Geodesic
Triada technique for numerically solving 3d problems of impurity transport by underground waters
Matematičeskoe modelirovanie, Tome 13 (2001) no. 2, pp. 78-85.

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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. 
@article{MM_2001_13_2_a8,
     author = {O. M. Velichko and V. V. Gorev and I. V. Gorev and Yu. N. Deryugin and D. K. Zc.lenckii and A. I. Panov and A. A. Savelyev and V. V. Selin and A. G. Subbotin and B. P. Tikhomirov and A. N. Chekalin},
     title = {Triada technique for numerically solving 3d problems of impurity transport by underground waters},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {78--85},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2001_13_2_a8/}
}
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%A A. A. Savelyev
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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. Matematičeskoe modelirovanie, Tome 13 (2001) no. 2, pp. 78-85. http://geodesic.mathdoc.fr/item/MM_2001_13_2_a8/