A Simplified Neural Network Model for Compressible Two-Gas Flows

The practical ghost fluid method (PGFM) utilizes velocity solutions of Riemann problems to model the interface evolution of compressible multi-material flows. This paper presented a simplified neural network model for two-gas flows by predicting the velocity solution of Riemann problem based on the neural network model embedded with physical constraints. Firstly, a method for converting the sampling range of the neural network model from unbounded domain to bounded domain was proposed, which holds true for the perfect gas equation of state. It can improve the generalization performance of the model under different initial conditions. Based on this transformation method, a simpler neural network structure was further proposed. The training result of the neural network can be effectively improved by reducing the input dimensions from 5 to 3. The neural network model was applied to the PGFM. Numerical validation of the neural network model was carried out through typical one-dimensional and two-dimensional gas flow problems. The results show that the simplified network model can achieve similar computational accuracy compared with existing neural network models. In terms of training efficiency of neural networks, the simplified neural network has obvious advantages. Moreover, because the simplified neural network has fewer sampling dimensions, it is convenient to try denser sampling to improve fitting accuracy and such method has more development potential.