A nonoscillatory discontinuous Galerkin transport scheme on the cubed sphere

Monthly Weather Review

Volumn 140, Issue 9, 2012, Pages 3106-3126

  Zhang, Yifan ^a   Nair, Ramachandran D ^b  

^a BROWN UNIVERSITY   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Numerical analysis modeling

Indexed keywords

ATMOSPHERIC TRACER; BENCHMARK TESTS; CARTESIANS; CURVILINEAR COORDINATE; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; DISCRETIZATIONS; ESSENTIALLY NON-OSCILLATORY; NON-ORTHOGONAL; NONOSCILLATORY; NUMERICAL SOLUTION; PARALLEL EFFICIENCY; SMALL AMPLITUDE; SMOOTH REGIONS; SPHERICAL GEOMETRIES; SPURIOUS OSCILLATIONS; THIRD-ORDER; TRANSPORT SCHEMES;

BENCHMARKING; GALERKIN METHODS;

SPHERES;

GALERKIN METHOD; GEOMETRY; NUMERICAL METHOD; NUMERICAL MODEL; WEATHER FORECASTING;

EID: 84867946286     PISSN: 00270644     EISSN: 15200493     Source Type: Journal    
DOI: 10.1175/MWR-D-11-00287.1     Document Type: Article

References (30)

1. Balsara, D. S., C. Altman, C.-D. Munz, and M. Dumbser, 2007: Sub-cell based indicator for troubled zones inRKDGschemes and a novel class of hybrid RKDG1HWENO schemes. J. Comput. Phys., 226, 586-620.
2. Chen, C., and F. Xiao, 2008: Shallow water model on cubed-sphere by multi-moment finite volume method. J. Comput. Phys., 227, 5019-5044.
3. Cockburn, B., 1997: An introduction to the Discontinuous- Galerkin method for convection-dominated problems. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, A. Quarteroni, Ed., Vol. 1697, Lecture Notes in Mathematics, Springer, 151-268.
4. A. Quarteroni, and C.-W. Shu, 1989: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comput., 52, 411-435.
5. A. Quarteroni, S. Hou, and C.-W. Shu, 1990: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comput., 54, 545-581.
6. Flyer, N., and G. B. Wright, 2007: Transport schemes on a sphere using radial basis functions. J. Comput. Phys., 226, 1059-1084.
7. Giraldo, F., J. Hesthaven, and T. Warburton, 2002: Nodal highorder discontinuous Galerkin methods for spherical shallow water equations. J. Comput. Phys., 181, 499-525.
8. Gottlieb, S., C.-W. Shu, and E. Tadmor, 2001: Strong stabilitypreserving high-order time discretization methods. SIAM Rev., 43 (1), 89-112.
9. Iskandarani, M., J. Levin, B.-J. Choi, and D. Haidgovel, 2005: Comparison of advection schemes for high-order h-p finite element and finite volume methods. Ocean Modell., 10, 233-252.
10. Krivodonova, L., 2007: Limiters for high-order discontinuous Galerkin methods. J. Comput. Phys., 226, 879-896.
11. Läuter, M., F. X. Giraldo, D. Handorf, and K. Dethloff, 2008: Adiscontinuous Galerkin method for shallow water equations in spherical triangular coordinates. J. Comput. Phys., 227,10226-10242.
12. LeVeque, R. J., 2002: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, 558 pp.
13. 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.
14. Liu, X.-D., and S. Osher, 1996: Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I. SIAM J. Numer. Anal., 33, 760-779.
15. Luo, H., J. D. Baum, and R. Lohner, 2007: A Hermite WENObased limiter for discontinuous Galerkin method on unstructured grids. J. Comput. Phys., 225, 686-713.
16. Nair, R. D., and C. Jablonowski, 2008: Moving vortices on the sphere: A test case for horizontal advection problems. Mon. Wea. Rev., 136, 699-711.
17. Nair, R. D., and P. H. Lauritzen, 2010: A class of deformational flow test cases for linear transport problems on the sphere. J. Comput. Phys., 229, 8868-8887.
18. Nair, R. D., S. Thomas, and R. Loft, 2005a: A discontinuous Galerkin global shallow water model. Mon. Wea. Rev., 133, 876-888.
19. Nair, R. D., S. Thomas, and R. Loft, 2005b: A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 133, 814-828.
20. Nair, R. D., M. N. Levy, and P. H. Lauritzen, 2011: Emerging numerical methods for atmospheric modeling. Numerical Techniques for Global Atmospheric Models, P. Lauritzen et al., Eds., Vol. 80, Lecture Notes in Computational Science and Engineering, Springer, 251-311.
21. Pudykiewicz, J. A., 2006: Numerical solution of the reactionadvection- diffusion equation on the sphere. J. Comput. Phys., 213, 358-390.
22. Pudykiewicz, J. A., 2011: On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid. J. Comput. Phys., 230, 1956-1991.
23. Qiu, J., and C.-W. Shu, 2005a: Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: Two dimensional case. Comput. Fluids, 34, 642-663.
24. Qiu, J., and C.-W. Shu, 2005b: Runge-Kutta discontinuous Galerkin method using WENO limiters. SIAM J. Sci. Comput., 26, 907-929.
25. Sadourny, R., 1972: Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev., 100, 136-144.
26. Shu, C.-W., 1997: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, A. Quarteroni, Ed., Vol. 1697, Lecture Notes in Mathematics, Springer, 325-432.
27. Ullrich, P. A., C. Jablonowski, and B. van Leer, 2010: High-order finite-volume methods for the shallow-water equations on the sphere. J. Comput. Phys., 229, 6104-6134.
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.
29. Zhang, X., and C.-W. Shu, 2010: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys., 229, 3091-3120.
30. Zhang, X., and C.-W. Shu, 2011: Maximum-principle-satisfying and positivity- preserving high-order schemes for conservation laws: Survey and new developments. Proc. Roy. Soc., A467, 2752-2776.