Stochastic Galerkin Finite Volume Shallow Flow Model: Well-Balanced Treatment over Uncertain Topography
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 3
Abstract
Stochastic Galerkin methods can quantify uncertainty at a fraction of the computational expense of conventional Monte Carlo techniques, but such methods have rarely been studied for modeling shallow water flows. Existing stochastic shallow flow models are not well-balanced, and their assessment has been limited to stochastic flows with smooth probability distributions. This paper addresses these limitations by formulating a one-dimensional stochastic Galerkin shallow flow model using a low-order Wiener-Hermite polynomial chaos expansion with a finite volume Godunov-type approach, incorporating the surface gradient method to guarantee well-balancing. Preservation of a lake at rest over uncertain topography is verified analytically and numerically. The model is also assessed using flows with discontinuous and highly non-Gaussian probability distributions. Prescribing constant inflow over uncertain topography, the model converges on a steady-state flow that is subcritical or transcritical depending on the topography elevation. Using only four Wiener-Hermite basis functions, the model produces probability distributions comparable to those from a Monte Carlo reference simulation with 2,000 iterations while executing about 100 times faster. Accompanying model software and simulation data are openly available online.
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Acknowledgments
This work is part of the SEAMLESS-WAVE project (Software Infrastructure for Multi-Purpose Flood Modelling at Various Scales Based on Wavelets), which is funded by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant No. EP/R007349/1. For information about the SEAMLESS-WAVE project visit https://www.seamlesswave.com. The authors are grateful to the editors and anonymous reviewers for their helpful comments.
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Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Dec 10, 2018
Accepted: Aug 15, 2019
Published online: Jan 13, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 13, 2020
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