Free Access
Volume 43, Number 5, September-October 2009
Page(s) 929 - 955
Published online 12 June 2009
  1. P. Amorim, M. Ben-Artzi and P.G. LeFloch, Hyperbolic conservation laws on manifolds: total variation estimates and the finite volume method. Methods Appl. Anal. 12 (2005) 291–323. [MathSciNet]
  2. M. Ben-Artzi and P.G. LeFloch, Well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds. Ann. H. Poincaré Anal. Non Linéaire 24 (2007) 989–1008. [CrossRef]
  3. D.A. Calhoun, C. Helzel and R.J. LeVeque, Logically rectangular grids and finite volume methods for PDEs in circular and spherical domains. SIAM Rev. 50 (2008) 723–752. Available at [NASA ADS] [CrossRef] [MathSciNet]
  4. J.Y.-K. Cho and L.M. Polvani, The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids 8 (1996) 1531–1552. [NASA ADS] [CrossRef]
  5. M. Dikpati and P.A. Gilman, A “shallow-water” theory for the sun's active longitudes. Astrophys. J. Lett. 635 (2005) L193–L196. [NASA ADS] [CrossRef]
  6. M.P. do Carmo, Riemannian geometry, Mathematics: Theory & Applications. Birkhäuser Boston Inc., Boston, USA (1992).
  7. R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563–594. [CrossRef] [MathSciNet]
  8. J.A. Font, Numerical hydrodynamics and magnetohydrodynamics in general relativity. Living Rev. Relativ. 11 (2008) 7. URL (cited on June 8, 2009):
  9. P.A. Gilman, Magnetohydrodynamic “shallow-water” equations for the solar tachocline. Astrophys. J. Lett. 544 (2000) L79–L82. [NASA ADS] [CrossRef]
  10. F.X. Giraldo, Lagrange-Galerkin methods on spherical geodesic grids. J. Comput. Phys. 136 (1997) 197–213. [CrossRef] [MathSciNet]
  11. F.X. Giraldo, High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere. J. Comput. Phys. 214 (2006) 447–465. [CrossRef] [MathSciNet]
  12. R. Iacono, M.V. Struglia and C. Ronchi, Spontaneous formation of equatorial jets in freely decaying shallow water turbulence. Phys. Fluids 11 (1999) 1272–1274. [CrossRef]
  13. J. Jost, Riemannian Geometry and Geometric Analysis. Springer Universitext, Springer (2002).
  14. D. Lanser, J.G. Blom and J.G. Verwer, Spatial discretization of the shallow water equations in spherical geometry using osher's scheme. J. Comput. Phys. 165 (2000) 542–565. [CrossRef]
  15. J.M. Martíand E. Müller, Numerical hydrodynamics in special relativity. Living Rev. Relativ. 6 (2003) 7. URL (cited on June 8, 2009):
  16. M.J. Miranda, D. Pallara, F. Paronetto and M. Preunkert, Heat semigroup and functions of bounded variation on Riemannian manifolds. J. reine angew. Math. 613 (2007) 99–119. [CrossRef] [MathSciNet]
  17. M. Rancic, R.J. Purser and F. Mesinger, A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates. Q. J. R. Meteorolog. Soc. 122 (1996) 959–982.
  18. C. Ronchi, R. Iacono and P.S. Paolucci, The cubed sphere: A new method for the solution of partial differential equations in spherical geometry. J. Comput. Phys. 124 (1996) 93–114. [NASA ADS] [CrossRef] [MathSciNet]
  19. J.A. Rossmanith, A wave propagation algorithm for hyperbolic systems on the sphere. J. Comput. Phys. 213 (2006) 629–658. [CrossRef] [MathSciNet]
  20. J.A. Rossmanith, D.S. Bale and R.J. LeVeque, A wave propagation algorithm for hyperbolic systems on curved manifolds. J. Comput. Phys. 199 (2004) 631–662. [NASA ADS] [CrossRef] [MathSciNet]
  21. D.A. Schecter, J.F. Boyd and P.A. Gilman, “Shallow-water” magnetohydrodynamic waves in the solar tachocline. Astrophys. J. Lett. 551 (2001) L185–L188. [NASA ADS] [CrossRef]
  22. Y. Tsukahara, N. Nakaso, H. Cho and K. Yamanaka, Observation of diffraction-free propagation of surface acoustic waves around a homogeneous isotropic solid sphere. Appl. Phys. Lett. 77 (2000) 2926–2928. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you