耦合流体动力学方程的神经网络模型研究

Neural Network Flow Field Prediction Model Coupled with Fluid Dynamics Equations

摘要: 在流体力学中应用深度学习的技术成为研究热点，但是目前使用的纯粹数据驱动的神经网络模型，不具备物理知识定律的可解释性，而且作为预测模型时，其预测准确度较差。基于此，提出了耦合物理定律的神经网络模型，以层流二维圆柱绕流为例，实现了对流体动力学方程(N-S方程)的耦合与近似求解，并对模型的短时流场预测能力进行了验证。结果表明：该模型可以使用少量的训练数据对控制方程进行近似求解，对相应已知时刻的流场进行重建；进行未知时刻流场的预测时，与相同条件下纯数据驱动的神经网络流场预测模型相比，该模型具有更小的预测误差。

Abstract: In recent years, the application of deep learning technology in fluid mechanics has become a re-search hotspot. However, currently pure data-driven neural network models do not have the inter-pretability of the laws of physical knowledge, and when used as a prediction model, its prediction accuracy is poor. Based on this, a neural network model coupled with the laws of physics was de-veloped. Taking laminar two-dimensional cylindrical flow as an example, the approximate solution of the N-S equation was achieved, and the short-term flow field prediction ability of the model was verified. The results show that the model can use a small amount of training data to approximate the governing equations and reconstruct the corresponding flow field. When predicting the flow field, the model has smaller prediction error than pure data-driven neural network model under the same conditions.