一种求解非定常可压缩流动的流场信息融合的图神经网络方法  

A GNN-based Surrogate Model Involving Flow-field Message for Spatio-temporal Flow Simulations of Compressible Flows

作　　者：李思冶 孙振生 朱玉杰 Li Siye;Sun Zhensheng;Zhu Yujie(Rocket Force University of Engineering,Xian 710025,China)

机构地区：[1]中国人民解放军火箭军工程大学,陕西西安710025

出　　处：《气动研究与试验》2024年第1期39-49,共11页Aerodynamic Research & Experiment

摘　　要：传统数值方法基于网格的数值离散或者积分形式,其计算效率较低、耗时高并需要昂贵的计算资源。针对含有强间断的非定常可压缩流问题,本文提出了一种流场信息融合的图神经网络方法。首先,深入分析了计算流体力学(CFD)求解与图神经网络(GNN)方法的内涵联系,数学上明确了模型训练中的算子对象与任务,从而指导模型结构设计。为了增强模型的非线性逼近能力,通过激波识别器技术提取了流场局部的非线性特征,并将流场的物理、空间以及非线性信息嵌入图表征方法中。在此基础上,设计了一种基于聚合采样方法的流场信息融合的消息传递网络,通过此网络将流场不同尺度信息进行传播、聚合以及更新,从而预测流场的时空演化过程。此外,在编码器-解码器框架下将提取的流场信息转化为潜在的流体力学知识,实现端到端的模拟功能。最后,通过激波管问题、Shu-Osher问题以及二维黎曼问题验证了模型的有效性。结果表明,在一维与二维问题中,模型均可快速收敛,且变量相对误差在O(10^(-6))~O(10^(-7))量级;针对训练集外的时间尺度模拟,该模型具有良好的预测能力,且极大地提高了流场计算效率。Traditional numerical methods are grid-based numerical discretization or integration approaches,which introduce low computational efficiency,high time consumption,and require expensive computing resources.This paper propose a GNN-based surrogate model involving flow-field message for solving unsteady compressible flows with strong discontinuities.As first step,the inherent consistence between CFD approaches and GNN methods is analyzed in depth,which mathematically clarifies clarifies the operator objects and tasks during the model training and guides the designing of the model architecture.Moreover,to enhance nonlinear approximation capability of strong discontinuities,a shock detector method is leveraged to extract the local flow field messages,which are embedded into the graph representations to resolve the discontinuous solutions well.Then,a new flow-field-message-informed and SAGE(Sample and Aaggregate)-based message passing layer(FFMI-SAGE),aggregating the edge-weighted attributes with node features on different hop layers,is developed to diffuse and process the flow field messages.Furthermore,an end-to-end paradigm is conducted within the Encoder-Decoder framework to transform the extracted information from flow field into the latent knowledge about the underlying fluid mechanics.Finally,a variety of test cases including the sod tube problem,Shu-Osher problem and twodimensional Riemann problem are employed to demonstrate the effectiveness and generalizability of the proposed FFMIGNN model.The results show that in both one-and two-dimensional problems,the model training can converge quickly,and the relative error of variables is on the order of O(10^(-6))~O(10^(-7)).For predicting flow fields outside the training set,this model has attractive generalizability and greatly improves the efficiency of flow field calculation.

关 键 词：非定常可压缩流 强间断 图神经网络 流场信息融合 激波识别器 

分 类 号：O354[理学—流体力学]