Non-uniqueness of a stationary viscous flow in the square lid-driven cavity
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 130-143
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The article considers the classical benchmark problem in computational hydromechanics regarding a viscous incompressible flow in a square lid-driven cavity. An effective algorithm for solving a Navier–Stokes system of equations is proposed, that allows to construct stationary solutions on very detailed grids (up to $10^7$ grid points) for large (up to $10^5$) Reynolds numbers. Non-uniqueness of the stationary solution at large Reynolds numbers is shown. Special attention is given to the analysis of the main branch and one of the additional branches of the solution, appearing at relatively small $(\approx14000)$ Reynolds numbers.
Keywords:
Navier–Stokes equation, stationary solution, lid-driven cavity, multigrid, non-uniqueness, stability.
@article{UZKU_2009_151_3_a10,
author = {A. G. Egorov and A. N. Nuriev},
title = {Non-uniqueness of a~stationary viscous flow in the square lid-driven cavity},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {130--143},
publisher = {mathdoc},
volume = {151},
number = {3},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a10/}
}
TY - JOUR AU - A. G. Egorov AU - A. N. Nuriev TI - Non-uniqueness of a stationary viscous flow in the square lid-driven cavity JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2009 SP - 130 EP - 143 VL - 151 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a10/ LA - ru ID - UZKU_2009_151_3_a10 ER -
%0 Journal Article %A A. G. Egorov %A A. N. Nuriev %T Non-uniqueness of a stationary viscous flow in the square lid-driven cavity %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2009 %P 130-143 %V 151 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a10/ %G ru %F UZKU_2009_151_3_a10
A. G. Egorov; A. N. Nuriev. Non-uniqueness of a stationary viscous flow in the square lid-driven cavity. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 130-143. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a10/