Article information

2003 , Volume 8, Special issue, p.44-66

Shaidurov V.V., Rude U., Kireev I.V.

Completely splitting method for the Navier-Stokes problem

We consider two-dimensional time-dependent Navier-Stokes equations in a rectangular domain and study the method of full splitting [3-4]. On the physical level, this problem is splitted into two processes: convection-diffusion and work of pressure. The convection-diffusion step is further splitted in two geometric directions. To implement the finite element method, we use the approach with uniform square grids which are staggered relative to one another. This allows the Ladyzhenskaya-Babushka-Brezzi condition for stability of pressure to be fulfilled without usual diminishing the number of degrees of freedom for pressure relative to that for velocities. For pressure we take piecewise constant finite elements. As for velocities, we use piecewise bilinear elements.

Classificator Msc2000:
*65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65N55 Multigrid methods; domain decomposition

Keywords: fractional step, discretization, error, numerical experiment

Author(s):
Shaidurov Vladimir Victorovich
Dr. , Correspondent member of RAS, Professor
Position: Head of Research
Office: Federal Research Center Krasnoyarsk Science Center of the Siberian Branch of the Russian Academy of Science
Address: 660036, Russia, Krasnoyarsk 36, Akademgorodok 50, building 44
Phone Office: (391) 243 27 56
E-mail: shaidurov04@gmail.com
SPIN-code: 7075-6423

Rude U.
Office: University of Erlangen -- Nurnberg
Address: Germany, Erlangen, Krasnoyarsk 36, Akademgorodok 50, building 44

Kireev Igor' Valerievich
PhD. , Associate Professor
Position: Senior Research Scientist
Office: Institute of Computational Simulation of SB RAS
Address: 660036, Russia, Krasnoyarsk, Akademgorodok str, 50, build 44
Phone Office: (391) 249 47 39
E-mail: kiv@icm.krasn.ru
SPIN-code: 3804-0901


Bibliography link:
Shaidurov V.V., Rude U., Kireev I.V. Completely splitting method for the Navier-Stokes problem // Computational technologies. 2003. V. 8. The Special Issue: Proceedings of the Russian-German Advanced Research Workshop on Computer Science and High Performance Computing, Part 1. P. 44-66
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