Geodesic
Precise two-dimensional models for shallow water basins
Matematičeskoe modelirovanie, Tome 15 (2003) no. 10, pp. 17-34.

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

2D hydrodynamic model for the shallow water sea was built. In provides solution obtaining which satisfy physics conservation laws, under the conditions ratio length to depth $10^4\dots10^5$, depth overfall to $10^2$, level variation from $-100\%$ till some hundred percents of depth. Under model equations building (including grid equations), we kept meeting demands to save conditions of initial equation system. The optimization algorithm for typical guality grid functionals of grid building for real water basins under conditions of complicated boundary was worked out. The water flows modeling results for the Azov Sea are presented. 
@article{MM_2003_15_10_a1,
     author = {V. S. Vasil'ev and A. I. Sukhinov},
     title = {Precise two-dimensional models for shallow water basins},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {17--34},
     publisher = {mathdoc},
     volume = {15},
     number = {10},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_10_a1/}
}
TY  - JOUR
AU  - V. S. Vasil'ev
AU  - A. I. Sukhinov
TI  - Precise two-dimensional models for shallow water basins
JO  - Matematičeskoe modelirovanie
PY  - 2003
SP  - 17
EP  - 34
VL  - 15
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2003_15_10_a1/
LA  - ru
ID  - MM_2003_15_10_a1
ER  - 
%0 Journal Article
%A V. S. Vasil'ev
%A A. I. Sukhinov
%T Precise two-dimensional models for shallow water basins
%J Matematičeskoe modelirovanie
%D 2003
%P 17-34
%V 15
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2003_15_10_a1/
%G ru
%F MM_2003_15_10_a1
V. S. Vasil'ev; A. I. Sukhinov. Precise two-dimensional models for shallow water basins. Matematičeskoe modelirovanie, Tome 15 (2003) no. 10, pp. 17-34. http://geodesic.mathdoc.fr/item/MM_2003_15_10_a1/

[1] Fletcher K., Vychislitelnye metody v dinamike zhidkostei, T. 1, Mir, M., 1991, 50 pp.; Т. 2, 552 с.

[2] Filatov N. N., Gidrodinamika ozer, Nauka, Spb., 1991 | Zbl

[3] Agoshkov V. I., Saleri F., “Recent Developments in the Numerical Simulation of Shallow Water Equations. III-Boundary Conditions and Finite Element Approximations in the River Flow Calculations”, Matem. modelirovanie, 8:9 (1996), 3–24 | MR | Zbl

[4] Voltsinger N. E., Klevannyi K. A., Pelinovskii E. N., Dlinnovolnovaya dinamika pribrezhnoi zony, Gidrometeoizdat, L., 1989

[5] Surzhikov S. T., “Vychislitelnaya model izluchayuschego termika v nestatsionarnykh dinamicheskikh peremennykh”, Matem. modelirovanie, 7:8 (1995), 3–24 | MR

[6] Roberts D. V., Forester K. K., “Metod chislennogo resheniya parabolicheskoi zadachi o techeniyakh v kanalakh proizvolnogo poperechnogo secheniya”, Raketnaya tekhnika i kosmonavtika, 17:1 (1979), 37–46

[7] Krivtsov V. M., “Ob odnoi skheme priblizhennoi faktorizatsii dlya rascheta techenii gaza v kanalakh”, Zh. vychisl. matem. i matem. fiziki, 34:11 (1994), 1680–1692 | MR | Zbl

[8] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[9] Rkhi S. M., Chou U. L., “Chislennyi raschet obtekaniya profilya s otryvom u zadnei kromki”, Aerodinamicheskaya tekhnika, 2:7 (1984), 33–43

[10] Samarskii A. A., Popov Yu. L., Raznostnye metody resheniya zadach gazovoi dinamiki, Ucheb. posobie: Dlya Vuzov. 3-e izd., dop., Nauka, Fizmatlit, M., 1992 | MR

[11] Koretskii V. V., Lyubimov D. A., “Modifitsirovannyi metod priblizhennoi faktorizatsii dlya rascheta potentsialnykh prostranstvennykh techenii v kanalakh”, Zh. vychisl. matem. i matem. fiziki, 30:10 (1990), 1553–1570 | MR

[12] Samarskii A. A., Teoriya raznostnykh skhem, 3-e izd., ispr., Nauka, M., 1989 | MR

[13] Makhanov S. S., Semenov A. Yu., “Dvumernyi neotritsatelnyi algoritm rascheta sechenii zhidkosti v otkrytykh ruslakh”, Zh. vychisl. matem. i matem. fiziki, 36:4 (1996), 97–105 | MR | Zbl

[14] Surkov F. A., Bronfman A. M., Cherkus E. A. i dr., “Modelirovanie abioticheskikh faktorov ekosistemy Azovskogo morya”, Izvestiya Severo-kavkazkogo nauchnogo tsentra vysshei shkoly. Estestvennye nauki, 1977, no. 2, 21–49

[15] Krukier L. A., “Matematicheskoe modelirovanie gidrodinamiki Azovskogo morya pri realizatsii proektov rekonstruktsii ego sistemy”, Matem. modelirovanie, 3:9 (1991), 3–20 | MR