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Article information
2026 , Volume 31, ¹ 2, p.5-14
Kornev A.A.
Numerical simulation of Couette - Taylor flows based on quasi-gasdynamic equations
The paper presents quasi-hydrodynamic equations in a cylindrical coordinate system provided that the solution is independent of the angular coordinate as well as an algorithm for constructing the corresponding finite-difference scheme. Within framework of this approach, the problem of fluid motions enclosed between two coaxial cylinders is numerically investigated, the inner cylinder rotates at a constant angular velocity while the outer one is at rest. In particular, an unstable subspace in the vicinity of the Couette flow is constructed for a certain selected (beyond critical) viscosity. This allowed showing that the phase portrait of the global dynamics of the appeared Taylor vortices is completely determined by the unstable modes available in the system. The results obtained are the basis for solving the problem of global stabilization of the unstable Couette flow as well as approximation of the global attractor of the corresponding semidynamic system.
Keywords: quasi-hydrodynamic equations, Couette flow, Taylor vortices
doi: 10.25743/ICT.2026.31.2.002
Author(s):
Kornev Andrei Alekseevich
Dr. , Professor
Position: Leading research officer
Office: M.V.Lomonosov Moscow State University, Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences
Address: 119991, Russia, Moscow, 1, Leninskiye Gory
E-mail: kornev@mech.math.msu.su
Bibliography link:
Kornev A.A. Numerical simulation of Couette - Taylor flows based on quasi-gasdynamic equations // Computational technologies. 2026. V. 31. ¹ 2. P. 5-14
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