The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type
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Andrei A. Kornev
Abstract
A system of Navier-Stokes equations with a right-hand side is considered in the case when the system approximately describes the motion of a thin layer of a viscous incompressible fluid in an annular domain under the action of external electromagnetic force. The problem possesses an unstable two-stream nonstationary main flow and a set of quasistationary solutions of vortex type for the tested range of parameters. A method of study of the general dynamic pattern is proposed in the paper. The method is based on the construction of control boundary conditions specified on the internal boundary of the annulus and providing the stabilization of considered unstable modes. The problem of boundary stabilization of the main and secondary flows is also solved numerically and we obtained that it is sufficient to take into account only a part of unstable modes in the construction of stabilizing conditions for the main flow. The method based on the partial stabilization of the main flow is first proposed for stabilization of secondary flows, which essentially simplifies the implementation of the algorithm. Formulations of the problems and numerical algorithms are presented.
Funding: The work was supported by the Russian Foundation for Basic Research (project no. 15-01-08023).
References
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© 2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Preface
- Efficient synthesis of optimal multiband filter
- A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
- A Newton-type method for non-linear eigenproblems
- The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type
- Monotone discretizations for diffusion equations on triangular and tetrahedral meshes
- A posteriori estimates for a coupled piezoelectric model
- The triviality condition for kernels of quadratic mappings and its application in optimization methods
Artikel in diesem Heft
- Frontmatter
- Preface
- Efficient synthesis of optimal multiband filter
- A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle
- A Newton-type method for non-linear eigenproblems
- The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type
- Monotone discretizations for diffusion equations on triangular and tetrahedral meshes
- A posteriori estimates for a coupled piezoelectric model
- The triviality condition for kernels of quadratic mappings and its application in optimization methods
