"Yin-Yang grid": An overset grid in spherical geometry

Geochemistry, Geophysics, Geosystems

Volumn 5, Issue 9, 2004, Pages

  Kageyama, Akira ^a   Sato, Tetsuya ^a  

^a JAPAN AGENCY FOR MARINE EARTH SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Chimera grid; Geodynamo; Mantle convection; Overset grid; Spherical geometry; Yin Yang grid

Indexed keywords

EID: 12344263563     PISSN: 15252027     EISSN: 15252027     Source Type: Journal    
DOI: 10.1029/2004GC000734     Document Type: Article

References (54)

1. Baumgardner, J. (1985), Three-dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys., 39, 501-511.
2. Bercovici, D., G. Schubert, G. A. Glatzmaier, and A. Zebib (1989), Three dimensional thermal convection in a spherical shell, J. Fluid Mech., 206, 75-104.
3. Browning, G. L., J. J. Hack, and P. N. Swarztrauber (1989), A comparison of three numerical methods for solving differential equations on the sphere, Mon. Weather Rev., 117, 1058-1075.
4. Bunge, H.-P., and J. R. Baumgardner (1995), Mantle convection modeling on parallel virtual machines, Comput. Phys., 9, 207-215.
5. Buning, P. G., I. T. Chiu, S. Obayashi, Y. M. Rizk, and J. L. Steger (1988), Numerical simulation of the integrated space shuttle vehicle in ascent, AIAA Pap. 88-4359-Cp, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
6. Busse, F. (1975), Patterns of convection in spherical shells, J. Fluid Mech., 72, 67-85.
7. Busse, F. H., and N. Riahi (1982), Patterns of convection in spherical shells, Part 2, J. Fluid Mech., 123, 283-301.
8. Cao, H. V., T. Y. Su, and S. E. Rogers (1998), Navier-Stokes analysis of a 747 high lift configuration, AIAA Pap. 98-2623, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
9. 2 dynamo using a finite element method, Phys. Earth Planet. Inter., 128, 35-50.
10. Chesshire, G., and W. D. Henshaw (1990), Composite overlapping meshes for the solution of partial differential equations, J. Comput. Phys., 90, 1-64.
11. Christensen, U., P. Olson, and G. A. Glatzmaier (1999), Numerical modelling of the geodynamo: A systematic parameter study, Geophys. J. Int., 138, 393-409.
12. Christensen, U. R., et al. (2001), A numerical dynamo benchmark, Phys. Earth Planet. Inter., 128, 25-34.
13. Dormy, E., P. Cardin, and D. Jault (1998), MHD flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field, Earth Planet. Sci. Lett., 160, 15-30.
14. Dudhia, J., and J. F. Bresch (2002), A global version of the PSU-NCAR mesoscale model, Mon. Weather Rev., 130, 2989-3007.
15. Duque, E. P. N., R. C. Strawn, J. Ahmad, and R. Biswas (1996), An overset grid Navier-Stokes Kirchhoff-surface method for rotorcraft aeroacoustic predictions, AIAA Pap. 96-0152, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
16. Eby, M., and G. Holloway (1994), Grid transformation for incorporating the Arctic in a global ocean model, Clim. Dyn., 10, 241-247.
17. Glatzmaier, G. (1984), Numerical simulations of stellar convective dynamos. I. The model and method, J. Comput. Phys., 55, 461-484.
18. Glatzmaier, G. (1988), Numerical simulations of mantle convection: Time-dependent, three-dimensional, compressible, spherical shell, Geophys. Astrophys. Fluid Dyn., 43, 223-264.
19. Habata, S., M. Yokokawa, and S. Kitawaki (2003), The Earth Simulator System, NEC Res. Dev., 44(1), 21-26.
20. Harder, H., and U. R. Christensen (1996), A one-plume model of martian mantle convection, Nature, 380, 507-509.
21. Hernlund, J. W., and P. J. Tackley (2003), Three-dimensional spherical shell convection at infinite Prandtl number using the ''cubed sphere'' method, paper presented at Second MIT Conference on Computational Fluid and Solid Mechanics, Mass. Inst. of Technol., Cambridge.
22. Ishihara, N., and S. Kida (2002), Dynamo mechanism in a rotating spherical shell: Competition between magnetic field and convection vortices, J. Fluid Mech., 465, 1-32. (Pubitemid 34955930)
23. Iwase, Y. (1996), Three-dimensional infinite Prandtl number convection in a spherical shell with temperature-dependent viscosity, J. Geomagn. Geoelectr., 48, 1499-1514.
24. Kageyama, A., and T. Sato (1997a), Generation mechanism of a dipole field by a magnetohydrodynamic dynamo, Phys. Rev. E, 55, 4617-4626.
25. Kageyama, A., and T. Sato (1997b), Velocity and magnetic field structures in a magnetohydrodynamic dynamo, Phys. Plasmas, 4, 1569-1575.
26. Kageyama, A., and T. Sato (1997c), Dipole field generation by an MHD dynamo, Plasma Phys. Controlled Fusion, 39, A83-A91.
27. Kageyama, A., K. Watanabe, and T. Sato (1993), Simulation study of a magnetohydrodynamic dynamo: Convection in a rotating spherical shell, Phys. Fluids B, 5, 2793-2805.
28. Kageyama, A., T. Sato, K. Watanabe, R. Horiuchi, T. Hayashi, Y. Todo, T. Watanabe, and H. Takamaru (1995), Computer simulation of a magnetohydrodynamic dynamo, II, Phys. Plasmas, 2, 1421-1431.
