The pseudospectral method in thermal convection models of a rotating spherical shell for parallel computers

Authors

Keywords:

spherical functions, Chebyshev polynomials, geostrophic state, cluster systems

Abstract

The numerical application and parallelization of the classical thermal convection models for a spherical shell are discussed. These models are used in the modern planetary dynamo models with consideration of the inner core rotation due to the viscous forces. Several scaling tests for a parallel model with the parallelization in the radial direction for a cluster computing systems are considered. The test results confirm a good scalability of the method for typical three-dimensional grids of 643 nodes.

Author Biography

M.Yu. Reshetnyak

References

  1. Braginsky S.I., Roberts P.H. Equations governing convection in Earth’s core and the geodynamo // Geophys. Astrophys. Fluid Dynamics. 1995. 79. 1-95.
  2. Jones C.A. Convection-driven geodynamo models // Phil. Trans. R. Soc. London. 2000. Т. A 358. 873-897.
  3. Christensen U.R., Wicht J. Numerical dynamo simulations // Treatise on Geophysics. Vol. 8: Core Dynamics. Amsterdam: Elsevier, 2007. 245-282.
  4. Glatzmaier G.A., Roberts P.H. A three-dimension convective dynamo solution with rotating and finitely conducting inner core and mantle // Phys. Earth Planet. Inter. 1995. 91. 63-75.
  5. Hejda P., Reshetnyak M. Control volume method for the dynamo problem in the sphere with the free rotating inner core // Studia Geoph. et Geod. 2003. 47. 147-159.
  6. Wadleigh K.R., Crawford I.L. Software optimization for high-performance computing. Upper Saddle River: Prentice Hall, 2000.
  7. Simitev R. Convection and magnetic field generation in rotating spherical fluid shells. Ph.D. Thesis. University of Bayreuth. Bayreuth, 2004 (http://www.phy.uni-bayreuth.de/theo/tp4/members/simitev.html).
  8. Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A. Spectral methods in Fluids Dynamics. New York: Springer-Verlag, 1988.
  9. Glatzmaier G. Numerical simulations of stellar convective dynamos. I. The model and method // J. Comp. Physics. 1984. 55. 461-484.
  10. Tilgner A. Spectral methods for the simulation of incompressible flows in spherical shells // Int. J. Numer. Meth. Fluids. 1999. 30. 713-724.
  11. Zhang K., Jones C.A. The effect of hyperviscosity on geodynamo models // Geophys. Res. Lett. 1997. 24. 2869-2872.
  12. Adams J.C., Swarztrauber P.N. SPHEREPACK 3.2: A Model Development Facility (http://www.cisl.ucar.edu/css/software/spherepack/).
  13. Clune T.C., Elliott J.R., Miesch M.S., Toomre J., Glatzmaier G.A. Computational aspects of a code to study rotating turbulent convection in spherical shells // Parallel Computing. 1999. 25. 361-380.
  14. Решетняк М.Ю. Тейлоровский цилиндр и конвекция в сферической оболочке // Геомагнетизм и аэрономия. 2010. 50, N 2. 273-283.

Published

21-02-2011

How to Cite

Решетняк М. The Pseudospectral Method in Thermal Convection Models of a Rotating Spherical Shell for Parallel Computers // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2011. 12. 77-84

Issue

Section

Section 1. Numerical methods and applications