Numerical solution of optimal magnetic suppression of natural convection in magneto-hydrodynamic flows by empirical reduction of modes

Computers and Fluids

Volumn 31, Issue 3, 2002, Pages 309-334

  Park, H M ^a   Jung, W S ^a  

^a Sogang University   (South Korea)

Author keywords

Control of natural convection; Karhunen Lo ve Galerkin procedure

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; NATURAL CONVECTION; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

LINEAR SUBSPACES;

MAGNETOHYDRODYNAMICS;

FLOW CONTROL; MAGNETOHYDRODYNAMICS; MATHEMATICAL ANALYSIS; NATURAL CONVECTION;

EID: 0036497379     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0045-7930(01)00042-1     Document Type: Article

References (21)

1. Park HM, Lee MW. An efficient method of solving the Navier-Stokes equations for flow control. Int J Numer Meth Engng 1998;41:1133-51.
2. Series RW, Hurle DTJ. The use of magnetic fields in semiconductor crystal growth. J Crystal Growth 1991;113:305-28.
3. Sterl A. Numerical simulation of liquid metal MHD flows in rectangular ducts. J Fluid Mech 1990;216:161-91.
4. Gad-el-Hak M. Flow control. Appl Mech Rev 1989;42:261-93.
5. Gunzburger MD, Hou L, Svobodny TP. Boundary velocity control of incompressible flow with an application to viscous drag reduction. SIAM J Control Optimiz 1991;30:167-81.
6. Abergel F, Temam R. On some control problems in fluid mechanics. Theoret Comput Fluid Dyn 1990;1:303-25.
7. Fattorini HO, Sritharan SS. Existence of optimal controls for viscous flow problems. Proc R Soc Lond A 1992;439:81-102.
8. Park HM, Cho DH. Low dimensional modeling of now reactors. Int J Heat Mass Transfer 1996;39:3311-23.
9. Loève M. Probability theory. 4th ed. New York: Springer; 1977.
10. Lumley JL. Stochastic tools in turbulence. New York: Academic Press; 1971.
11. Park HM, Sirovich L. Turbulent thermal convection in a finite domain: numerical results. Phys Fluids A 1990;2:1659-68.
12. Aubry N, Holmes P, Lumley JL, Stone E. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J Fluid Mech 1988;192:115-73.
13. Deane AE, Kevrekidis IG, Karniadakis GE, Orszag SA. Low dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys Fluids 1991;3:23-37.
14. Moin P, Bewley T. Feedback control of turbulence. Appl Mech Rev 1996;47:s3-s13.
15. Coller BD, Holmes P. Suppression of bursting. Automatica 1997;33:1-11.
16. Ferziger JH, Peric M. Computational methods for fluid dynamics, New York: Springer; 1996.
17. Ku HC, Taylor TD, Hirsh RS. Pseudospectral methods for solution of incompressible Navier-Stokes equations. Comput Fluids 1987;15:195-214.
18. Courant R, Hilbert D. Methods of mathematical physics 1. New York: Wiley; 1962.
19. Temam R. Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia, PA, 1983.
20. Fletcher R, Reeves RM. Function minimization by conjugate gradients. The Comput J 1964;7:149-54.
21. Polak E. Computational methods in optimization. New York: Academic Press; 1971.