A POD-based reduced-order model for uncertainty analyses in shallow water flows

ABSTRACT

This work presents an intrusive reduced-order model (IROM) for uncertainty propagation analyses for flood flows. The 2D shallow water equations are reduced using Galerkin’s projection onto bases obtained from the snapshot-based proper orthogonal decomposition technique. To speed up the computations, the non-polynomial and nonlinear momentum and friction terms are judiciously approximated and the time accuracy issues are addressed using the principal interval decomposition technique. The performance of the IROM is investigated in some test cases. Also, this model is applied to the study of uncertainty propagation for a hypothetical flood in a real river, to derive a probabilistic flood map. The upstream discharge and the Manning roughness coefficient are considered as the uncertain parameters. For relatively small variations around the mean of the inputs, the comparisons of the statistical moments (mean and standard deviation) of the water depth show errors, between the reduced and full models, less than 0.72%. These simulations were completed at up to 50 times faster using the proposed reduced model.

KEYWORDS:

• Free surface flows
• shallow water equations
• model reduction
• proper orthogonal decomposition
• principal interval decomposition
• probabilistic flood maps

Acknowledgements

We are grateful to Hydro-Québec (Direction Barrages et Infrastructures) and NSERC (National Science and Engineering Research Council of Canada) for supporting this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) [grant number 491880 - 15].