Research On Turbulence Modeling Theory With Machine Learning

Navier-Stokes equations describing the flowing state over partial differential equations as a model,is difficult to be solved in a closed-form expression way under most circumstance in turbulent issues.The participation of Reynolds-Average on the one hand simplifies the Navier-Stokes equations,and on the other hand leads to the closure problem,promotes the development of the theory who is aiming at modeling high quality supplementary equations,which under that situations are in demand.Until recent years has the machine learning theory by which people are attempted to make breakthrough cooperated with turbulent issues in a interdisciplinary way.In this paper we stand ourselves out by means of using neural network algorithm of machine learning to reexplore the traditional turbulent modeling issues with the data of flow around a square cylinder by LES under the circumstance of classical time-averaged RANS model.Firstly,the traditional turbulent modeling issues belongs to regression problem in machine learning.So in this paper we establish a five-layer back-propagation neural network guided with SSE and updated with gradient-decent algorithms.Secondly,given the characters of Boussinesq hypothesis and target outputs,we choose the gradient of velocity to displacement as input features under the occasion of comparing the discrepancy of target output consequences derived from different input features.Finally,we update the model with a broader data area,give a prediction of normalized Reynolds-stress anisotropy tensor in expansion and flowing dimension of square cylinder and establish the mathematics model of normalized Reynolds-stress anisotropy tensor in a machine learning way,which is quite beneficial to the construction of Reynolds-stress constitutive model.