An EBE finite element method for simulating nonlinear flows in rotating spheroidal cavities

International Journal for Numerical Methods in Fluids

Volumn 63, Issue 3, 2010, Pages 395-414

  Chan, Kit H ^a   Zhangk, Keke ^b   Liao, Xinhao ^c  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF EXETER   (United Kingdom)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Finite element methods; Incompressible flow; Methods; Navier Stokes; Partial differential; Rotation; Spheroids; Validation

Indexed keywords

DISCRETIZATIONS; ELEMENT BY ELEMENTS; INCOMPRESSIBLE FLUID; NAVIER STOKES; NONLINEAR FLOW; NUMERICAL SIMULATION; PARALLELIZATIONS; PARTIAL DIFFERENTIAL; RESONANT FORCING; SPHEROIDAL CAVITIES; SPHEROIDAL GEOMETRY;

COMPUTER SIMULATION; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; ROTATION;

FINITE ELEMENT METHOD;

EID: 77953604422     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2088     Document Type: Article

References (37)

1. Gubbins D, Roberts PH. Magnetohydrodynamics of the Earth's core. In Geomagnetism, vol. 2, Jacobs JA (ed.). Academic Press: London, 1987; 1-183.
2. Bullard EC. The magnetic flux within the earth. Proceedings of the Royal Society A 1949; 197:433-453.
3. Malkus WVR. Precession of the earth as the cause of geomagnetism. Science 1968; 136:259-264.
4. Vanyo JP, Wilde P, Cardin P, Olson P. Experiments on precessing flows in the Earth's liquid core. Geophysical Journal International 1995; 121:136-142.
5. Noir J, Cardin P, Jault D, Masson JP. Experimental evidence of non-linear resonance effects between retrograde precession and the tilt-over mode within a spheroid. Geophysical Journal International 2003; 154:407-416.
6. Tilgner A. Precession driven dynamos. Physics of Fluids 2005; 17:034104.
7. Lacaze L, Herreman W, Le Bars M, Le Dizs S, Le Gal P. Magnetic field induced by elliptical instability in a rotating spheroid. Geophysical and Astrophysical Fluid Dynamics 2006; 100:299-317.
8. Tilgner A. Kinematic dynamos with precession driven flow in a sphere. Geophysical and Astrophysical Fluid Dynamics 2007; 100:1-9.
9. Peterson DM, Hummel CA, Pauls TA, Armstrong JT, Benson JA, Gilbreath GC, Hindsley RB, Hutter DJ, Johnston KJ, Mozurkewich D, Schmitt HR. Vega is a rapidly rotating star. Nature 2006; 440:896-899.
10. Walker MR, Barenghi CF. High resolution numerical dynamos in the limit of a thin disk galaxy. Geophysical and Astrophysical Fluid Dynamics 1994; 76:265-281.
11. Stewartson K, Roberts PH. On the motion of a liquid in a spheroidal cavity of a precessing rigid body. Journal of Fluid Mechanics 1963; 17:1-20.
12. Roberts PH, Stewartson K. On the motion of a liquid in a spheroidal cavity of a precessing rigid body: II. Mathematical Proceedings of the Cambridge Philosophical Society 1965; 61:279-288.
13. Zhang K, Busse F. Convection driven magnetohydrodynamic dynamos in rotating spherical shells. Geophysical and Astrophysical Fluid Dynamics 1989; 49:97-116.
14. Glatzmaier GA, Roberts PH. A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle. Physics of the Earth and Planetary Interiors 1995; 91:63-75.
15. Sarson GR, Jones CA. A convection driven geodynamo reversal model. Physics of the Earth and Planetary Interiors 1999; 111:3-20.
16. Lorenzani S, Tilgner A. Fluid instabilities in precessing spheroidal cavities. Journal of Fluid Mechanics 2001; 447:111-128.
17. Schmitt D. Numerical study of viscous modes in a rotating spheroid. Journal of Fluid Mechanics 2006; 567:399-414.
18. Chan K, Zhang K, Li L, Liao X. A new generation of convection-driven spherical dynamos using EBE finite element method. Physics of the Earth and Planetary Interiors 2007; 163:251-265.
19. 2 dynamo using a finite element method. Physics of the Earth and Planetary Interiors 2001; 128:35-50.
20. Zhang K, Chan KH, Zou J, Liao X, Schubert G. A three-dimensional spherical nonlinear interface dynamo. Astrophysical Journal 2003; 596:663-679.
21. Karniadakis GE, Israeli M, Orszag SA. High-order splitting methods for the incompressible Navier-Stokes equations. Journal of Computational Physics 1991; 97:414-443.
22. Kress W, L̈otstedt P. Time step restrictions using semi-explicit methods for the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 2006; 195(33-36):4433-4447.
23. Everett ME. A three-dimensional spherical mesh generator. Geophysical Journal International 1997; 130:193-200.
24. Liu A, Joe B. Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision. Mathematics of Computation 1996; 65(215):1183-1200.
25. Persson PO, Strang G. A simple mesh generator in MATLAB. SIAM Review 2004; 46(2):329-345.
26. Hood P, Taylor C. Navier-Stokes equations using mixed-interpolation. In Finite Element Methods in Flow Problems, Oden JT, Zienkiewicz OC, Gallagher RH, Taylor C (eds). UAH Press: Huntsville, 1974; 57-66.
27. Zienkiewicz OC. The Finite Element Method (3rd edn). McGraw-Hill: London, 1977.
28. Brezzi F, Fortin M. Mixed and. Hybrid Finite Element Methods. Springer: Berlin, Heidelberg, 1991.
29. Girault V, Raviart P. Finite Element Approximation of the Navier-Stokes Equations. Springer: New York, 1981.
30. Codina R. A nodal-based implementation of a stabilized finite element method for incompressible flow problems. International Journal for Numerical Methods in Fluids 2000; 33:737-766.
31. Behr M. Stabilized finite element methods for incompressible flows with emphasis on moving boundaries and interfaces. Ph.D. Thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, 1992.
32. Behr M, Johnson A, Kennedy J, Mittal S, Tezduyar TE. Computation of incompressible flows with implicit finite element implementations on the Connection Machine. Computer Methods in Applied Mechanics and Engineering 1993; 108:99-118.
33. Margetts L. Parallel finite element analysis. Ph.D. Thesis, University of Manchester, U.K., 2002.
34. van der Vorst HA. BiCGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific Computing 1992; 13:631-644.
35. Sleijpen GLG, Fokkema DR. BiCGstab(L) for linear equations involving unsymmetric matrices with complex spectrum. Electronic Transactions on Numerical Analysis 1993; 1:11-32.
36. Girault V, Raviart P. Finite Element Methods for Navier-Stokes Equations Theory and Algorithms. Springer: Berlin, 1986.
37. Zhang K, Liao X, Earnshaw P. On inertial waves and oscillations in a rapidly rotating fluid spheroid. Journal of Fluid Mechanics 2004; 504:1-40.