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

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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. 
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     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},
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     volume = {2},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a2/}
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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/