Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

Xia, Chuan‐An; Pasetto, Damiano; Hu, Bill X.; Putti, Mario; Guadagnini, Alberto

doi:10.1016/j.jhydrol.2020.125257

Cited by 8 publications

(6 citation statements)

References 65 publications

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“…Xie et al [8] applied a multiscale finite element method for groundwater flow in heterogeneous media. The application of the Monte Carlo method in similar research was reported by Xia et al [9]. Moreover, meshfree techniques are gaining attention in the simulation of groundwater flow, and the literature reported includes the meshfree collocation method [5,6], element-free Galerkin method [10], meshless local Petrov-Galerkin method [11], and immersed boundary method [12].…”

Section: Introductionmentioning

confidence: 67%

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Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

et al. 2022

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Potential flow formed by doublet flow has been well applied in environmental applications and geothermal designs such as reservoir and fuel injectors. Most of the doublet flow is assumed based on the sink and source with equivalent strength and distance from the origin, forming the well-known Rankine oval structure when a far-field flow is superposed. A semi-analytical method is formulated to systematically investigate the unsymmetrical doublet flow with different strengths of sink and source. The general mathematical expression for unsymmetrical doublet flow is derived analytically before the streamline and the potential line can be visualised via a numerical approach. The results revealed that the doublet flows altered the Rankine oval structure to form aerofoil-like geometry. When the far-field flow interferes with the general Doublet configuration, unique flow structures such as convex, concave, and various wing shapes could be generated. The current study provides new insight on producing aerodynamic curves for the design of bio-inspired structures.

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Section: Introductionmentioning

confidence: 67%

“…and upon the substitution of Equations ( 6) and (7) into Equation ( 8), the stream function now becomes Equation (9).…”

Section: Mathematical Formulation Of Unsymmetrical Doublet Flowmentioning

confidence: 99%

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

et al. 2022

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“…Furthermore, it's important to assess the uncertainties in measurements and model assumptions. Therefore, this study also employed sensitivity analysis or the use of Monte Carlo simulations to understand how uncertainties in isotopic signatures and other parameters affect the flow component estimates [45].…”

Section: Isotopic End-member Mixing Analysismentioning

confidence: 99%

Innovative Assessment of Mun River Flow Components through ANN and Isotopic End-Member Mixing Analysis

Chomcheawchan,

Pawana,

Julphunthong

et al. 2024

Preprint

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This study innovatively assesses the Mun River flow components in Thailand, integrating Artificial Neural Networks (ANN) and Isotopic (18O) End-Member Mixing Analysis (IEMMA). It quantifies the contributions of the Upper Mun River (UMR) and Chi River (CR) to the overall flow, revealing a discrepancy in their estimated contributions. ANN predicts the UMR and CR contribute approximately 70.1% and 29.5% respectively, while IEMMA indicates a more pronounced disparity with 84% from UMR and 16% from CR. This divergence highlights the distinct perspectives of ANN, focusing on hydrological data patterns, and IEMMA, emphasizing isotopic signatures. Despite discrepancies, both methods validate UMR as a significant contributor to the overall flow, highlighting their utility in hydrological research. The findings underscore the complexity of river systems and advocate for an integrated approach of river flow analysis for a comprehensive understanding, crucial for effective water resource management and planning.

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“…As opposed to a local approach, a Global Sensitivity Analysis (GSA) method has the advantage of considering statistics associated with the entire support space within which uncertain model parameters can vary, possibly taking into account effects stemming from parameter interactions (e.g., Ciriello et al., 2013; Razavi & Gupta, 2015; Xia et al., 2018 and references therein). GSA approaches are broadly employed in hydrology and Earth system sciences (Bittner et al., 2021; Mai et al., 2020; Pianosi & Wagener, 2015; Reusser et al., 2011; Wang et al., 2020; Xia et al., 2020). Amongst these, the classical strategy grounded on the variance‐based Sobol indices (Homma & Saltelli, 1996) is very frequently used.…”

Section: Introductionmentioning

confidence: 99%

Comparative Assessment of Two Global Sensitivity Approaches Considering Model and Parameter Uncertainty

Dai,

Liu,

Guadagnini

et al. 2024

Water Resources Research

Self Cite

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Global Sensitivity Analysis (GSA) is key to assisting appraisal of the behavior of hydrological systems through model diagnosis considering multiple sources of uncertainty. Uncertainty sources typically comprise incomplete knowledge in (a) conceptual and mathematical formulation of models and (b) parameters embedded in the models. In this context, there is the need for detailed investigations aimed at a robust quantification of the importance of model and parameter uncertainties in a rigorous multi‐model context. This study aims at evaluating and comparing two modern multi‐model GSA methodologies. These are the first GSA approaches embedding both model and parameter uncertainty sources and encompass the variance‐based framework based on Sobol indices (as derived by Dai & Ye, 2015, https://doi.org/10.1016/j.jhydrol.2015.06.034) and the moment‐based approach upon which the formulation of the multi‐model AMA indices (as derived by Dell'Oca et al., 2020, https://doi.org/10.1029/2019wr025754) is based. We provide an assessment of various aspects of sensitivity upon considering a joint analysis of these two approaches in a multi‐model context. Our work relies on well‐established scenarios that comprise (a) a synthetic setting related to reactive transport across a groundwater system and (b) an experimentally‐based study considering heavy metal sorption onto a soil. Our study documents that the joint use of these GSA approaches can provide different while complementary information to assess mutual consistency of approaches and to enrich the information content provided by GSA under model and parameter uncertainty. While being related to groundwater settings, our results can be considered as reference for future GSA studies coping with model and parameter uncertainty.

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Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

Cited by 8 publications

References 65 publications

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

Innovative Assessment of Mun River Flow Components through ANN and Isotopic End-Member Mixing Analysis

Comparative Assessment of Two Global Sensitivity Approaches Considering Model and Parameter Uncertainty

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