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International Conference on Environmental Mathematical Modeling and Numerical Analysis (Rostov-on-Don)
Triada technique for numerically solving 3d problems of impurity transport by underground waters
O. M. Velichkoa, V. V. Goreva, I. V. Goreva, Yu. N. Deryugina, D. K. Zc.lenckiia, A. I. Panova, A. A. Savelyevb, V. V. Selina, A. G. Subbotina, B. P. Tikhomirova, A. N. Chekalinb a Federal State Unitary Enterprise 'Russian Federal Nuclear Center — All-Russian Research Institute of Experimental Physics'
b Kazan State University
Abstract:
The paper considers the 3D problem of transport and distribution of water soluble
impurities caused by local sources in underground waters. Model equations include the
filter equation and the impurity mass transport equation. To solve numerically problems,
an irregular grid consisting of parallelepipeds with oblique-angled quadrangle in its
foundation is constructed. The finite differences method is used for digitizing differential
equations. When approximating the filter equation, a real operaror method is used: a difference analog grad operator is related to grid nodes and a conjugate div operator is specified in centers of this grid cells. To solve the equation of water soluble pollutant
distribution numerically, the principle of splitting by physical processes is used. The
whole process is split into four processes: impurity transport; taking account of sorption;
diffusion with taking account of dispersion and taking account of chemical reactions in a pore volume and at the fluid-matrix interface. Each of these processes is calculated using
an explicit method. To solve the transport equation, both the method of particles and
the difference method are used. The paper gives results of several test computations.
Received: 29.11.1999
Citation:
O. M. Velichko, V. V. Gorev, I. V. Gorev, Yu. N. Deryugin, D. K. Zc.lenckii, A. I. Panov, A. A. Savelyev, V. V. Selin, A. G. Subbotin, B. P. Tikhomirov, A. N. Chekalin, “Triada technique for numerically solving 3d problems of impurity transport by underground waters”, Matem. Mod., 13:2 (2001), 78–85
Linking options:
https://www.mathnet.ru/eng/mm680 https://www.mathnet.ru/eng/mm/v13/i2/p78
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