基于神经网络的格子玻尔兹曼算法

Lattice Boltzmann Method Based on Neural Network

在科学研究和工业应用的复杂流域、多相流以及多物理流动问题的处理中,相较于传统计算流体力学方法(Computational Fluid Dynamics,CFD),格子玻尔兹曼算法(Lattice Boltzmann Method,LBM)具有程序结构简单、对复杂边界和非线性问题适应性强以及便于并行计算等诸多优点。然而,其作为一种显式算法,在计算过程中的迭代次数较多,进而消耗大量计算资源。利用神经网络在预测与回归方面的强大能力,基于LBM设计了一个具备单隐藏层的浅层人工神经网络预测模型并将其命名为ML-LBM(Machine Learning LBM)模型。该模型通过动态调整碰撞算子中不同驰豫时间,以粗化网格来重现精细分辨的参考模拟。对于顶盖驱动流问题,模型完成训练后,对测试集均方误差在6×10-5以下,精度得到了保障。相较于经典LBGK模型,ML-LBM模型的计算效率提升约9倍。

Compared with traditional Computational Fluid Dynamics(CFD),computational fluid dynamics for complex drainage basins,multiphase flows,and multi-physical flow problems for scientific research and industrial applications,the Lattice Boltzmann Method(LBM)has many advantages,such as simple program structure,strong adaptability to complex boundary and nonlinear problems,and convenient parallel computation.However,as an explicit algorithm,it has many iterations in the calculation process,which consumes a lot of computing resources.Based on the powerful ability of neural network in prediction and regression,a shallow artificial neural network prediction model with single hidden layer is designed based on LBM and named as ML-LBM(Machine Learning LBM)model.The model reproduces the reference simulation of fine resolution by coarsening the mesh by dynamically adjusting the different relaxation times in the collision operator.For the problem of the top drive flow,the mean square error of the test set is less than 6×10-5 after the model is trained,and the accuracy is guaranteed.Compared with the classical LBGK model,the computational efficiency of ML-LBM model is improved by about 9 times.