Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1998-2016
Voir la notice de l'article provenant de la source Math-Net.Ru
Numerical implementations of a new fast-converging iterative method with boundary condition splitting are constructed for solving the Dirichlet initial-boundary value problem for the nonstationary Stokes system in the gap between two coaxial cylinders. The problem is assumed to be axially symmetric and periodic along the cylinders. The construction is based on finite-difference approximations in time and bilinear finite-element approximations in a cylindrical coordinate system. A numerical study has revealed that the iterative methods constructed have fairly high convergence rates that do not degrade with decreasing viscosity (the error is reduced by approximately 7 times per iteration step). Moreover, the methods are second-order accurate with respect to the mesh size in the max norm for both velocity and pressure.
@article{ZVMMF_2010_50_11_a12,
author = {M. B. Soloviev},
title = {Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1998--2016},
publisher = {mathdoc},
volume = {50},
number = {11},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a12/}
}
TY - JOUR AU - M. B. Soloviev TI - Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2010 SP - 1998 EP - 2016 VL - 50 IS - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a12/ LA - ru ID - ZVMMF_2010_50_11_a12 ER -
%0 Journal Article %A M. B. Soloviev %T Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2010 %P 1998-2016 %V 50 %N 11 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a12/ %G ru %F ZVMMF_2010_50_11_a12
M. B. Soloviev. Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1998-2016. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a12/