Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 41-44, 2007, Pages 4184-4195

  Luo, Zhendong ^a   Zhu, Jiang ^b   Wang, Ruiwen ^b   Navon, I M ^c  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

^c FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Error estimate; Mixed finite element method; Numerical simulation; Proper orthogonal decomposition technique

Indexed keywords

COMPUTER SIMULATION; ESTIMATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

GRAVITY MODEL; PROPER ORTHOGONAL DECOMPOSITION (POD);

GRAVITATION;

COMPUTER SIMULATION; ESTIMATION; FINITE ELEMENT METHOD; GRAVITATION; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34547660515     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.04.003     Document Type: Article

References (29)

1. Cane M.A. The response of an equatorial ocean to simple wind stress patterns. Part I. Model formulation and analytical results. J. Mar. Res. 37 (1979) 233-252
2. Seager R., Zebiak S.E., and Cane M.A. A model of the tropical Pacific Sea surface temperature climatology. J. Geophys. Res. 93 (1988) 1265-1280
3. Yu L., and O'Brien J.J. Variational data assimilation for determining the seasonal net surface flux using a tropical Pacific Ocean model. J. Phys. Oceanogr. 5 (1995) 2319-2343
4. Fukunaga K. Introduction to Statistical Recognition (1990), Academic Press, London
5. Jolliffe I.T. Principal Component Analysis (2002), Springer, Berlin
6. Crommelin D.T., and Majda A.J. Strategies for model reduction: comparing different optimal bases. J. Atmos. Sci. 61 (2004) 2206-2217
7. Majda A.J., Timofeyev I., and Vanden-Eijnden E. Systematic strategies for stochastic mode reduction in climate. J. Atmos. Sci. 60 (2003) 1705-1722
8. Selten F. Baroclinic empirical orthogonal functions as basis functions in an atmospheric model. J. Atmos. Sci. 54 (1997) 2100-2114
9. Holmes P., Lumley J.L., and Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry (1996), Cambridge University Press, Cambridge
10. Berkooz G., Holmes P., and Lumley J.L. The proper orthogonal decomposition in analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1993) 539-575
11. Cazemier W., Verstappen R.W.C.P., and Veldman A.E.P. Proper orthogonal decomposition and low-dimensional models for driven cavity flows. Phys. Fluid 10 (1998) 1685-1699
12. D. Ahlman, F. Serlund, J. Jackson et al., Proper orthogonal decomposition for time dependent lid-driven cavity flows, Research Report of Science Technology at University of Florida, 2005.
13. Lumley J.L. Coherent structures in turbulence. In: Meyer R.E. (Ed). Transition and Turbulence (1981), Academic Press, London 215-242
14. Aubry N., Holmes P., Lumley J.L., et al. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Dyn. 192 (1988) 115-173
15. Sirovich L. Turbulence and the dynamics of coherent structures. Parts I-III. Q. Appl. Math. 45 3 (1987) 561-590
16. Roslin R.D., Gunzburger M.D., Nicolaides R., et al. A self-contained automated methodology for optimal flow control validated for transition delay. AIAA J. 35 (1997) 816-824
17. H.V. Ly, H.T. Tran, Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor, Technical Report, CRSC-TR98-12 (Center for Research in Scientific Computation), North Carolina State University, 1998.
18. J. Ko, A.J. Kurdila, O.K. Redionitis et al., Synthetic jets, their reduced order modeling and applications to flow control, AIAA Paper number 99-1000, 37 Aerospace Sciences Meeting & Exhibit, Reno, 1999.
19. Moin P., and Moser R.D. Characteristic-eddy decomposition of turbulence in channel. J. Fluid Mech. 200 (1989) 417-509
20. Rajaee M., Karlsson S.K.F., and Sirovich L. Low dimensional description of free shear flow coherent structures and their dynamical behavior. J. Fluid Mech. 258 (1994) 1401-1402
21. Cao Y.H., Zhu J., Luo Z.D., and Navon I.M. Reduced order modeling of the upper tropical Pacific Ocean model using proper orthogonal decomposition. Comput. Math. Appl. 52 (2006) 1373-1386
22. Ly H.V., and Tran H.T. Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor. Q. Appl. Math. 60 4 (2002) 631-656
23. Sirovich L. Turbulence and the dynamics of coherent structures. Parts I-III. Q. Appl. Math. XLV 3 (1987) 561-590
24. Adams R.A. Sobolev Space (1975), Academic Press, New York
25. Luo Z.D., Zhu J., Zen Q.C., et al. Mixed finite element methods for the shallow water equations including current and silt sedimentation (I), the continuous-time case. Appl. Math. Mech. 25 1 (2004) 80-92
26. Luo Z.D., Zhu J., Zen Q.C., et al. Mixed finite element methods for the shallow water equations including current and silt sedimentation (II), the discrete-time case along characteristics. Appl. Math. Mech. 25 2 (2004) 186-202
27. Stricherz J., O'Brien J.J., and Legler D.M. Atlas of Florida State University Tropical Pacific Winds for TOGA 1966-1985 (1992), Florida State University, Tallahassee, FL
28. Ciarlet P.C. Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam
29. Luo Z.D. Mixed Finite Element Methods and Applications (2006), Chinese Science Press, Beijing