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DOI | 10.1002/2017WR020905 |
Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media | |
Tartakovsky, A. M.1; Panzeri, M.2; Tartakovsky, G. D.3; Guadagnini, A.2 | |
2017-11-01 | |
发表期刊 | WATER RESOURCES RESEARCH
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ISSN | 0043-1397 |
EISSN | 1944-7973 |
出版年 | 2017 |
卷号 | 53期号:11 |
文章类型 | Article |
语种 | 英语 |
国家 | USA; Italy |
英文摘要 | Equations governing flow and transport in randomly heterogeneous porous media are stochastic and scale dependent. In the moment equation (ME) method, exact deterministic equations for the leading moments of state variables are obtained at the same support scale as the governing equations. Computable approximations of the MEs can be derived via perturbation expansion in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for standard deviation smaller than one. Here, we consider steady-state saturated flow in a porous medium with random second-order stationary conductivity field. We show it is possible to identify a support scale , where the typically employed approximate formulations of MEs yield accurate (statistical) moments of a target state variable. Therefore, at support scale and larger, MEs present an attractive alternative to slowly convergent Monte Carlo (MC) methods whenever lead-order statistical moments of a target state variable are needed. We also demonstrate that a surrogate model for statistical moments can be constructed from MC simulations at larger support scales and be used to accurately estimate moments at smaller scales, where MC simulations are expensive and the ME method is not applicable. Plain Language Summary Equations governing flow and transport in randomly heterogeneous porous media are stochastic and scale dependent. In the moment equation method, exact deterministic equations for the leading moments of state variables are obtained at the same support scale as the governing equations. Computable approximations of these equations can be derived via perturbation expansion in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for standard deviation smaller than one. Here, we consider steady-state saturated flow in a porous medium with random second-order stationary conductivity field. We show it is possible to identify a support scale, where the typically employed approximate formulations of moment equations yield accurate moments of a target state variable. |
英文关键词 | flow in porous media randomness uncertainty quantification scale dependence |
领域 | 资源环境 |
收录类别 | SCI-E |
WOS记录号 | WOS:000418736700040 |
WOS关键词 | STEADY-STATE FLOW ; STOCHASTIC MOMENT EQUATIONS ; LOCALIZED ANALYSES ; PROBABILISTIC COLLOCATION ; DATA ASSIMILATION ; GROUNDWATER-FLOW ; SOLUTE TRANSPORT ; TRANSIENT FLOW ; SUPPORT SCALE ; SPARSE GRIDS |
WOS类目 | Environmental Sciences ; Limnology ; Water Resources |
WOS研究方向 | Environmental Sciences & Ecology ; Marine & Freshwater Biology ; Water Resources |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://119.78.100.173/C666/handle/2XK7JSWQ/21860 |
专题 | 资源环境科学 |
作者单位 | 1.Pacific Northwest Natl Lab, Computat Math Grp, Richland, WA 99352 USA; 2.Politecn Milan, Dipartimento Ingn Civile & Ambientale, Milan, Italy; 3.Pacific Northwest Natl Lab, Hydrol Grp, Richland, WA USA |
推荐引用方式 GB/T 7714 | Tartakovsky, A. M.,Panzeri, M.,Tartakovsky, G. D.,et al. Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media[J]. WATER RESOURCES RESEARCH,2017,53(11). |
APA | Tartakovsky, A. M.,Panzeri, M.,Tartakovsky, G. D.,&Guadagnini, A..(2017).Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media.WATER RESOURCES RESEARCH,53(11). |
MLA | Tartakovsky, A. M.,et al."Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media".WATER RESOURCES RESEARCH 53.11(2017). |
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