标题： 使用神经网络减少出流边界对气动性能的影响 显示英文标题

标题： Reduction of Outflow Boundary Influence on Aerodynamic Performance using Neural Networks

摘要： 在利用计算流体力学预测气动阻力和/或声辐射时，出口边界条件的精确处理仍然是一个关键挑战。 这一点在使用格子玻尔兹曼方法（LBM）作为数值解法时尤为明显，因为LBM常常受到人工反射误差的影响。 本文研究了使用神经网络（NN）来减轻这些不利的边界效应，并满足截断域需求。 提出了两种基于NN的方法：(1) 直接重建出口边界处未知的粒子分布函数；(2) 通过动态调整参数增强现有的特征边界条件（CBC）。 直接重建模型是在二维圆柱障碍物流动生成的数据上进行训练的。 阻力、升力和斯特劳哈尔数被用来测试新的边界条件。 我们分析了不同雷诺数和受限域尺寸下的结果，在这些情况下，与传统的Zou & He边界条件相比，该条件显示出显著改善的预测能力。 为了检验基于NN的重建的鲁棒性，相同的条件被应用于NACA0012翼型的模拟中，再次提供了准确的空气动力学性能预测。 神经增强的CBC在二维传导涡基准问题上进行了评估，在最小化密度误差方面表现出比具有固定参数的CBC更优越的性能。 这些发现突显了NN集成边界条件在提高LBM模拟气动和声辐射准确性以及减少计算成本方面的潜力。 显示英文摘要

摘要： The accurate treatment of outflow boundary conditions remains a critical challenge in computational fluid dynamics when predicting aerodynamic forces and/or acoustic emissions. This is particularly evident when employing the lattice Boltzmann method (LBM) as the numerical solution technique, which often suffers from inaccuracies induced by artificial reflections from outflow boundaries. This paper investigates the use of neural networks (NN) to mitigate these adverse boundary effects and enable truncated domain requirements. Two distinct NN-based approaches are proposed: (1) direct reconstruction of unknown particle distribution functions at the outflow boundary; and (2) enhancement of established characteristic boundary conditions (CBC) by dynamically tuning their parameters. The direct reconstruction model was trained on data generated from a 2D flow over a cylindrical obstruction. The drag, lift, and Strouhal number were used to test the new boundary condition. We analyzed results for various Reynolds numbers and restricted domain sizes where it demonstrated significantly improved predictions when compared with the traditional Zou & He boundary condition. To examine the robustness of the NN-based reconstruction, the same condition was applied to the simulation of a NACA0012 airfoil, again providing accurate aerodynamic performance predictions. The neural-enhanced CBC were evaluated on a 2D convected vortex benchmark and showed superior performance in minimizing density errors compared to CBCs with fixed parameters. These findings highlight the potential of NN-integrated boundary conditions to improve accuracy and reduce computational expense of aerodynamic and acoustic emissions simulations with the LBM.