Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

Applied Mathematics and Mechanics (English Edition)

Volumn 29, Issue 6, 2008, Pages 705-714

  Xu, Xin Sheng ^a   Wang, Ga Ping ^a   Sun, Fa Ming ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Hamiltonian system; Rectangular domain; Stokes flow; Symplectic eigensolutions; Symplectic eigenvalues

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; TWO DIMENSIONAL;

(I ,J) CONDITIONS; ADJOINT; ANALYTICAL AND NUMERICAL METHODS; ANALYTICAL METHODS; EIGEN SOLUTIONS; EIGEN VALUES; EIGEN-SOLUTIONS; FUNDAMENTAL PROBLEMS; HAMILTONIAN SYSTEMS; LOCAL EFFECTS; NUMERICAL EXAMPLES; RECTANGULAR DOMAINS; SPRINGER (CO); STOKES FLOWS; SYMPLECTIC; TWO-DIMENSIONAL (2D);

NUMERICAL METHODS;

EID: 46749122755     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-008-0602-3     Document Type: Article

References (22)

1. Burggraf O R. Analytical and numerical studies of the structure of steady separated flows[J]. J Fluid Mech, 1966, 24:113-151.
2. Pan F, Acrivos A. Steady flows in rectangular cavities[J]. J Fluid Mech, 1967, 28:643-655.
3. Kelmanson M A, Lonsdale B. Eddy genesis in the double-lid-driven cavity[J]. Q J Mech Appl Math, 1996, 49(4):633-655.
4. Lin C S. Numerical simulation of Stokes flow in a double-lid-driven cavity[J]. J Nanjing Inst Technol, 2004, 2:29-35 (in Chinese).
5. Joseph D D, Sturges L. The convergence of biorthogonal series for biharmonic and Stokes flow edge problems: Part II[J]. SIAM J Appl Math, 1978, 34:7-26.
6. Smith R C T. The bending of a semi-infinite strip[J]. Austral J Sci Res, 1952, 5:227-237.
7. Sturges L D. Stokes flow in a two-dimensional cavity with moving end walls[J]. Phys Fluids, 1986, 29(5):1731-1734.
8. Shankar P N. The eddy structure in Stokes flow in a cavity[J]. J Fluid Mech, 1993, 250:371-383.
9. Gaskell P H, Savage M D, Summers J L, Thompson H M. Stokes flow in closed, rectangular domains[J]. Appl Math Model, 1998, 22:727-743.
10. Khuri S A. Biorthogonal series solution of Stokes flow problems in sectorial regions[J]. SIAM J Appl Math, 1996, 56(1):19-39.
11. Meleshko V V. Steady Stokes flow in a rectangular cavity[J]. Proc Roy Soc London A, 1996, 452:1999-2022.
12. Meleshko V V. Gomilko A M. Infinite systems for a biharmonic problem in a rectangle[J]. Proc Roy Soc London A, 1997, 453:2139-2160.
13. Srinivasan R. Accurate solutions for steady plane flow in the driven cavity. I. Stokes flow[J]. Zeitschrift für Angewandte Mathematik und Physik, 1995, 46(4):524-545.
14. Weiss R F, Florsheim B H. Flow in a cavity at low Reynolds number[J]. Phys Fluids, 1965, 8:1631-1635.
15. Munson B R, Sturges L D. Low Reynolds number flow in a rotating tank with barriers[J]. Phys Fluids, 1983, 26:1173-1176.
16. Shen C, Floryan J M. Low Reynolds number flow over cavities[J]. Phys Fluids, 1985, 28(11):3191-3202.
17. Taneda S. Visualization of separating Stokes flows[J]. J Phys Soc Jpn, 1979, 46:1935-1942.
18. O'Brien V. Closed streamlines associated with channel flow over a cavity[J]. Phys Fluids, 1972, 15:2089-2097.
19. Wang C Y. Flow over a surface with parallel grooves[J]. Phys Fluids, 2003, 15(5):1114-1121.
20. Zhong W X. Duality system in applied mechanics and optimal control[M]. New York: Kluwer Academic Publishers, 2004, 188-191
21. Zhang H Q, Alatancang, Zhong W X. The Hamiltonian system and completeness of symplectic orthogonal system[J]. Appl Math Mech-Engl Ed, 1997, 18(3):237-242. DOI 10.1007/BF 02453366
22. Xu X S, Wang G P. Method of symplectic eigensolutions in Stokes flow[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(5):682-687.