Free Access
Issue
ESAIM: M2AN
Volume 43, Number 5, September-October 2009
Page(s) 929 - 955
DOI https://doi.org/10.1051/m2an/2009013
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] [Google Scholar]
  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] [Google Scholar]
  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 http://www.amath.washington.edu/~rjl/pubs/circles. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  6. M.P. do Carmo, Riemannian geometry, Mathematics: Theory & Applications. Birkhäuser Boston Inc., Boston, USA (1992). [Google Scholar]
  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] [Google Scholar]
  8. J.A. Font, Numerical hydrodynamics and magnetohydrodynamics in general relativity. Living Rev. Relativ. 11 (2008) 7. URL (cited on June 8, 2009): http://www.livingreviews.org/lrr-2008-7. [Google Scholar]
  9. P.A. Gilman, Magnetohydrodynamic “shallow-water” equations for the solar tachocline. Astrophys. J. Lett. 544 (2000) L79–L82. [NASA ADS] [CrossRef] [Google Scholar]
  10. F.X. Giraldo, Lagrange-Galerkin methods on spherical geodesic grids. J. Comput. Phys. 136 (1997) 197–213. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  13. J. Jost, Riemannian Geometry and Geometric Analysis. Springer Universitext, Springer (2002). [Google Scholar]
  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] [Google Scholar]
  15. J.M. Martíand E. Müller, Numerical hydrodynamics in special relativity. Living Rev. Relativ. 6 (2003) 7. URL (cited on June 8, 2009): http://www.livingreviews.org/lrr-2003-7. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  19. J.A. Rossmanith, A wave propagation algorithm for hyperbolic systems on the sphere. J. Comput. Phys. 213 (2006) 629–658. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]

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