Geodesic
Numerical solution to initial value problems for the Navier--Stokes equations in closed regions based on splitting method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 321-332.

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

On the basis of splitting method with respect to physical processes, a numerical method is proposed for solving initial value problems for the Navier– Stokes equations written in the terms of “eddy – current” variables. For the solution to the implicit difference systems a modified method of “two-field” (separate) calculation of the stream function and vorticite is suggested. For the first time in solving the Poisson equation for stream function two boundary conditions are simultaneously used on the boundaries ($\psi=\partial\psi/\partial n=0)$. A stability analysis in the linear approach is made. Some test numerical examples are given. 
@article{SJVM_1999_2_4_a2,
     author = {A. F. Voevodin and T. V. Yushkova},
     title = {Numerical solution to initial value problems for the {Navier--Stokes} equations in closed regions based on splitting method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {321--332},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a2/}
}
TY  - JOUR
AU  - A. F. Voevodin
AU  - T. V. Yushkova
TI  - Numerical solution to initial value problems for the Navier--Stokes equations in closed regions based on splitting method
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1999
SP  - 321
EP  - 332
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a2/
LA  - ru
ID  - SJVM_1999_2_4_a2
ER  - 
%0 Journal Article
%A A. F. Voevodin
%A T. V. Yushkova
%T Numerical solution to initial value problems for the Navier--Stokes equations in closed regions based on splitting method
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1999
%P 321-332
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a2/
%G ru
%F SJVM_1999_2_4_a2
A. F. Voevodin; T. V. Yushkova. Numerical solution to initial value problems for the Navier--Stokes equations in closed regions based on splitting method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 321-332. http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a2/

[1] Rouch P., Vychislitelnaya gidrodinamika, Mir, M., 1975

[2] Tarunin E. L., Vychislitelnyi eksperiment v zadachakh svobodnoi konvektsii, Izd-vo Irkutskogo universiteta, Irkutsk, 1990

[3] Marchuk G. I., Dymnikov V. P., Zalesnyi V. B., Lykosov V. N., Galin V. Ya., Matematicheskoe modelirovanie obschei tsirkulyatsii atmosfery i okeana, Gidrometeoizdat, L., 1984

[4] Sinyaev V. N., “Ob odnom printsipe postroeniya konechno-raznostnykh skhem, osnovannykh na zakonakh sokhraneniya polnoi energii”, Chisl. metody MSS, 5:2 (1974), 108–115

[5] Marchuk G. I., Metody rasschepleniya, Nauka, M., 1988 | MR

[6] Yanenko N. N., Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka. Sib. otd-nie, Novosibirsk, 1967 | MR

[7] Voevodin A. F., “O korrektnosti metoda progonki dlya raznostnykh uravnenii”, Chisl. metody MSS, 3:5 (1972), 17–26 | MR

[8] Voevodin A. F., Shugrin S. M., Chislennye metody resheniya odnomernykh sistem, Nauka, Novosibirsk, 1981

[9] Voevodin A. F., “Ustoichivost i realizatsiya neyavnykh skhem dlya uravnenii Stoksa”, Zhurn. vychisl. matem. i mat. fiziki, 33:1 (1993), 119–130 | MR | Zbl

[10] Fadeev D. K., Fadeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M., L., 1963 | MR

[11] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[12] Voevodin A. F., “Ustoichivost konechno-raznostnykh granichnykh uslovii dlya vikhrya na tverdoi stenke”, Zhurn. vychisl. matem. i mat. fiziki, 38:5 (1998), 855–859 | MR | Zbl