Definition and interests of reciprocity and reciprocity gap principles for groundwater flow problems

Hariga, Nejla T.; Abda, Amel Ben; Bouhlila, Rachida; Dreuzy, Jean‐Raynald de

doi:10.1016/j.advwatres.2010.04.015

Cited by 12 publications

(8 citation statements)

References 12 publications

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“…Investigating the adaptability of the method to more general flows with source terms would also be of great importance for applications. Transient problems could also be examined, like in [41] or more recently in [43,44].…”

Section: Final Comments and Discussionmentioning

confidence: 99%

An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry

Nœtinger¹

2013

Multiscale Model. Simul.

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Most natural or synthetic materials possess a multiscale structure that can have a major impact on large scale transport properties. In particular, the effective conductivity associated to thermal, electrical, or hydraulic transfers depends on its microstructure. In practice, it can be determined using some analytical formula working in limited configurations. More generally, it can be obtained numerically by solving a closure problem that maps the microscale to the macroscale. The resulting effective coefficient depends on the local properties as well on the geometry of the inclusions. The goal of this work is to give explicit formulae relating the sensitivity of large scale effective conductivity with respect to local microscale parameters directly using the solution of the mapping problem. The proposed formula is direct and does not imply solving any additional adjoint problem. It needs only evaluation of volume or surface integrals involving the mapping problem solution. The associated numerical cost is negligible once the mapping closure problem has been solved. Practical applications can be found for solving inverse problems, for optimizing a microstructure shape, fulfilling an imposed constraint like maximizing or minimizing the overall conductivity.

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Section: Final Comments and Discussionmentioning

confidence: 99%

An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry

Nœtinger¹

2013

Multiscale Model. Simul.

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“…Drawdowns governed by (1) follow the so-called Lorentz reciprocity (Lorentz, 1896). This implies that a signal w b a ðtÞ=Q a monitored in a well located in x b while withdrawing the flow rate Q a in x a coincides with the signal w a b ðtÞ=Q b observed in x a while pumping Q b in x b (Bruggeman, 1972;Raghavan, 2009;Hariga et al, 2010;Delay et al, 2011Delay et al, , 2012. In the case of a model simulation of hydraulic tomography performed through (1) by considering a set of wells, each of them being pumped sequentially while observing at the others, vectors w…”

Section: Theoretical Backgroundmentioning

confidence: 98%

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

Marinoni

Delay

Ackerer

et al. 2016

Journal of Hydrology

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“…In previous papers, authors have exploited this splitting but without recovering the wells' positions [22]. Whereas in [23], they present only the reciprocity and the reciprocity gap principles for groundwater problems with complete boundary data.…”

Section: Introductionmentioning

confidence: 96%

“…This principle gives rise to solving a linear system with matrix easy to compute, but we have to know the complete data on the whole domain's boundary. This method has been used for electrostatic dipoles identification [14], for pollutant sources identification [15] with the heat equation, for inclusion identification [5], for hydraulic parameter recovering [23] and others.…”

Section: Introductionmentioning

confidence: 99%

Recovering data in groundwater: boundary conditions and Wells’ positions and fluxes

Tlatli-Hariga

Bouhlila²,

Abda

2011

Comput Geosci

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In this paper, we present an original methodology for recovering boundary conditions and hydraulic parameters in an aquifer domain. Boundary data are identified from the knowledge of over-specified boundary data on another part of the boundary. Then parameters, here wells' positions and fluxes, are recovered by the use of the reciprocity principle (Andrieux and Ben Abda, Mech Res Commun 20:415-420, 1993; Andrieux and Ben Abda, Inverse Probl 12:553-564, 1996). The boundary recovering method is based on the minimization of an energy-like error functional (Andrieux et al., Inverse Probl 22:115-133;Baranger and Andrieux, 2010).

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Definition and interests of reciprocity and reciprocity gap principles for groundwater flow problems

Cited by 12 publications

References 12 publications

An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry

An Explicit Formula for Computing the Sensitivity of the Effective Conductivity of Heterogeneous Composite Materials to Local Inclusion Transport Properties and Geometry

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

Recovering data in groundwater: boundary conditions and Wells’ positions and fluxes

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