Abstract
A numerical scheme of higher-order approximation in space for the single-phase multicomponent flow in porous media is presented. The mathematical model consists of Darcy velocity, transport equations for components of a mixture, pressure equation and associated relations for physical quantities such as viscosity or density. The discrete problem is obtained via discontinuous Galerkin method for the discretization of transport equations with the combination of mixed-hybrid finite element method for the discretization of Darcy velocity and pressure equation both using higher-order approximation. Subsequent problem is solved with the fully mass-conservative iterative IMPEC method. Numerical experiments of 2D flow are carried out.
The work was supported by the Czech Science Foundation project no. 21-09093S Multiphase flow, transport, and structural changes related to water freezing and thawing in the subsurface, by the Ministry of Education, Youth and Sports of the Czech Republic under the OP RDE grant number CZ.02.1.01/0.0/0.0/16_019/0000778 Centre for Advanced Applied Sciences, and by the Student Grant Agency of the Czech Technical University in Prague, grant no. SGS20/184/OHK4/3T/14.
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Gális, P., Mikyška, J. (2021). Mathematical Modeling of the Single-Phase Multicomponent Flow in Porous Media. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12747. Springer, Cham. https://doi.org/10.1007/978-3-030-77980-1_16
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