Approximate Solution Of Nonlinear Partial Differential Equation And Prediction Of Flow Field Based On Neural Network

Computational fluid dynamics is a discipline that uses discrete methods to solve fluid dynamics equations in computers.However,in some complex geometric shapes and flow problems,numerical simulation methods often have the disadvantages of modeling difficulties and slow calculation speeds.In recent years,with the continuous development of machine learning technology,people have tried to apply its nonlinear fitting ability to computational fluid dynamics as a fast calculation aid for numerical simulation.In this paper,one-dimensional Burgers equation,two-dimensional laminar flow around a cylinder and three-dimensional turbulent channel flow are taken as examples to establish corresponding neural network models respectively,and the approximate solution of nonlinear partial differential equations(groups)and flow field prediction are explored.First,taking the one-dimensional Burgers equation as an example,the pure data-driven fully-connected neural network model was used to approximate the Burgers equation to realize the reconstruction of the flow field in the computational domain.The pure data-driven method belongs to a black box model.In the solution process,the lack of a direct solution process of nonlinear partial differential equations results in poor physical interpretability.Therefore,based on this,a neural network model coupled with nonlinear partial differential equation(groups)was developed.This model was successfully applied to the Burgers equation and achieved good results.The pure data-driven fully-connected neural network model and coupled with nonlinear partial differential equations neural network were extended to two-dimensional fluid dynamics equations(N-S equations),and the approximate solution of N-S equations was realized.Then,two approximate solutions of nonlinear partial differential equations were applied to the prediction model of the flow field.The prediction and identification of the physical parameters of the flow medium and the prediction of the development trend of the flow field were carried out.The results proved that using neural network models not only have accurate prediction and identification of relevant parameters in the flow field but also play an effective role in the short-term prediction problem of the flow field.At the same time,the LSTM neural network model coupled with the N-S equations was developed,andthe errors of several flow field prediction models in short-term prediction of the flow field were compared.The impaction of physical laws can effectively improve the prediction ability of the models.Finally,considering the computational efficiency and accuracy of the model,a pure data-driven LSTM neural network model was selected to construct a flow field prediction model for the turbulent channel flow,which proved the applicability of the neural network algorithm in turbulent modeling.