Geodesic
Numerical modelling of microscopic dynamics of in-situ leaching
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 726-733.

Voir la notice de l'article provenant de la source Math-Net.Ru

Dissolution of the solid ground by an acid is one of subprocesses of in-situ leaching. The objective of this paper is the numerical simulation of these processes at the porous level. The case of two spatial variables is considered. We admit the fluid dynamics to be described by stationary Stokes equations, while acid concentration is described by the convection-diffusion equation. The problem is completed with boundary and initial conditions. For the numerical simulation of the problem, the method of finite differences on staggered grids is used. At each time step, the fluid velocity components are computed iteratively by the successive over-relaxation method. The fluid pressure, the concentration of acid and the position of the free boundary are determined using an explicit scheme. To define the boundary condition for the acid concentration at the free boundary, a system of nonlinear equations is solved by the iterative Newton method. Results of the numerical experiments are presented and discussed. In particular, the results obtained can help in analyzing the motion of the free solid/liquid interface and the mechanisms of physical and chemical processes there.
Keywords: leaching, free boundary, microscopic model, numerical solution. 
@article{SEMR_2016_13_a97,
     author = {A. S. Zhumali and G. V. Reshetova},
     title = {Numerical modelling of microscopic dynamics of in-situ leaching},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {726--733},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a97/}
}
TY  - JOUR
AU  - A. S. Zhumali
AU  - G. V. Reshetova
TI  - Numerical modelling of microscopic dynamics of in-situ leaching
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2016
SP  - 726
EP  - 733
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2016_13_a97/
LA  - en
ID  - SEMR_2016_13_a97
ER  - 
%0 Journal Article
%A A. S. Zhumali
%A G. V. Reshetova
%T Numerical modelling of microscopic dynamics of in-situ leaching
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2016
%P 726-733
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2016_13_a97/
%G en
%F SEMR_2016_13_a97
A. S. Zhumali; G. V. Reshetova. Numerical modelling of microscopic dynamics of in-situ leaching. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 726-733. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a97/

[1] R. Burridge, G. B. Keller, “Poroelasticity equations derived from microstructure”, Journal of Acoustic Society of America, 1981, 1140–1146 | DOI | Zbl

[2] A. Meirmanov, Mathematical models for poroelastic flows, AtlantisPress, Paris, 2013 | MR

[3] L. V. Ovsyannikov, Introduction to continuum mechanics, Novosibirsk State University, Novosibirsk, 1977

[4] N. L. Glinka, General chemistry, Integral-press, M., 2005