Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development
The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic fra...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2018-03-01
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| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://www.hydrol-earth-syst-sci.net/22/1993/2018/hess-22-1993-2018.pdf |
| _version_ | 1811326115091841024 |
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| author | A. Dib M. L. Kavvas |
| author_facet | A. Dib M. L. Kavvas |
| author_sort | A. Dib |
| collection | DOAJ |
| description | The Saint-Venant equations are commonly used as the
governing equations to solve for modeling the spatially varied unsteady flow
in open channels. The presence of uncertainties in the channel or flow
parameters renders these equations stochastic, thus requiring their solution
in a stochastic framework in order to quantify the ensemble behavior and the
variability of the process. While the Monte Carlo approach can be used for
such a solution, its computational expense and its large number of
simulations act to its disadvantage. This study proposes, explains, and
derives a new methodology for solving the stochastic Saint-Venant equations
in only one shot, without the need for a large number of simulations. The
proposed methodology is derived by developing the nonlocal
Lagrangian–Eulerian Fokker–Planck equation of the characteristic form of
the stochastic Saint-Venant equations for an open-channel flow process, with
an uncertain roughness coefficient. A numerical method for its solution is
subsequently devised. The application and validation of this methodology are
provided in a companion paper, in which the statistical results computed by
the proposed methodology are compared against the results obtained by the
Monte Carlo approach. |
| first_indexed | 2024-04-13T14:43:52Z |
| format | Article |
| id | doaj.art-f6fc4280a603412b9ba5ea6d1b1e93b2 |
| institution | Directory Open Access Journal |
| issn | 1027-5606 1607-7938 |
| language | English |
| last_indexed | 2024-04-13T14:43:52Z |
| publishDate | 2018-03-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj.art-f6fc4280a603412b9ba5ea6d1b1e93b22022-12-22T02:42:49ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382018-03-01221993200510.5194/hess-22-1993-2018Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical developmentA. Dib0M. L. Kavvas1Department of Civil and Environmental Engineering, University of California, Davis, 95616, USADepartment of Civil and Environmental Engineering, University of California, Davis, 95616, USAThe Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian–Eulerian Fokker–Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.https://www.hydrol-earth-syst-sci.net/22/1993/2018/hess-22-1993-2018.pdf |
| spellingShingle | A. Dib M. L. Kavvas Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development Hydrology and Earth System Sciences |
| title | Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development |
| title_full | Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development |
| title_fullStr | Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development |
| title_full_unstemmed | Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development |
| title_short | Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development |
| title_sort | ensemble modeling of stochastic unsteady open channel flow in terms of its time space evolutionary probability distribution part 1 theoretical development |
| url | https://www.hydrol-earth-syst-sci.net/22/1993/2018/hess-22-1993-2018.pdf |
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