High-order Galerkin methods for scalable global atmospheric models

Computers and Geosciences

Volumn 33, Issue 8, 2007, Pages 1022-1035

  Levy, Michael N ^a   Nair, Ramachandran D ^b   Tufo, Henry M ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Atmospheric modeling; Cubed sphere; Discontinuous Galerkin methods; High order methods; Spectral element methods; Transport equation

Indexed keywords

COMPUTER SIMULATION; DOMAIN DECOMPOSITION METHODS; FINITE ELEMENT METHOD; GALERKIN METHODS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

ATMOSPHERIC MODELING; CUBED SPHERE; DISCONTINUOUS GALERKIN METHODS; HIGH-ORDER METHODS; SPECTRAL ELEMENT METHODS; TRANSPORT EQUATION;

EARTH ATMOSPHERE;

COMPUTER SIMULATION; DOMAIN DECOMPOSITION METHODS; EARTH ATMOSPHERE; FINITE ELEMENT METHOD; GALERKIN METHODS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

ADVECTION; ATMOSPHERIC MODELING; FINITE ELEMENT METHOD; GALERKIN METHOD;

EID: 34250633578     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cageo.2006.12.004     Document Type: Article

References (22)

1. Baggag, A., Atkins, H., Keyes, D., 1999. Parallel implementation of the discontinuous Galerkin method. NASA/CR-1999-209646 ICASE Report No. 99-35, 8pp.
2. Cheruvu, V., Nair, R.D., Tufo, H.M., 2007. A spectral finite volume transport scheme on the sphere. Applied Numerical Mathematics, 57, in press, doi:10.1016/j.apnum.2006.09.008.
3. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Mathematics of Computation 52 186 (1989) 411-435
4. Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Journal of Scientific Computing 16 3 (2001) 173-261
5. Dennis, J., Levy, M., Nair, R., Tufo, H., Voran, T., 2005. Towards an efficient and scalable discontinuous Galerkin atmospheric model. IEEE International Parallel & Distributed Processing Symposium, vol. 14(14), p. 257a.
6. Deville, M.O., Fisher, P.F., Mund, E.H., 2002. High-order Methods for Incompressible Fluid Flow, Cambridge University Press, Cambridge, 499pp.
7. Gottlieb S., Shu C.W., and Tadmore E. Strong stability preserving high-order time integration methods. SIAM Review 43 (2001) 89-112
8. Harkin, A., 1995. A Legendre spectral element method for the rotational Navier-Stokes equations. Master's Thesis, Massachusetts Institute of Technology, 41pp.
9. Iskandarani M., Levin J., Choi B.-J., and Haidvogel D. Comparison of advection schemes for high-order h-p finite element and finite volume methods. Ocean Modelling 10 (2005) 233-252
10. Karniadakis, G.E., Sherwin, S.J., 1999. Spectral/hp Element Methods for CFD. Oxford University Press, New York, NY, 390pp.
11. Loft, R.D., Thomas, S.J., Dennis, J.M., 2001. Terascale spectral element dynamical core for atmospheric general circulation models. ACM/IEEE Supercomputing 2001 Conference, p. 26.
12. Nair, R.D., Tufo, H.M., 2006. A scalable high-order dynamical core for climate modeling. Proceedings of International Conference on Mesoscale Process in Atmosphere, Ocean, and Environment Systems. IMPA 2006, IITD, New Delhi, India.
13. Nair R.D., Thomas S.J., and Loft R.D. A discontinuous Galerkin global shallow water model. Monthly Weather Review 133 (2005) 876-888
14. Nair R.D., Thomas S.J., and Loft R.D. A discontinuous Galerkin transport scheme on the cubed-sphere. Monthly Weather Review 133 (2005) 814-828
15. Patera A.T. A spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics 54 (1984) 468-488
16. Qiu J., and Shu C.-W. Runge-Kutta discontinuous Galerkin method using WENO limiters. SIAM Journal on Scientific Computing 26 3 (2005) 907-929
17. Rančić M., Purser R.J., and Mesinger F. A global shallow-water model using an expanded spherical cube: Genomic versus conformal coordinates. Royal Meteorological Society Quarterly Journal 122 (1996) 959-982
18. Ronchi C., Iacono R., and Paolucci P.S. The "cubed sphere": a new method for the solution of partial differential equations in spherical geometry. Journal of Computational Physics 124 (1996) 93-114
19. Sadourny R. Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Monthly Weather Review 100 2 (1972) 136-144
20. Taylor M., Tribbia J., and Iskandarani M. The spectral element method for the shallow water equations on the sphere. Journal of Computational Physics 130 (1997) 92-108
21. Washington, W.M., Parkinson, C.L., 2005. An Introduction to Three-dimensional Climate Modeling. University Science Books, Sausalito, CA, 353pp.
22. 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. Journal of Computational Physics 102 (1992) 211-224