期刊
WATER RESOURCES RESEARCH
卷 49, 期 6, 页码 3215-3228出版社
AMER GEOPHYSICAL UNION
DOI: 10.1002/wrcr.20136
关键词
model reduction; Monte Carlo simulation; groundwater modeling
资金
- NSF [EAR-0910507]
- ARO [W911NF-10-1-0124]
- AECOM endowment
- European Commission [FP7-ENV-2009-1-244151]
- CARIPARO Foundation
- Ing. Aldo Gini Foundation
- University of Padua [STPD08RWBY]
- Directorate For Geosciences [0910507] Funding Source: National Science Foundation
- Division Of Earth Sciences [0910507] Funding Source: National Science Foundation
We present a model-order reduction technique that overcomes the computational burden associated with the application of Monte Carlo methods to the solution of the groundwater flow equation with random hydraulic conductivity. The method is based on the Galerkin projection of the high-dimensional model equations onto a subspace, approximated by a small number of pseudo-optimally chosen basis functions (principal components). To obtain an efficient reduced-order model, we develop an offline algorithm for the computation of the parameter-independent principal components. Our algorithm combines a greedy algorithm for the snapshot selection in the parameter space and an optimal distribution of the snapshots in time. Moreover, we introduce a residual-based estimation of the error associated with the reduced model. This estimation allows a considerable reduction of the number of full system model solutions required for the computation of principal components. We demonstrate the robustness of our methodology by way of numerical examples, comparing the empirical statistics of the ensemble of the numerical solutions obtained using the traditional Monte Carlo method and our reduced model. The numerical results show that our methodology significantly reduces the computational requirements (CPU time and storage) for the solution of the Monte Carlo simulation, ensuring a good approximation of the mean and variance of the head. The analysis of the empirical probability density functions at the observation wells suggests that our reduced model produces good results and is most accurate in the regions with large drawdown.
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