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Numerical stabilization of unstable solutions to Navier-Stokes equations from the domain boundary

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Abstract

In order to stabilize an unstable solution to Navier-Stokes equations with the help of boundary conditions, a discrete analogue of the algorithm proposed by A. V. Fursikov in the differential case is constructed. A Quette flow between rotating cylinders is taken as an unstable solution. A complete calculation cycle of stabilization is performed and the obtained results are discussed

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References

  1. D. D. Joseph, Stability of Fluid Motions I, II, Springer Tracts in Natural Philosophy, Vols. 27, 28 (Springer, 1976; Mir, Moscow, 1981).

  2. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis (North-Holland, Amsterdam, New York, Oxford, 1979; Mir, Moscow, 1981).

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  3. A. A. Ivanchikov, “Study of a Spectral Problem Connected with the Stability of the Quette Flow between Rotating Cylinders,” Numerical Methods and Programming 6(2), 55 (2005).

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  4. A. V. Fursikov, “Stabilizability of Two-Dimensional Navier-Stokes Equations with Help of a Boundary Feedback Control,” J. Math. Fluid Mech. 3, 259 (2001).

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  5. E. V. Chizhonkov, “Numerical Aspects of one Stabilization Method,” Rus. J. Numer. Anal. Math. Modelling 18(5), 363 (2003).

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  6. E. V. Chizhonkov and A. A. Ivanchikov, “On Numerical Stabilization of Solutions of Stokes and Navier-Stokes Equations by the Boundary Conditions,” Russ. J. Numer. Anal. Math. Modelling 19(6), 477 (2004).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. A. Ivanchikov

Authors
  1. A. A. Ivanchikov
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Additional information

Original Russian Text © A. A. Ivanchikov, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 26–30.

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Ivanchikov, A.A. Numerical stabilization of unstable solutions to Navier-Stokes equations from the domain boundary. Moscow Univ. Math. Bull. 62, 237–241 (2007). https://doi.org/10.3103/S0027132207060046

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  • DOI: https://doi.org/10.3103/S0027132207060046

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