Identification of aquifer point sources and partial boundary condition from partial overspecified boundary data

Hariga, Najla Tlatli; Bouhlila, Rachida; Abda, Amel Ben

doi:10.1016/j.crte.2007.11.006

Cited by 14 publications

(16 citation statements)

References 8 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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“…Within the framework of groundwater flow scenario, reciprocity between two interference pumping tests was analyzed by Bruggeman [9] for Darcian flows in an unbounded, heterogeneous porous medium. Hariga and al [13][14][15]7] have also applied the reciprocity principle in groundwater flows by using sources and boundary conditions as forcing terms and the resulting head field as a consequence. In this research, the reciprocity principle is applied to the transport equation to recover the features of the pollutant point sources in aquifers.…”

Section: Introductionmentioning

confidence: 99%

Identification of aquifer pollution’s point sources with the Reciprocity Principle

Hariga¹,

Bouhlila²

2021

Preprint

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The principle of reciprocity, called Maxwell-Bettitheorem, initially used in mechanics in an elastic structure, establishes a relation of equality between two distinct strains under different loads. In this paper, we extend and apply this principle to flow and solute transport equations in porous media, in order to perform the pollution sources identification in aquifers. We developed general 2D expressions of the reciprocity principle for transient transport problems. This model leads to a linear equations set, with point sources coordinates, concentrations and associated water fluxes as unknowns. The proposed model is then applied to the Rocky Mountain Arsenal aquifer, where polluted water is injected into a well in the domain. The proposed inverse technique successfully recovered the position and the pollutant concentration in addition to the associated water flux. Moreover, we developed and implemented the inverse method for different knowledge levels of the degrees of the aquifer contamination, i.e. more or less data available in the field. Multiple pollution point sources and noisy data situations are also developed and tested with high efficiency. The proposed method would be easy and useful to be implemented in the modeling software now widely used by researchers and groundwater managers. It can thus be applied in real case studies, to help authorities and regulators to efficiently identify the polluters and the contamination process i.e. its location, onset, duration and the associated mass and water fluxes.

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“…The data completion problem was studied by Hariga et al 14,15 and Mansouri et al 16 for the diffusion equation and by CimetiÈre et al 17 and Escriva et al 18 for the identification of cracks. Hamdi 19 has used the same method in order to identify pollution sources in the case of the stationary two‐dimensional advection‐diffusion‐reaction equation.…”

Section: Introductionmentioning

confidence: 99%

Data completion problem for the advection‐diffusion equation with aquifer point sources

Hassin

Hariga

Khayat

2020

Math Methods in App Sciences

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We consider the inverse problem of recovering the missing flux and concentration on some part of a boundary of an aquifer using overspecified measurements available on some accessible part. The aquifer is under the action of point-forces located inside the domain and governed by the advection-diffusion equation. The method used is based on a fictitious domain decomposition. Numerical tests are done attesting the performance of the identification process.

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Identification of aquifer point sources and partial boundary condition from partial overspecified boundary data

Cited by 14 publications

References 8 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 aquifer pollution’s point sources with the Reciprocity Principle

Data completion problem for the advection‐diffusion equation with aquifer point sources

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