An Algebraic Turbulence Model Based On Machine Learning

Turbulence as the universal form of the fluid is the key problem in fluid dynamics.The numerical simulation of turbulence is mainly divided into direct numerical simulation,large eddy simulation and Reynolds average numerical simulation.Since direct numerical simulation and large eddy simulation directly or partially solve the Navier-Stokes equation,the computational complexity is too high,and the existing computing resources cannot meet the needs of the simulation.The Reynolds average numerical simulation uses the mass/Renault averaging method to obtain the average solution of turbulent flow for a period of time.Due to the introduction of the eddy viscosity coefficient,the original equation needs to add an additional equation to solve the eddy viscosity coefficient to close the RANS equation.The Spalart-Allmaras turbulence model is added to the RANS equation,which significantly increases the complexity of the system.The high-order discontinuous Galerkin method(DG)cannot quickly obtain a closed solution.Based on the simulated data which simulated by Spalart-Allmaras turbulence model,the artificial neural network algorithm is adopted to construct the algebraic turbulence model.The main research work of this thesis is as follows:(1)In view of the shortcomings of the inefficiency of the OBS pruning process,this thesis proposes the feature selection algorithm “ANN-OBS” which considers the concept of weight "contribution" and improves the pruning algorithm..This thesis applies ANN-OBS algorithm to the feature selection of eddy viscosity coefficient and compares the new method with the other two alternatives ReliefF and TreeBagger.The comparison results verify the practicability and effectiveness of the proposed method.(2)The Spalart-Allmaras turbulence model is proposed,based on experience and the principle of dimensional analysis and Galilean invariance,to calculate the eddy viscosity coefficient.In this thesis,the simulation data is generated from the Spalart-Allmaras turbulence model.The ANN-OBS feature selection algorithm is used to obtain the characteristic variables affecting the eddy viscosity coefficient,and the neural network is trained offline.The trained neural network is used as an algebraic model to replace the Spalart-Allmaras turbulence modelin the Discontinuous Galekin solution.The experimental results show that compared with the traditional “DG+SA ” method,“ DG+ANN ” method can significantly reduce the number of convergence steps and time complexity.(3)Due to the small magnitude of the viscosity coefficients near object surface,the relative errorof the eddy viscosity coefficient predicted by the “DG+ANN” model is large.In order to improve the generalization of neural network,this thesis proposes a framework based on SVM.The test data are dispatched to different networks according to the coefficient distribution calculated by SVM,and the predicted output is obtained by weighting.Compared with the results predicted directly from neural network,the SVM-based method improves the prediction ability of the model.The numerical simulation results show that the new method improves the calculation accuracy of the viscosity coefficients near object surface.