Immersed boundary method for the MHD flows of liquid metals

Journal of Computational Physics

Volumn 228, Issue 3, 2009, Pages 903-920

  Grigoriadis, D G E ^a   Kassinos, S C ^a   Votyakov, E V ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Circular cylinder; Complex geometries; Conducting fluid; Immersed boundary method; Incompressible flow; MHD flow

Indexed keywords

CIRCULAR CYLINDERS; CURRENT DENSITY; ELECTRIC POTENTIAL; MAGNETOHYDRODYNAMICS; NUMERICAL METHODS; REYNOLDS NUMBER; TURBULENT FLOW;

COMPLEX GEOMETRIES; COMPUTATIONAL COSTS; CONDUCTING FLUID; FLOW SOLVER; FORCINGS; HARTMANN; IMMERSED BOUNDARY METHODS; MHD FLOW; MHD SIMULATION; RESOLUTION REQUIREMENTS;

INCOMPRESSIBLE FLOW;

EID: 57649103628     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.10.017     Document Type: Article

References (41)

1. Morley N.B., Smolentsev S., Barleon L., Kirillov I.R., and Takahashi M. Liquid Magnetohydrodynamics - recent progress and future direction for fusion. Fusion Eng. Design 51-52 (2000) 701-713
2. Müller U., and Bühler L. Magnetohydrodynamics in Channels and Containers (2001), Springer
3. Moreau R. Magnetohydrodynamics (1990), Kluwer
4. D.D. Papailiou, Magneto-fluid-mechanic turbulent vortex streets. In Fourth Beer-Sheva Seminar on MHD Flows and Turbulence, AIAA, 1984, pp. 152-173.
5. Kolesnikov Y., and Tsinober A. An experimental study of two-dimensional turbulence behind a grid. Fluid Dyn. 9 (1972) 621-624
6. Lahjomri J., Caperan P., and Alemany A. The cylinder wake in a magnetic field aligned with the velocity. J. Fluid Mech. 253 (1993) 421-448
7. Mück B., Günther C., Müller U., and Bühler L. Three-dimensional MHD flows in rectangular ducts with internal obstacles. J. Fluid Mech. 418 (2000) 265-295
8. Mutschke G., Gerbeth G., Shatrov V., and Tomboulides A. Two and three-dimensional instabilities of the cylinder wake in an aligned magnetic field. Phys. Fluids 9 (1997) 3114-3116
9. Sekhar T.V.S., Sivakumar R., Kumar H., and Ravi kumar T.V.R. Effect of aligned magnetic field on the steady viscous flow past a circular cylinder. Appl. Math. Modell. 31 (2007) 130-139
10. Mutschke G., Shatrov V., and Gerbeth G. Cylinder wake control by magnetic fields in liquid metal flows. Exp. Thermal Fluid Sci. 16 (1998) 92-99
11. Moin P., and Iaccarino G. Complex Effects in Large Eddy Simulations, in Complex effects in Large Eddy Simulations. Lecture Notes in Computational Science and Engineering 56 (2007), Springer
12. Kalitzin G., Templeton J.A., and Medic G. A Near-Wall Eddy-Viscosity Formulation for LES. Complex effects in Large Eddy Simulations, Lecture notes in computational Science and Engineering 56 (2007), Springer
13. Pothérat A., Sommeria J., and Moreau R. Effective boundary conditions for magnetohydrodynamic flows with thin Hartmann layers. Phys. Fluids 14 1 (2002) 403-410
14. Widlund O. Wall functions for numerical modeling of laminar MHD flows. Eur. J. Mech. B/Fluids 22 (2003) 221-237
15. Peskin C.S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (1972) 252-271
16. Goldstein D., Handler R., and Sirovich L. VDirect numerical simulation of turbulent flow over a modeled riblet covered surface. J. Fluid Mech. 302 (1995) 333-376
17. Udaykumar H.S., Mittal R., Rampunggoon P., and Khanna A. A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys. 174 (2001) 345-380
18. Tseng Y.-H., and Ferziger J.H. A ghost-cell immersed boundary method for flow in complex geometry. J. Comput. Phys. 192 (2003) 593-623
19. Fadlun E.A., Verzicco R., Orlandi P., and Mohd-Yusof J. Combined immersed boundary finite-difference methods for three-dimensional complex simulations. J. Comput. Phys. 161 2 (2000) 35-60
20. Yang J., and Balaras E. An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries. J. Comput. Phys. 215 1 (2006) 12-40
21. Kim J., Kim D., and Choi H. An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171 (2001) 132-150
22. Mohd-Yusof J. Development of immersed boundary methods for complex geometries. Annual Research Briefs 1998 325-336. Center Turbulence Res. 12 (1998) 1-2
23. Grigoriadis D.G.E., Bartzis J.G., and Goulas A. LES of the flow past a rectangular cylinder using the immersed boundary concept. Int. J. Num. Meth. Fluids 41 (2003) 615-632
24. Lai M.C., and Peskin C.S. An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160 (2000) 705-719
25. Verzicco R., Orlandi P., Mohd-Yusof J., and Haworth D. LES in complex geometries using boundary body forces. AIAA J. 38 (2000) 427-433
26. Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations. Comput. Fluids 33 (2004) 375-404
27. Mittal R., and Iaccarino G. Immersed boundary methods. Annu. Rev. Fluid Mech. 37 (2005) 239-261
28. Grigoriadis D.G.E., Bartzis J.G., and Goulas A. Efficient treatment of complex geometries for large-eddy simulations of turbulent flows. Comput. Fluids 33 (2004) 201-222
29. Schumann U. A direct method for the solution of Poisson's equation with Neumann boundary conditions on a staggered grid of arbitrary size. J. Comput. Phys. 20 (1976) 171-182
30. Swarztrauber P.N. The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle. J. Comput. Phys. 19 (1977) 490-501
31. Wilhelmson R.B., and Ericksen J.H. Direct solutions for Poisson's equation in three dimensions. J. Comput. Phys. 25 (1977) 319-331
32. Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
33. Ni M.-J., Munipalli R., Morley N.B., Huang P., and Abdou M.A. A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system. J. Comput. Phys. 227 (2007) 174-204
34. Davidson P.A. An Introduction to Magnetohydrodynamics. Cambridge Texts in Applied Mathematics (2001), Cambridge University Press
35. Gilmanov A., Sotiropoulos F., and Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J. Comput. Phys. 191 2 (2003) 660-669
36. Leboucher L. Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic Internal flows at high Hartmann Number. J. Comput. Phys. 150 (1999) 181-198
37. Ni M.-J., Munipalli R., Morley N.B., Huang P., and Abdou M.A. Validation strategies of HIMAG in interfacial flow computation for fusion applications. Fusion Eng. Design 81 (2006) 1535-1541
38. Pauley L.L., Moin P., and Reynolds W.C. A numerical study of unsteady laminar boundary layer separation. TF-34, Thermoscience Division, Stanford University, Dept. Mech. Eng. (1988)
39. Williamson H.K. Vortex dynamics in the cylinder wake. J. Fluid Mech. 328 (1996) 345-539
40. Zhang H.Q., Fey U., Noack B.R., König M., and Eckelmann H. On the transition of the cylinder wake. Phys. Fluids 7 4 (2001) 779-794
41. Mutschke G., Gerbeth G., Shatrov V., and Tomboulides A. The scenario of three-dimensional instabilities of the cylinder wake in an external magnetic field: a linear stability analysis. Phys. Fluids 13 3 (2001) 723-734