Skip to main content
Have a personal or library account? Click to login
On the use of reduced grids in conjunction with the Equator-Pole grid system Cover

On the use of reduced grids in conjunction with the Equator-Pole grid system

By:   
Open Access
|Jan 2020

References

  1. Allen, T. and Zerroukat, M. 2015. A moist Boussinesq shallow water equations set for testing atmospheric models. J. Comput. Phys. 290, 5572.
  2. Allen, T. and Zerroukat, M. 2016. A deep non-hydrostatic compressible atmospheric model on Yin-Yang grid. J. Comput. Phys. 319, 4460. doi:10.1016/j.jcp.2016.05.022
  3. Bao, L., Nair, R. D. and Tufo, H. M. 2014. A mass and momentum flux-form higher-order discontinuous Galerkin shallow water model on the cubed-sphere. J. Comput. Phys. 271, 224243. doi:10.1016/j.jcp.2013.11.033
  4. Chen, C., Li, X., Shen, X. and Xiao, F. 2014. Global shallow water models based on multi-moment constrained finite volume method and three quasi-uniform spherical grids. J. Comput. Phys. 271, 191223. doi:10.1016/j.jcp.2013.10.026
  5. Gates, W. L. and Riegel, A. 1963. A study of numerical errors in the integration of barotropic flow on a spherical grid. J. Geophys. Res. 67, 406423.
  6. Giraldo, F. X. 2006. High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on rotating sphere. J. Comput. Phys. 214, 447465. doi:10.1016/j.jcp.2005.09.029
  7. Hortal, M. and Simmons, A. J. 1991. Use of reduced Gaussian grids in spectral models. Mon. Wea. Rev. 119, 10571074. doi:10.1175/1520-0493(1991)119<;1057:UORGGI>2.0.CO;2
  8. Kageyama, A. and Sato, T. 2004. The Yin-Yang grid: an overset grid in spherical geometry. Geochem. Geophys. Geosyst. 5, 1–15.
  9. Kreiss, H.-O. and Oliger, J. 1972. Comparison of accurate methods for the integration of hyperbolic equations. Tellus A 24, 199215.
  10. Kurihara, Y. 1965. Integration of the primitive equations on a spherical grid. Mon. Weather Rev. 95, 399415.
  11. Läuter, M., Handorf, D. and Dethloff, K. 2005. Unsteady analytical solutions of the spherical shallow water equations. J. Comput. Phys. 210, 535553. doi:10.1016/j.jcp.2005.04.022
  12. Läuter, M., Giraldo, F. X., Handorf, D. and Dethloff, K. 2008. A discontinuous Galerkin method for the shallow water equations using spherical triangular coordinates. J. Comput. Phys. 227, 1022610243. doi:10.1016/j.jcp.2008.08.019
  13. Layton, A. T. 2002. Cubic spline collocation methods for the shallow water equations on the sphere. J. Comput. Phys. 179, 578592. doi:10.1006/jcph.2002.7075
  14. Li, J. G. 2018. Shallow water equations on a spherical multiple-cell grid. Q. J. R. Meteorol. Soc. 144, 112. doi:10.1002/qj.3139
  15. Nair, R. D., Thomas, S. J. and Loft, R. D. 2005. A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev. 133, 814828. doi:10.1175/MWR2890.1
  16. Pudykiewics, J. A. 2011. On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid. J. Comput. Phys. 230, 19561991. doi:10.1016/j.jcp.2010.11.045
  17. Putman, W. M. and Lin, S.-J. 2007. Finite-volume transport on various cubed-sphere grids. J. Comput. Phys. 227, 5578. doi:10.1016/j.jcp.2007.07.022
  18. Qaddouri, A. and Lee, V. and 2011. The Canadian global environmental multi scale model on the Yin-Yang grid system. Q. J. R. Meteorol. Soc. 137, 19131926. doi:10.1002/qj.873
  19. Ronchi, C., Iacono, R. and Paolucci, P. S. 1996. The cubed sphere: a new method for the solution of partial differential equations in spherical geometry. J. Comput. Phys. 124, 93114. doi:10.1006/jcph.1996.0047
  20. Sadourny, R. 1972. Conservative finite-differencing of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev. 100, 136144. doi:10.1175/1520-0493(1972)100<;0136:CFAOTP>2.3.CO;2
  21. Staniforth, A. J. and Thuburn, J. 2012. Horizontal grids for global weather and climate prediction models: a review. Q. J. R. Meteorol. Soc. 138, 126. doi:10.1002/qj.958
  22. Starius, G. 2014. A solution to the pole problem for the shallow water equations on the sphere. TWMS J. Pure Appl. Math. 5, 152170.
  23. Starius, G. 2018. ‘The Equator-Pole grid system’: An overset grid system for the sphere, with an optimal uniformity property. Tellus A 70, 114.. doi:10.1080/16000870.2018.1541373
  24. Tolstykh, M. A. and Shashkin, V. V. 2012. Vorticity-divergence mass-conserving semi-Lagrangian shallow water model using the reduced grid on the sphere. J. Comput. Phys. 231, 42054233. doi:10.1016/j.jcp.2012.02.016
  25. Ullrich, P. A., Jablonowski, C. and van Leer, B. 2010. High-order finite-volume methods for the shallow-water equations on the sphere. J. Comput. Phys. 229, 61046134. doi:10.1016/j.jcp.2010.04.044
  26. Williamson, D. L. 1968. Integration of the barotropic vorticity equation on a spherical geodesic grid. Tellus 20, 642653.
  27. Williamson, D. L. 2007. The evolution of dynamical cores for global atmospheric model. J. Meteorol. Soc. Jpn. 85B, 241269. doi:10.2151/jmsj.85B.241
  28. Williamson, D. L., Drake, J. B., Hack, J. J., Jakob, R. and Swarztrauber, P. N. 1992. A standard test set for numerical approximation to the shallow water equations in spherical geometry. J. Comput. Phys. 102, 211224. doi:10.1016/S0021-9991(05)80016-6
Language: English
Page range: 1792736 - 1792736
Published on: Jan 1, 2020
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2020 Göran Starius, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.