295 / 2024-02-29 09:30:36

Application of Physics-Informed Neural Network in Shallow Water Equations

Dam break; PINN; SWEs; SCM

Dam-break is a catastrophic flow phenomenon that could cause severe casualties and property damage. So far, shallow water equations (SWEs) are widely recognized as the most suitable mathematical formula for describing the dam-break flow. In order to solve SWEs with complex boundaries, we propose a new approach based on the physics-informed neural network (PINN) method combined with the split-coefficient matrix method (SCM), namely SCM-PINN, in which water depth and velocity are approximated. The new approach transforms SWEs into characteristic forms, and the Taylor series is introduced to obtain spatial derivatives corresponding to different characteristic coefficients. Unlike traditional PINN, the proposed SCM-PINN could select corresponding differential operators for calculation according to wave propagation directions, leading to accurately capturing of flow patterns. The proposed approach is applied to three challenging cases to investigate the feasibility and validity, in which its performance for flow regimes is compared with the analytical and numerical solutions. The results indicate that the proposed method can accurately simulate not only flow fields formed under discontinuous initial conditions but also that under the complicated interactions of wave-structures and wave-wave, including reflected shock waves at the square cylinder and the vortex-like motion at the four corners of the block, as well as the wake formed behind the structure. Moreover, the new approach can successfully describe flow morphologies formed under irregular boundaries, especially the flow around obstacle pair openings, countercurrent waves propagating toward upstream and the standing-wave propagating toward downstream. The proposed SCM-PINN provide new approaches for depicting dam-break flow patterns.