On Topological Optimization and Pollution in Porous Media

Faye, Ibrahima; Sy, Alassane; Seck, Diaraf

doi:10.1007/978-3-540-74339-2_14

Cited by 3 publications

(6 citation statements)

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“…This approach consists in studying the variation of the functional according to the variation of the domain. Many works have improved this method, for instance, one can cite References 4,10‐17.…”

Section: Topological Optimizationmentioning

confidence: 99%

“…Topological optimization is proven to be valuable for studying pollution problems. 3,4 Numerical results will be presented in the case of Neumann and Dirichlet case around the holes. In this part, we will generalize the descent optimization algorithms used in Reference 5 by extending them to three dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…In the following, we will present the model of pollution in a porous medium in the non‐permanent case studied in Reference 3 by considering the concentration of the pollutants. Note that the permanent case has been studied in Reference 4. After that, we make some assumptions on the conductivity and the density in order to improve the model of pollutants transfer in porous media.…”

Section: Introductionmentioning

confidence: 99%

“…It is one of the branches of optimization methods like shape optimization. Topological optimization is proven to be valuable for studying pollution problems 3,4 . Numerical results will be presented in the case of Neumann and Dirichlet case around the holes.…”

Section: Introductionmentioning

confidence: 99%

“…It is proved by Faye et al in Reference 4 that pollutants transfer under realistic assumptions can be modeled by the following Equation (1):…”

Section: Introduction and Modeling Of Pollution In Porous Mediamentioning

confidence: 99%

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Topological optimization applied to a variable density and conductivity model of pollution in porous media

Dia

Faye

2022

Engineering Reports

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This article deals with modeling and numerical study of pollutants transfer in porous media by topological optimization. Indeed we perform the modeling of pollution in porous media in non‐permanent cases by assuming the variability or not of some parameters such as the conductivity and the density. The model of pollutants transfer obtained in the case when the conductivity and the density are constant is similar to meadows of few coefficients to the one obtained by varying (with respect to the space) only the conductivity. By taking into account the space variability of density, conductivity, and diffusion under some assumptions we obtain a more realistic model of pollutants transfer. Topological optimization applied to these models allows reaching numerically the optimal design of a least squared functional. In fact, topological derivatives are used as descent direction and permit to creation of circular or cylindrical holes in order to decrease the considered cost function. Numerical results obtained are presented for Neumann and Dirichlet conditions on the boundary of the holes for 2 and 3 dimensions in nonpermanent cases of pollutants transfer.

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Section: Topological Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is proved by Faye et al in Reference 4 that pollutants transfer under realistic assumptions can be modeled by the following Equation (1):…”

Section: Introduction and Modeling Of Pollution In Porous Mediamentioning

confidence: 99%