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On numerical stabilization of unstable Couette flow by boundary conditions. (English) Zbl 1130.76058

Summary: In order to stabilize the unstable Couette flow by boundary conditions, we construct a discrete analogue of the algorithm proposed for the differential case by A. V. Fursikov [Math. Sb. 192, No. 4, 593–639 (2001); translation from Mat. Sb. 192, No. 4, 115–160 (2001; Zbl 1019.93047)]. We carry out a complete stabilization computation cycle and discuss the results obtained.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids

Citations:

Zbl 1019.93047

Software:

LAPACK
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Full Text: DOI

References:

[1] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide, SIAM, Philadelphia, PA, 1999.
[2] K. I. Babenko and A. L. Afendikov, Fundamentals of Numerical Analysis. Mir, Moscow, 1989 (in Russian). · Zbl 0969.76535
[3] K. I. Babenko and A. L. Afendikov, On stability and bifurcation of the Couette flow between rotating cylinders. Preprint IPM USSR Akad. Sci., No. 99, 1981 (in Russian).
[4] DOI: 10.1515/rnam.2003.18.5.363 · doi:10.1515/rnam.2003.18.5.363
[5] DOI: 10.1515/rnam.2004.19.6.477 · doi:10.1515/rnam.2004.19.6.477
[6] DOI: 10.2307/2004575 · Zbl 0198.50103 · doi:10.2307/2004575
[7] A. V. Fursikov, Real process corresponding to the 3D Navier-Stokes system and its feedback stabilization from boundary. The M. I. Vishik Seminar, AMS Translations Serie 2, 2002, Vol. 206, pp. 95-123. · Zbl 1036.76010
[8] Math. Collection 192 (4) pp 115– (2001)
[9] DOI: 10.1007/PL00000972 · Zbl 0983.93021 · doi:10.1007/PL00000972
[10] DOI: 10.1016/0021-9991(82)90058-4 · Zbl 0511.76031 · doi:10.1016/0021-9991(82)90058-4
[11] DOI: 10.1002/cpe.785 · Zbl 1141.76438 · doi:10.1002/cpe.785
[12] Math. Model. Numer. Anal. 30 (5) pp 637– (1996)
[13] Kh. D. Ikramov, Nonsymmetric Eigenvalue Problem. Nauka, Moscow, 1991 (in Russian). · Zbl 0752.65032
[14] Comp. Meth. Program. 6 (2) pp 55– (2005)
[15] Comp. Meth. Program. 4 (2) pp 58– (2003)
[16] D. Joseph, Stability of Fluid Motions. Springer, Heidelberg, 1976. · Zbl 0345.76023
[17] O. A. Ladyzhenskaya, Mathematical Problems of Viscous Incompressible Fluid Dynamics. Nauka, Moscow, 1970 (in Russian). · Zbl 0215.29004
[18] DOI: 10.1137/0907058 · Zbl 0599.65018 · doi:10.1137/0907058
[19] R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis. North-Holland, Amsterdam, 1977. · Zbl 0383.35057
[20] DOI: 10.1007/BF00281240 · Zbl 0233.76054 · doi:10.1007/BF00281240
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