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On the effective diffusion in the Sierpiński carpet

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Abstract

In this work, we use the method of volume averaging to upscale the pore-scale diffusion equation on the Sierpiński carpet. Based on the isotropy condition in the fractal structure and the fact that the ratio of length scales in the Sierpiński carpet is constant, a general expression for the effective diffusion coefficient regarding the iteration of the fractal structure is suggested. Additionally, a general expression is recommended when such a ratio is not constant. The comparison between the direct numerical simulations and the results obtained from the upscaled model suggests that using a simplified expression for the effective diffusion coefficient is an attractive option when simulating large-scale fractal systems.

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Authors and Affiliations

  1. Facultad de Ciencias de la Tierra, Universidad Autonoma de Nuevo Leon, Ex Hacienda de Guadalupe, 67700, Linares, Mexico

    C. G. Aguilar-Madera & J. A. Briones-Carrillo

  2. CONACYT-Centro de Ingeniería y Desarrollo Industrial, Ciudad del Carmen, 24150, Campeche, Mexico

    E. C. Herrera-Hernández

  3. Área de Ingeniería en Recursos Energéticos, Universidad Autónoma Metropolitana Iztapalapa, Ciudad de México, 09340, Mexico

    G. Espinosa-Paredes

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  1. C. G. Aguilar-Madera
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  2. E. C. Herrera-Hernández
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  3. G. Espinosa-Paredes
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  4. J. A. Briones-Carrillo
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Correspondence to E. C. Herrera-Hernández.

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Aguilar-Madera, C.G., Herrera-Hernández, E.C., Espinosa-Paredes, G. et al. On the effective diffusion in the Sierpiński carpet. Comput Geosci 25, 467–473 (2021). https://doi.org/10.1007/s10596-020-10016-z

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