Diffusion experiments with a global discontinuous galerkin shallow-water model

Monthly Weather Review

Volumn 137, Issue 10, 2009, Pages 3339-3350

  Nair, Ramachandran D ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION DIFFUSION EQUATION; COEFFICIENT OF DIFFUSION; CURVILINEAR COORDINATE SYSTEMS; DIFFUSION COEFFICIENTS; DIFFUSION EXPERIMENTS; DISCONTINUOUS GALERKIN; DISCRETIZATIONS; FIRST ORDER SYSTEMS; LOCAL DISCONTINUOUS GALERKIN METHOD; QUADRILATERAL ELEMENTS; RATE OF CONVERGENCE; REFERENCE SOLUTION; SECOND ORDERS; SHALLOW WATER EQUATIONS; SHALLOW-WATER; SHALLOW-WATER MODELS; SIMULATED RESULTS;

ADVECTION; APPROXIMATION THEORY; GALERKIN METHODS;

DIFFUSION;

ADVECTION-DIFFUSION EQUATION; DIFFUSION; GALERKIN METHOD; NUMERICAL MODEL; SHALLOW-WATER EQUATION;

EID: 70449093424     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/2009MWR2843.1     Document Type: Article

References (28)

1. Arnold, D. N., F. Brezzi, B. Cockburn, and L. D. Marini, 2002: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39, 1749-1779.
2. Bassi, F., and S. Rebay, 1997: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys., 131, 267-279.
3. Burkhardt, U., and E. Becker, 2006: A consistent diffusion-dissipation parameterization in the ECHAM climate model. Mon. Wea. Rev., 134, 1194-1204.
4. Chen, C., and F. Xiao, 2008: Shallow water model on cubed-sphere by multi-moment finite volume method. J. Comput. Phys., 227, 5019-5044.
5. Cockburn, B., and C.-W. Shu, 1998: The local discontinuous Galerkin for convection diffusion systems. SIAM J. Numer. Anal., 35, 2440-2463.
6. Cockburn, B., and C.-W. Shu, 2001: The Runge-Kutta discontinuous Galerkin method for convection-dominated problems. J. Sci. Comput., 16, 173-261.
7. Collins, W. D., and Coauthors, 2004: Description of the NCAR Community Atmosphere Model (CAM3.0). NCAR Tech. Note NCAR/TN-464+STR, National Center for Atmospheric Research, Boulder, CO, 226 pp.
8. Dawson, C., and V. Aizinger, 2002: The local discontinuous Galerkin method for advection-diffusion equations arrising in groundwater and surface water applications. Inst. Math Appl., 131, 231-242.
9. Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp.
10. Galewsky, J., L. M. Polvani, and R. K. Scott, 2004: An initial-value problem to test numerical models of the shallow water equations. Tellus, 56A, 429-440.
11. Gelb, A., and J. P. Gleeson, 2001: Spectral viscosity for shallow water equations in spherical geometry. Mon. Wea. Rev., 129, 2346-2360.
12. Giraldo, F. X., and M. Restelli, 2008: A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases. J. Comput. Phys., 227, 3849-3877.
13. Gottlieb, S., C. W. Shu, and E. Tadmor, 2001: Strong stability preserving high-order time discretization methods. SIAM Rev., 43, 89-112.
14. Henderson, R. D., 1999: Adaptive spectral element method for turbulance and transition. High-Order Methods for Computational Physics, T. J. Barth and H. Deconinck, Eds., Vol. 9, Lecture Notes in Computational Science and Engineering, Springer, 225-324.
15. Karniadakis, G. E., and S. Sherwin, 2005: Spectral/hp Element Methods for Computational Fluid Dynamics. Oxford University Press, 686 pp.
16. Leith, C. E., 1971: Atmospheric predictability and two-dimensional turbulance. J. Atmos. Sci., 28, 145-161.
17. Levy, M. N., R. D. Nair, and H. M. Tufo, 2007: High-order Galerkin method for scalable global atmospheric models. Comput. Geosci., 33, 1022-1035.
18. Nair, R. D., and H. M. Tufo, 2007: Petascale atmospheric general circulation models. J. Phys. Conf. Ser., 78, 012078, doi:10.1088/1742-6596/78/1/012078.
19. Nair, R. D., S. J. Thomas, and R. D. Loft, 2005a: A discontinuous Galerkin global shallow water model. Mon. Wea. Rev., 133, 876-888.
20. Nair, R. D., S. J. Thomas, and R. D. Loft, 2005b: A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 133, 814-828.
21. Nair, R. D., H.-W. Choi, and H. M. Tufo, 2009: Computational aspects of a scalable high-order discontinuous Galerkin atmospheric dynamical core. Comput. Fluids, 38, 309-319.
22. Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer-Verlag, 710 pp.
23. Persson, P.-O., and J. Peraire, 2006: Sub-cell shock capturing for discontinuous Galerkin methods. Proc. 44th AIAA Aerospace Science Meeting and Exhibit, Reno, NV, AIAA, 2006-112.
24. Sadourny, R., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136-144.
25. Smagorinsky, J., 1963: General circulation experiments with the primitive equations: 1. The basic experiment. Mon. Wea. Rev., 91, 99-165.
26. St-Cyr, A., C. Jablonowski, J. M. Dennis, H. M. Tufo, and S. J. Thomas, 2008: A comparison of two shallow water models with non-conforming advaptive grids. Mon. Wea. Rev., 136, 1898-1922.
27. Taylor, M., J. Edwards, S. Thomas, and R. Nair, 2007: A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere. J. Phys. Conf. Ser., 78, 012074, doi:10.1088/ 1742-6596/78/1/012074.
28. Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, 211-224.