A general Neural Particle Method for hydrodynamics modeling

Abstract

Neural Particle Method (NPM) is a newly proposed Physics-Informed Neural Network (PINN) based, truly meshfree method for hydrodynamics modeling. In the NPM, PINN is applied to globally approximate field variables, and the high-order Implicit Runge–Kutta (IRK) method is used to treat the time integration. The NPM can easily achieve incompressibility and deal with the free-surface problem. However, the NPM is currently limited to inviscid hydrodynamics problems and is computationally expensive. In this work, we developed a general NPM (gNPM) for viscous hydrodynamics modeling. In the gNPM, a single pressure is output as the predicted pressure field rather than the multiple pressures in the original NPM. Thus, the size of the neural network is greatly reduced, making the gNPM computationally more efficient. Besides, the spatial derivatives in the governing equations are calculated with respect to the current spatial coordinates rather than the predicted space. In this manner, the gNPM is more straightforward to be implemented. Furthermore, by considering the viscous term in the conservation of momentum, the gNPM can be applied for viscous hydrodynamics modeling. The effectiveness and robustness of the gNPM have been demonstrated through several hydrodynamics benchmark cases with different boundary conditions. We highlight that the proposed gNPM is able to cope with highly uneven particle distributions, while the traditional meshfree method can produce severe failure.