arXiv:2603.19841physics.flu-dyncs.LG2026-03

用图神经网络预测复杂网格上的化学反应生成率,提升大涡模拟精度。

Modeling subgrid scale production rates on complex meshes using graph neural networks

  • 基于图神经网络,直接从滤波后的组分和温度预测生成率。
  • 在未见的50%氢气混合比例下仍保持低误差,跨组分泛化能力强。
  • 无需重网格化,对不同滤波宽度和复杂几何均表现稳健,适合工程应用。

大涡模拟(LES)需要对滤波后的生成率进行闭合,因为解析场中缺少决定化学源项的所有相关性。本文提出一种图神经网络(GNN),从滤波后的质量分数和温度输入中预测非均匀网格上的滤波物种生成率。采用湍流预混氢-甲烷喷射火焰的直接数值模拟数据集,氢含量分别为10%、50%和80%,所有场均采用与操作网格匹配的Favre滤波。学习基于由网格点连接构建的子域图进行。使用一组精简的反应物、中间体和产物,其滤波生成率作为目标。模型在10%和80%混合比上训练,在未见的50%混合比上评估以测试跨组成泛化能力。与在滤波状态直接计算的无闭合参考解及需重网格化的卷积神经网络基线相比,该GNN在分布内和分布外情况下均表现出更低误差,并更接近参考数据的统计特性。此外,模型在不同滤波宽度下无需重新训练即可保持良好泛化性能,粗分辨率下误差仍受控。后向台阶配置进一步验证了其在实际几何中的预测有效性。结果表明,GNN可作为复杂网格上稳健的数据驱动闭合模型。

原文摘要 · Abstract (English)

Large-eddy simulations (LES) require closures for filtered production rates because the resolved fields do not contain all correlations that govern chemical source terms. We develop a graph neural network (GNN) that predicts filtered species production rates on non-uniform meshes from inputs of filtered mass fractions and temperature. Direct numerical simulations of turbulent premixed hydrogen-methane jet flames with hydrogen fractions of 10%, 50%, and 80% provide the dataset. All fields are Favre filtered with the filter width matched to the operating mesh, and learning is performed on subdomain graphs constructed from mesh-point connectivity. A compact set of reactants, intermediates, and products is used, and their filtered production rates form the targets. The model is trained on 10% and 80% blends and evaluated on the unseen 50% blend to test cross-composition generalization. The GNN is compared against an unclosed reference that evaluates rates at the filtered state, and a convolutional neural network baseline that requires remeshing. Across in-distribution and out-of-distribution cases, the GNN yields lower errors and closer statistical agreement with the reference data. Furthermore, the model demonstrates robust generalization across varying filter widths without retraining, maintaining bounded errors at coarser spatial resolutions. A backward facing step configuration further confirms prediction efficacy on a practically relevant geometry. These results highlight the capability of GNNs as robust data-driven closure models for LES on complex meshes.

大涡模拟图神经网络化学闭合多组分反应

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