The spectral element method (SEM) on variable-resolution grids: Evaluating grid sensitivity and resolution-aware numerical viscosity

Geoscientific Model Development

Volumn 7, Issue 6, 2014, Pages 2803-2816

  Guba, O ^a   Taylor, M A ^b   Ullrich, P A ^c   Overfelt, J R ^b   Levy, M N ^d  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUE; NUMERICAL MODEL; SENSITIVITY ANALYSIS; SHALLOW WATER; SPECTRAL ANALYSIS; VISCOSITY;

EID: 84914703502     PISSN: 1991959X     EISSN: 19919603     Source Type: Journal    
DOI: 10.5194/gmd-7-2803-2014     Document Type: Article

References (22)

1. Ainsworth, M. and Wajid, H.: Dispersive and dissipative behavior of the spectral element method, SIAM J. Numer. Anal., 47, 3910-3937, 2009.
2. Baer, F., Wang, H., Tribbia, J., and Fournier, A.: Climate modeling with spectral elements, Mon.Weather Rev., 134, 3610-3624, 2006.
3. Blacker, T. D. and Stephenson, M. B.: Paving: a new approach to automated quadrilateral mesh generation, Int. J. Numer. Meth. Eng., 32, 811-847, 1991.
4. Boville, B.: Sensitivity of simulated climate to model resolution, J. Climate, 4, 469-485, 1991.
5. Dennis, J. M., Edwards, J., Evans, K. J., Guba, O., Lauritzen, P. H., Mirin, A. A., St.-Cyr, A., Taylor, M. A., andWorley, P. H.: CAMSE: a scalable spectral element dynamical core for the Community Atmosphere Model, Int. J. High Perform. C., 26, 74-89, 2012.
6. Dobrev, V., Kolev, T., and Rieben, R.: High-order curvilinear finite element methods for Lagrangian hydrodynamics, SIAM J. Sci. Comput., 34, B606-B641, 2012.
7. Fournier, A., Taylor, M., and Tribbia, J.: The spectral element atmosphere model (SEAM): high-resolution parallel computation and localized resolution of regional dynamics, Mon. Weather Rev., 132, 726-748, 2004.
8. Lauter, M., Giraldo, F. X., Handorf, D., and Dethloff, K.: A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates, J. Comput. Phys., 227, 10226-10242, 2008.
9. Marras, S., Kopera, M. A., and Giraldo, F. X.: Simulation of Shallow Water Jets with a Unified Element-based Continuous/Discontinuous Galerkin Model with Grid Flexibility on the Sphere, Q. J. Roy. Meteor. Soc., in press, 2014.
10. Nair, R. D., Thomas, S., and Loft, R.: A discontinuous Galerkin transport scheme on the cubed-sphere, Mon. Weather Rev., 133, 814-828, 2005.
11. Persson, P.-O. and Strang, G.: A simple mesh generator in MATLAB, SIAM Rev., 46, 329-345, 2004.
12. Rancic, M., Purser, R., and Mesinger, F.: A global shallow-water model using an expanded spherical cube: gnomonic versus conformal coordinates, Q. J. Roy. Meteor. Soc., 122, 959-982, 1996.
13. Ringler, T. D., Jacobsen, D., Gunzburger, M., Ju, L., Duda, M., and Skamarock, W.: Exploring a multi-resolution modeling approach within the shallow-water equations, Mon. Weather Rev., 139, 3348-3368, 2011.
14. Sadourny, R.: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids, Mon. Weather Rev., 100, 136-144, 1972.
15. St.-Cyr, A., Jablonowski, C., Dennis, J. M., Tufo, H. M., and Thomas, S. J.: A comparison of two shallow water models with non-conforming adaptive grids, Mon. Weather Rev., 136, 1898-1922, 2008.
16. Takahashi, Y., Hamilton, K., and Ohfuchi, W.: Explicit global simulation of the mesoscale spectrum of atmospheric motions, Geophys. Res. Lett., 33, L12812, doi: 10.1029/2006GL026429, 2006.
17. Taylor, M. A. and Fournier, A.: A compatible and conservative spectral element method on unstructured grids, J. Comput. Phys., 229, 5879-5895, 2010.
18. Weller, H., Weller, H. G., and Fournier, A.: Voronoi, Delaunay, and block-structured mesh refinement for solution of the shallow-water equations on the sphere, Mon. Weather Rev., 137, 4208-4224, 2009.
19. Williamson, D. L., Drake, J. B., Hack, J. J., Jakob, R., and Swarztrauber, P. N.: A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys., 102, 211-224, 1992.
20. Yu, M., Giraldo, F. X., Peng, M., and Wang, Z.: Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling, J. Comput. Phys., in review, 2014.
21. Zarzycki, C., Jablonowski, C., and Taylor, M.: Using variableresolution meshes to model tropical cyclones in the Community Atmosphere Model, Mon.Weather Rev., 142, 1221-1239, 2014a.
22. Zarzycki, C. M., Levy, M. N., Jablonowski, C., Overfelt, J. R., Taylor, M. A., and Ullrich, P. A.: Aquaplanet Experiments Using CAM's Variable-Resolution Dynamical Core, J. Climate, 27, 5481-5503, doi: 10.1175/JCLI-D-14-00004.1, 2014.b.