输入维度从5个减少到3个, 有效提高神经网络的训练效果。将该神经网络代理模型应用于PGFM程序框架, 通过典型的一维与二维两气体流动问题进行数值验证与对比分析。结果表明, 简化的网络模型与已有研究的神经网络模型相比, 能取得精度相近的计算结果。而在神经网络训练效率上, 简化神经网络具有明显优势。同时因为简化神经网络采样维度少, 方便尝试加密采样提高拟合精度, 更具备发展潜力。

     

  • 图  1  PGFM定义虚拟流体状态的示意图[7]

    Figure  1.  Illustration of the PGFM for defining ghost fluid states[7]

    图  2  考虑物理约束的人工神经网络示意图

    Figure  2.  Illustration of the artificial neural network with physical constraints

    图  3  简化神经网络标准化原理示意图

    Figure  3.  Illustration of the neural network after simplification

    图  4  神经网络训练误差收敛图

    Figure  4.  Convergence of neural network training errors

    图  5  网络预测值与精确解绝对误差对比图

    Figure  5.  Absolute errors between exact and predicted velocities

    图  6  算例1计算结果对比

    Figure  6.  Comparison of calculation results for case 1

    图  7  算例2计算结果对比

    Figure  7.  Comparison of calculation results for case 2

    图  8  空气中激波扫过氦气泡算例的计算域(单位:mm)

    Figure  8.  Computational domain of an air shock impinging on a helium bubble(unit: mm)

    图  9  激波扫过氦气泡算例纹影对比图

    Figure  9.  Comparison of the schlieren for an air shock impinging on a helium bubble

    表  1  各神经网络代理模型

    Table  1.   Various neural network models

    No. relation of p relation of ρ neural network inputs
    1 pLpR ρLρR {pL, ρL, Δu}
    2 pLpR ρLρR {pL, ρR, Δu}
    3 pLpR ρLρR {pR, ρR, Δu}
    4 pLpR ρLρR {pR, ρL, Δu}
    下载: 导出CSV

    表  2  算例2相对误差定量统计表

    Table  2.   Quantitative results of relative errors in case 2

    physical quantity solution 5-10-10-2 3-10-10-2 5-40-40-2 3-40-40-2
    pI exact solution 2.612 65
    predicted solution 2.696 19 2.630 79 2.602 56 2.613 61
    relative error 3.198% 0.694% 0.386% 0.037%
    uI exact solution -1.883 04
    predicted solution -1.822 54 -1.870 15 -1.890 35 -1.882 42
    relative error 3.213% 0.685% 0.388% 0.033%
    ρIL exact solution 1.936 21
    predicted solution 1.854 02 1.912 84 1.940 86 1.929 68
    relative error 4.245% 1.207% 0.240% 0.337%
    ρIR exact solution 0.447 01
    predicted
    solution
    0.453 51 0.446 26 0.443 87 0.445 01
    relative error 1.454% 0.168% 0.702% 0.447%
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-09-26
  • 修回日期:  2023-12-19

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