The compressible Neural Particle Method for Simulating Compressible Viscous Fluid Flows

Abstract: Particle methods play an important role in computational fluid dynamics, but they are among the most difficult to implement and solve. The most common method is smoothed particle hydrodynamics, which is suitable for problem settings that involve large deformations, such as tsunamis and dam breaking. However, the calculation can become unstable depending on the distribution of particles. In contrast, the neural particle method has high computational stability for various particle distributions is a machine learning method that approximates velocity and pressure in a spatial domain using neural networks. The neural particle method has been extended to viscous flows, but until now it has been limited to incompressible flows. In this paper, we propose the compressible neural particle method, which is a new feed-forward neural network-based method that extends the original neural particle method to model compressible viscous fluid flows. The proposed method uses neural networks to calculate the velocity and pressure of fluid particles at the next time step, and the Tait equation to calculate the density to handle the compressibility. The loss function is composed of the governing equations of compressible flow and the boundary conditions, which are free surface and solid boundary conditions. We demonstrate that the proposed method can accurately solve the compressible viscous fluid flow, a problem that was difficult to solve with the smoothed particle hydrodynamics method, by applying it to a dam breaking problem.