In the paper the bifurcation analysis methods for the study of stationary Navier-Stokes system of equations are presented. The study includes methods for location of different solutions, continuation of solution branches and identification of local bifurcations of the system. Application of these methods for solving the problem of the steady streaming around a circular cylinder oscillating with high frequency and small amplitude in a viscous fluid is considered.
система уравнений Навье-Стокса, бифуркационный анализ, метод продолжения по параметру, метод гомотопии, Navier-Stokes system of equations, bifurcation analysis, continuation method, homotopy method
1. K. Johannsen, Computational Geosciences, 7, 169-182 (2003).
2. S. K. Rahimian, et al., Computers Chemical Engineering, 35, 3, 403-411 (2011).
3. A.N. Nuriev, Vestn. Kaz. tehnologicheskogo un-ta., 16, 334-336 (2011).
4. Y.A. Kuznetsov, Elements of applied bifurcation theory. Springer, Berlin, 1995, 591 p.
5. N. Riley, Annual Review of Fluid Mechanics., 33, 43-65 (2001).
6. N. Riley, IMA Journal of Applied Mathematics, 3, 4, 419-434 (1967).
7. C.-Y. Wang, J. Fluid Mech, 32. 55-68 (1968).
8. G. Shlihting, Teoriya pogranichnogo sloya. Nauka, Moskva, 1974, 712 c.
9. K. Fletcher, Vychislitel'nye metody v dinamike zhidkostey: T.2. Mir, Moskva, 1991, 552 s.
10. R. Barrett et al. Templates for the solution of linear systems: building blocks for iterative methods. Society for Industrial Mathematics, 1987, 143 p.
11. J. Ju, G. Lapenta, Lecture Notes in Computer Science, 3514/2005, 601-666 (2005).
12. A.G. Egorov, A.N. Nuriev, Uchen. zap. Kaz. gos. un-ta. Ser. Fiz.-matem. Nauki, 151, 3, 130-143 (2009).
13. R.B. Lehoucq et al. ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM. Software, environments, tools, 1998, 142 p.
14. A.F. Bertelsen, J. Fluid Mech., 64, 3, 589-697 (1974).
15. M. Tatsuno, P.W. Bearman, J. Fluid Mech., 211, 157-182 (1990).
