Geodesic
Numerical modeling of chemical interaction between a fluid and rocks
Numerical methods and programming, Tome 20 (2019) no. 4, pp. 457-470.

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A new algorithm for the numerical modeling of chemical fluid-rock interaction at the pore scale is proposed. The algorithm is based on splitting the problem into physical processes. It is assumed that the fluid rate is low and the fluid flow is stabilized almost instantly in the case of small changes in the pore space geometry. In the pore space, thus, the fluid flow is modeled using the Stokes equation for steady flows. The chemical reactant transport is described by the convection-diffusion equation with Robin boundary conditions at the fluid-rock interface. The pore space boundary changes with time and is implicitly given by a level-set function. We use finite-difference schemes with immersed boundary conditions to solve the Stokes and convection-diffusion equations
Keywords: level-set function method, immersed boundary method, chemical dissolution. 
@article{VMP_2019_20_4_a9,
     author = {K. A. Gadylshina and T. S. Khachkova and V. V. Lisitsa},
     title = {Numerical modeling of chemical interaction between a fluid and rocks},
     journal = {Numerical methods and programming},
     pages = {457--470},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a9/}
}
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K. A. Gadylshina; T. S. Khachkova; V. V. Lisitsa. Numerical modeling of chemical interaction between a fluid and rocks. Numerical methods and programming, Tome 20 (2019) no. 4, pp. 457-470. http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a9/