Solving the discretised shallow water equations using non-uniform grids and machine-learning libraries

In this study, we extend our numerical framework for solving the Shallow Water Equations by introducing non-uniform structured grids. This enables us to have subdomains of different resolutions to capture important hydrodynamic features efficiently. The discretised equations are formulated as discrete convolutions, interpretable as untrained convolutional layers within a neural network. Communication between the subdomains through halo nodes is managed using precomputed indices, allowing efficient, vectorised updates across interfaces. The approach is platform-independent and could be integrated with trained neural networks, such as sub-grid or surrogate models. The results match analytical solutions for a circular dam break, and show good agreement with observations and existing models for the 2005 Carlisle flood. The use of non-uniform grids reduces computational cost, enabling scalable modelling for large domains. • We propose a non-uniform, structured grid approach for the shallow water equations. • The code can be run on CPUs, GPUs and the latest, energy-efficient AI processors. • Validation tests have been run for the Carlisle flooding event of 2005. • The approach reduces bottlenecks for large domains by using domain decomposition.