Geodesic
Solving Stokes equation in three-dimensional geometry using finite-difference method
Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 67-80

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Recent outstanding developments in three-dimensional structure investigation methods for porous and composite materials (e.g., microtomography, confocal microscopy, FIB-SEM) and improvements in computing resources made the simulation of various physical processes directly in three-dimensional geometry of such materials (pore-scale modeling) possible. These simulations can assess the effective properties of the material under study or improve our understanding of the governing physical processes in more detail. In this contribution we solve Stokes equation using the computational schemes of second and fourth accuracy order directly in the three-dimensional domain, which has the same geometry as microstructure of the investigated sample (obtained using X-ray microtomography scanning). Computed permeability value for the sandstone sample was found to be in a good agreement with laboratory measurements.
Keywords: porous media, permeability, X-ray microtomography, effective properties, pore-scale modeling. 
@article{MM_2015_27_6_a4,
     author = {R. V. Vasilyev and K. M. Gerke and M. V. Karsanina and D. V. Korost},
     title = {Solving {Stokes} equation in three-dimensional geometry using finite-difference method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {67--80},
     publisher = {mathdoc},
     volume = {27},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_6_a4/}
}
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R. V. Vasilyev; K. M. Gerke; M. V. Karsanina; D. V. Korost. Solving Stokes equation in three-dimensional geometry using finite-difference method. Matematičeskoe modelirovanie, Tome 27 (2015) no. 6, pp. 67-80. http://geodesic.mathdoc.fr/item/MM_2015_27_6_a4/