Inherently conservative nonpolynomial-based remapping schemes: Application to semi-Lagrangian transport

Monthly Weather Review

Volumn 136, Issue 12, 2008, Pages 5044-5061

  Norman, Matthew R ^a   Nair, Ramachandran D ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION SCHEMES; BASELINE METHODS; CARTESIANS; CASCADE SCHEMES; COMPUTATIONAL TIME; DEFORMATIONAL FLOWS; GLOBAL ERRORS; HYPERBOLIC METHODS; LOCAL EXTREMUM; MULTI-DIMENSIONAL PROBLEMS; NON-SMOOTH FUNCTIONS; NONSMOOTH DATUM; ORDER OF CONVERGENCES; PIECE WISE; PIECEWISE PARABOLIC METHODS; RATIONAL METHODS; RE MAPPINGS; SEMI-LAGRANGIAN; SINE WAVES; SOLID-BODY ROTATIONS; SUB GRIDS; TEST CASE;

DEGRADATION; LAGRANGE MULTIPLIERS; PULSE POSITION MODULATION;

PULSE MODULATION;

BASELINE SURVEY; GEOMETRY; LAGRANGIAN ANALYSIS; MAPPING;

EID: 64149089338     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/2008MWR2499.1     Document Type: Article

References (30)

1. Artebrant, R., and J. H. Schroll, 2005: Conservative logarithmic reconstructions and finite volume methods. SIAM J. Sci. Comput., 27, 294-314.
2. Artebrant, R., and J. H. Schroll, 2006: Limiter-free third order logarithmic reconstruction. SIAM J. Sci. Comput., 28, 359-381.
3. Carpenter, R. L., K. K. Droegemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the piecewise parabolic method (PPM) to meteorological modeling. Mon. Wea. Rev., 118, 586-612.
4. Colella, P., and P. R. Woodward, 1984: The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys., 54, 174-201.
5. Gates, W. L., E. S. Battern, A. B. Kahle, and A. B. Nelson, 1971: A documentation of the Mintz-Arakawa two-level atmospheric general circulation model. Tech. Rep. R-877-ARPA, Rand, Santa Monica, CA, 408 pp.
6. Gravel, S., and A. Staniforth, 1994: A mass-conserving semi-Lagrangian scheme for shallow-water equations. Mon. Wea. Rev., 122, 243-248.
7. Laprise, J. P. R., and A. Plante, 1995: A class of semi-Lagrangian integrated-mass (SLM) numerical transport algorithms. Mon. Wea. Rev., 123, 553-565.
8. Lauritzen, P. H., 2007: A stability analysis of finite-volume advection schemes permitting long time steps. Mon. Wea. Rev., 135, 2658-2673.
9. Lauritzen, and R. D. Nair, 2008: Monotone and conservative cascade remapping between spherical grids (CaRS): Regular latitude-longitude and cubed-sphere grids. Mon. Wea. Rev., 136, 1416-1432.
10. Leslie, L. M., and R. J. Purser, 1995: Three dimensional massconserving semi-Lagrangian schemes employing forward trajectories. Mon. Wea. Rev., 123, 2551-2566.
11. Lin, S. J., 2004: A "vertically Lagrangian" finite-volume dynamical core for global models. Mon. Wea. Rev., 132, 2293-2307.
12. Machenhaur, B. E., E. Kaas, and P. H. Lauritzen, 2008: Finite volume methods in meteorology. Handbook of Numerical Analysis: Special Volume on Computational Methods for the Atmosphere and the Oceans, Elsevier, in press.
13. Marquina, A., 1994: Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws. SIAM J. Sci. Comput., 15, 892-915.
14. Nair, R. D., 2004: Extension of a conservative cascade scheme on the sphere to large Courant numbers. Mon. Wea. Rev., 132, 390-395.
15. Nair, and B. Machenhauer, 2002: The mass-conservative cell-integrated semi-Lagrangian advection scheme on the sphere. Mon. Wea. Rev., 130, 649-667.
16. Nair, and H. M. Tufo, 2007: Petascale atmospheric general circulation models. J. Phys.: Conf. Series, 78, doi:10.1088/1742-6596/ 78/1/012078.
17. Nair, J. Cote, and A. Staniforth, 1999: Monotonic cascade interpolation for semi-Lagrangian advection. Quart. J. Roy. Meteor. Soc., 125, 197-212.
18. Nair, J. S. Scroggs, and F. H. M. Semazzi, 2002: Efficient conservative global transport schemes for climate and atmospheric chemistry models. Mon. Wea. Rev., 130, 2059-2073.
19. Priestley, A., 1993: A quasi-conservative version of the semi-Lagrangian advection scheme. Mon. Wea. Rev., 121, 621-629.
20. Rancic, M., 1995: Efficient, conservative, monotone remapping for semi-Lagrangian transport algorithms. Mon. Wea. Rev., 123, 1213-1217.
21. Serna, S., 2006: A class of extended limiters applied to piecewise hyperbolic methods. SIAM J. Sci. Comput., 28, 123-140.
22. Staniforth, A., and J. Cote, 1991: Semi-Lagrangian integration schemes for atmospheric models: A review. Mon. Wea. Rev., 119, 2206-2223.
23. 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, 221-224.
24. Willmott, C. J., and K. Matsuura, 2005: Advantages of the mean absolute error (MAE) over the mean square error (RMSE) in assessing average model performance. Climate Res., 30, 79-82.
25. Xiao, F., T. Yabe, X. Peng, and H. Kobayashi, 2002: Conservative and oscillation-less atmospheric transport schemes based on rational functions. J. Geophys. Res., 107, 4609, doi:10.1029/ 2001JD001532.
26. Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31, 335-362.
27. Zerroukat, M., N. Wood, and A. Staniforth, 2002: SLICE: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems. Quart. J. Roy. Meteor. Soc., 128, 2801-2820.
28. Zerroukat, M., N. Wood, and A. Staniforth, 2004: SLICE-S: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems on the sphere. Quart. J. Roy. Meteor. Soc., 130, 2649-2664.
29. Zerroukat, M., N. Wood, and A. Staniforth, 2005: A monotonic and positive-definite filter for a semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme. Quart. J. Roy. Meteor. Soc., 131, 2923-2936.
30. Zerroukat, M., N. Wood, and A. Staniforth, 2006: The parabolic spline method (PSM) for conservative transport problems. Int. J. Numer. Methods Fluids, 51 (11), 1297-1318.