29. Kageyama, A., M. M. Ochi, and T. Sato (1999), Flip-flop transitions of the magnetic intensity and polarity reversals in the magnetohydrodynamic dynamo, Phy. Rev. Lett., 82, 5409-5412.
30. Kuang, W., and J. Bloxham (1999), Numerical modeling of magnetohydrodynamic convection in a rapidly rotating spherical shell: Weak and strong field dynamo action, J. Comput. Phys., 153, 51-81.
31. Li, J., T. Sato, and A. Kageyama (2002), Repeated and sudden reversals of the dipole field generated by a spherical dynamo action, Science, 295, 1781-1960.
32. Machetel, P., M. Rabinowicz, and P. Bernardet (1986), Three-dimensional convection in spherical shells, Geophys. Astrophys. Fluid Dyn., 37, 57-84.
33. Matsui, H., and H. Okuda (2002), Development of a simulation code for MHD dynamo processes using the Geo-FEM platform, Int. J. Comput. Fluid Dyn., 18(4), 323-332.
34. Meakin, R. L. (1992), Computations of the unsteady flow about a generic wing/pylon/finned-store configurations, AIAA Pap. 92-4568-CP, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
35. Meakin, R. L. (1993), Moving body overset grid methods for complete aircraft tiltrotor simulations, AIAA Pap. 93-3350-CP, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
36. Ochi, M. M., A. Kageyama, and T. Sato (1999), Dipole and octapole field reversals in a rotating spherical shell: Magnetohydrodynamic dynamo simulation, Phys. Plasmas, 6, 777-787.
37. Phillips, N. (1957), A map projection system suitable for largescale numerical weather prediction, J. Meteorol. Soc. Jpn., 75, 262-267.
38. Phillips, N. A. (1959), Numerical integration of the primitive equations on the hemisphere, Mon. Weather Rev., 87, 333-345.
39. Rai, M. M. (1986), A conservative treatment of zonal boundaries for Euler equation calculations, J. Comput. Phys., 62, 472-503.
40. Ratcliff, J., G. Schubert, and A. Zebib (1996), Steady tetrahedral and cubic patterns of spherical shell convection with temperature-dependent viscosity, J. Geophys. Res., 101, 25,473-25,484.
41. Richards, M. A., W.-S. Yang, J. R. Baumgardner, and H.-P. Bunge (2001), Role of a low-viscosity zone in stabilizing plate tectonics: Implications for comparative terrestrial plan-etology, Geochem. Geophys. Geosyst., 2, doi:10.1029/2000GC000115.
42. Rogers, S. E., H. V. Cao, and T. Y. Su (1998), Grid generation for complex high-lift configurations, AIAA Pap. 98-3011, Am. Inst. of Aeronaut. and Astronau., Reston, Va.
43. Ronchi, C., R. Iacono, and P. S. Paolucci (1996), The ''cubed sphere'': A new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys., 124, 93-114.
44. Sakuraba, A., and M. Kono (1999), Effect of the inner core on the numerical solution of the magnetohydrodynamic dynamo, Phys. Earth Planet. Inter., 111, 105-121.
45. Shingu, S., et al. (2002), A 26.58 Tflops global atmospheric simulation with the spectral transform method on the Earth Simulator, paper presented at of the ACM/IEEE Super-computing SC'2002 Conference, Assoc. for Comput. Mach., Baltimore, Md.
46. Steger, J. L. (1982), On application of body conforming curvilinear grids for finite difference solution of external flow, in Numerical Grid Generation, edited by J.F. Thomposon, pp. 295-316, North-Holland, New York.
47. Steger, J.L., F.C. Dougherty, and J.A. Benek(1983), A chimera grid scheme, in Advances in Grid Generation, edited by K. N. Ghia and U. Ghia, pp. 59-69, Am. Soc. of Mech. Eng., New York.
48. Tabata, M., and A. Suzuki (2000), A stabilized finite element method for the rayleigh-benard equations with infinite prandtl number in a spherical shell, Comput. Methods Appl. Mech. Eng., 190, 387-402.
49. Takahashi, F., J. S. Katayama, M. Matsushima, and Y. Honkura (2001), Effects of boundary layers on magnetic field behavior in an MHD dynamo model, Phys. Earth Planet. Inter., 128, 149-161.
50. Tilgner, A. (1999), Spectral methods for the simulation of incompressible flow in spherical shells, Int. J. Numer. Methods Fluids, 30, 713-724.
51. Yokokawa, M., K. Itakura, A. Uno, T. Ishihara, and Y. Kaneda (2002), 16.4-tflops direct numerical simulation of turbulence by a fourier spectral method on the earth simulator, paper presented at the ACM/IEEE Supercomputing SC'2002 conference, Assoc. for Comput. Mach., Baltimore, Md.
52. Yoshida, M., and A. Kageyama (2004), Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell, Geophys. Res. Lett., 31, L12609, doi:10.1029/2004GL019970. (Pubitemid 39384097)
53. Zhang, S., and D. A. Yuen (1995), The influences of lower mantle viscosity stratification on 3D spherical-shell mantle convection, Earth Planet. Sci. Lett., 132, 157-166.
54. Zhong, S., M. T. Zuber, L. Moresi, and M. Gurnis (2000), Role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection, J. Geophys. Res., 105, 11, 063-11, 082.