Shaw, J. orcid.org/0000-0002-0928-3604 and Kesserwani, G. (2020) Stochastic Galerkin finite volume shallow flow model: well-balanced treatment over uncertain topography. Journal of Hydraulic Engineering, 146 (3). 04020005. ISSN 0733-9429
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2020 American Society of Civil Engineers. This is an author-produced version of a paper subsequently published in Journal of Hydraulic Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council (EPSRC) EP/R007349/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 31 Jul 2019 13:08 |
Last Modified: | 12 Jan 2024 15:37 |
Status: | Published |
Publisher: | American Society of Civil Engineers |
Refereed: | Yes |
Identification Number: | 10.1061/(ASCE)HY.1943-7900.0001705 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:148929 |