Dear Spiral user, We’re pleased to introduce Helix, https://helix.imperial.ac.uk/ Imperial’s new repository for research datasets. Please use Helix for all future dataset deposits. There is no change to Spiral - continue depositing as usual. For queries, contact the Research Data Management team at rdm-enquiries@imperial.ac.uk. Kind regards, the Spiral Team. The Spiral team
Solving the discretised shallow water equations using non-uniform grids and machine-learning libraries
File(s)
Author(s)
Nadimy, Amin
Chen, Boyang
Chen, Zimo
Heaney, Claire E
Pain, Christopher C
Type
Journal Article
Abstract
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.
Date Issued
2026-01-30
Date Acceptance
2025-10-22
Citation
Environmental Modelling & Software, 2026, 196
URI
URL
DOI
ISSN
1364-8152
Publisher
Elsevier
Journal / Book Title
Environmental Modelling & Software
Volume
196
Copyright Statement
© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Subjects
Computer Science
Computer Science, Interdisciplinary Applications
Engineering
Engineering, Environmental
Environmental Sciences
Environmental Sciences & Ecology
Finite element method
Flooding
INUNDATION
Life Sciences & Biomedicine
MODEL
Neural networks
Non-uniform grids
Petrov-Galerkin stabilisation
Physical Sciences
REFINEMENT
Science & Technology
Shallow water equations
SIMULATION
Technology
Water Resources
Publication Status
Published
Article Number
106752
Date Publish Online
2025-10-27