Constructing a surrogate model constitutive equation using U-Net for viscoelastic-fluid turbulence

Abstract

We applied a deep learning to construct a surrogate model of the constitutive equation to simulate the viscoelastic turbulent channel flow. We used U-Net, a convolutional neural network (CNN), to predict the conformation stress field from the instantaneous velocity field obtained from direct numerical simulation (DNS). We investigated the prediction accuracy of the conformation stress and the possibility of the surrogate model of U-Net as a DNS-CNN simulation. The mean profile of c_xx and the flow field were reproduced with high accuracy by using U-Net. However, the prediction accuracy of c_yy in the buffer layer, where polymer rotation is induced by vortices, is low. The predicted instantaneous fields exhibit noise caused by the convolution operation of U-Net. In the surrogate modeling of U-Net, we compared the result of the DNS-CNN simulation to the pure DNS. After 5000 steps, the instantaneous flow fields were slightly different, but the obtained statistics showed a good agreement between both simulations.