Geodesic
Numerical simulations for a~two-scale model in a~porous medium
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 37-46

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This paper deals with numerical simulations of a system of diffusion-reaction equations in the context of a porous medium. We start by giving a microscopic model and then an upscaled version (i.e., homogenized or continuum model) of it from previous works of the author. Since with the help of homogenization we obtain a macroscopic description of a model which is microscopically heterogeneous, via these numerical simulations we show that this macroscopic description approximates the microscopic model, which contains heterogeneities and oscillating terms at the pore scale, such as diffusion coefficients. 
@article{SJVM_2017_20_1_a3,
     author = {H. S. Mahato},
     title = {Numerical simulations for a~two-scale model in a~porous medium},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {37--46},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a3/}
}
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H. S. Mahato. Numerical simulations for a~two-scale model in a~porous medium. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 1, pp. 37-46. http://geodesic.mathdoc.fr/item/SJVM_2017_20_1_a3/