Solving the discretised shallow water equations using non-uniform grids and machine-learning libraries
Year: 2025
Type: article
Abstract: In this study, we extend our previous work on the numerical solution of the Shallow Water Equations by introducing non-uniform structured grids. This allows us to adjust the resolution of different subdomains in order to capture critical features. The discretised equations are formulated as a discrete convolution, which can be interpreted as a neural network convolutional layer. The proposed method retains the advantages of our previous approach, including platform-independent code compatible with CPUs, GPUs and AI-optimised processors, and the potential for seamless integration with trained neural networks such as sub-grid-scale models or surrogates. Our method compares well with the analytical solution of a circular dam break. For the Carlisle flooding event of 2005, good agreement is obtained, both with observations and other numerical solutions in the literature. The non-uniform grids reduce the computational burden, which is important for problems over large domains such as those found in hydrodynamic applications.
Authors: Amin Nadimy, Boyang Chen, Zimo Chen, Claire E. Heaney, Christopher C. Pain
Institution: Imperial College London
Language: English
Subfield: Earth-Surface Processes
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,500
OpenAlex ID: W4415569421