@article{fdi:010075163,
  title = {{A} 3-{D} semianalytical solution for density-driven flow in porous media},
  author = {{S}hao, {Q}. and {F}ahs, {M}. and {H}oteit, {H}. and {C}arrera, {J}. and {A}ckerer, {P}. and {Y}ounes, {A}nis},
  editor = {},
  language = {{ENG}},
  abstract = {{E}xisting analytical and semianalytical solutions for density-driven flow ({DDF}) in porous media are limited to 2-{D} domains. {I}n this work, we develop a semianalytical solution using the {F}ourier {G}alerkin method to describe {DDF} induced by salinity gradients in a 3-{D} porous enclosure. {T}he solution is constructed by deriving the vector potential form of the governing equations and changing variables to obtain periodic boundary conditions. {S}olving the 3-{D} spectral system of equations can be computationally challenging. {T}o alleviate computations, we develop an efficient approach, based on reducing the number of primary unknowns and simplifying the nonlinear terms, which allows us to simplify and solve the problem using only salt concentration as primary unknown. {T}est cases dealing with different {R}ayleigh numbers are solved to analyze the solution and gain physical insight into 3-{D} {DDF} processes. {I}n fact, the solution displays a 3-{D} convective cell (actually a vortex) that resembles the quarter of a torus, which would not be possible in 2-{D}. {R}esults also show that 3-{D} effects become more important at high {R}ayleigh number. {W}e compare the semianalytical solution to research ({T}ransport of {R}adio{AC}tive {E}lements in {S}ubsurface) and industrial ({COMSOL} {M}ultiphysics ({R})) codes. {W}e show cases (high {R}aleigh number) where the numerical solution suffers from numerical artifacts, which highlight the worthiness of our semianalytical solution for code verification and benchmarking. {I}n this context, we propose quantitative indicators based on several metrics characterizing the fluid flow and mass transfer processes and we provide open access to the source code of the semianalytical solution and to the corresponding numerical models.},
  keywords = {density-driven flow ; 3-{D} analytical solution ; {R}ayleigh number ; {F}ourier series solution ; benchmarking ; {COMSOL} {M}ultiphysics},
  booktitle = {},
  journal = {{W}ater {R}esources {R}esearch},
  volume = {54},
  numero = {12},
  pages = {10094--10116},
  ISSN = {0043-1397},
  year = {2018},
  DOI = {10.1029/2018wr023583},
  URL = {https://www.documentation.ird.fr/hor/fdi:010075163},
}