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. © 2020, Springer Nature Switzerland AG.

authors

• Aguilar-Madera C.G.
• Espinosa-Paredes G.
• Herrera Hernández Erik César

publication date

• 2021-01-01

published in

• Computational Geosciences  Journal

keywords

• Effective diffusion coefficient; Fractals; Solute transport; Upscaling; Volume averaging method diffusion; flow modeling; numerical model; porous medium; solute transport; upscaling

Digital Object Identifier (DOI)

• 10.1007/s10596-020-10016-z

PubMed ID

start page

• 467

end page

• 473

volume

• 25

issue

• 1