Three dimensional interface normal prediction for Volume-of-Fluid method using artificial neural network

In the numerical simulations of multi-phase flow using Volume-of-Fluid (VOF) method, the calculation of the interface normal is a crucial point. In this paper, a machine learning method is used to develop an artificial neural network (ANN) model to make more accurate prediction of the local normal vector from neighboring volume fractions. Spherical surfaces with different radii are intersected with a structural background grid to generate 84328 groups of data: 3×3×3 neighboring volume fractions are used as input, and normal vector as output. Using 90% data as training dataset, the ANN model is well trained by optimizing the number of hidden layers and the number of neurons on each layer. Using the remaining 10% data, normal predictions are made using ANN-VOF and the most used YOUNG and HEIGHT-FUNCTION methods. The RMSE of the ANN-VOF/YOUNG/ HEIGHT-FUNCTION methods are 0.008/0.022/0.045 respectively. In the reconstruction of a sinusoidal surface, the MSE of the ANN-VOF/YOUNG/ HEIGHT-FUNCTION methods are 0.008/0.018/0.041. It is demonstrated that the ANN-VOF method has better performance for interface normal prediction. The proposed method has a simple computational logic and does not need to deal with complex geometric topology, which lays the foundation for application in other more complex grids.