A fast solver of the shallow water equations on a sphere using a combined compact difference scheme

Journal of Computational Physics

Volumn 187, Issue 2, 2003, Pages 639-659

  Nihei, Tomonori ^a   Ishii, Katsuya ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Combined compact difference; Compact filter; Shallow water equations; Weather prediction

Indexed keywords

EQUATIONS OF MOTION; HARMONIC ANALYSIS; NUMERICAL METHODS;

COMBINED COMPACT DIFFERENCE; COMPACT DIFFERENCE SCHEME; COMPACT FILTER; FAST SOLVERS; SHALLOW WATER EQUATIONS; SHALLOW-WATER MODELS; SPHERICAL HARMONIC MODELS; STANDARD TESTS; TEST SETS; WEATHER PREDICTION;

SPHERES;

EID: 0037610973     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00152-9     Document Type: Article

References (19)

1. N.A. Adams, K. Shariff, A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems, J. Comput. Phys. 127 (1996) 27.
2. H.-B. Cheong, Double Fourier series on a sphere: applications to elliptic and vorticity equations, J. Comput. Phys. 157 (2000) 327.
3. H.-B. Cheong, Application of double Fourier series to the shallow-water equations on a sphere, J. Comput. Phys. 165 (2000) 261.
4. P.C. Chu, C. Fan, A three-point combined compact difference scheme, J. Comput. Phys. 140 (1998) 370.
5. B. Fornberg, A pseudospectral approach for polar and spherical geometries, SIAM J. Sci. Comput. 16 (5) (1995) 1071.
6. R. Hixon, Prefactored small-stencil compact schemes, J. Comput. Phys. 165 (2000) 522.
7. K. Ishioka, ispack-0.5, GFD Dennou Club, 2000. Available from .
8. R. Jakob-Chien, J.J. Hack, D.L. Williamson, Spectral transform solutions to the shallow water test set, J. Comput. Phys. 119 (1995) 164.
9. M.H. Kobayashi, On a class of Padé finite volume methods, J. Comput. Phys. 156 (1999) 137.
10. S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16.
11. S.-J. Lin, R.B. Rood, An explicit flux-form semi-Lagrangian shallow-water model on the sphere, Quart. J. R. Meteorol. Soc. 123 (1997) 2477.
12. K. Mahesh, A family of high order finite difference schemes with good spectral resolution, J. Comput. Phys. 145 (1998) 332.
13. H.L. Meitz, H.F. Fasel, A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation, J. Comput. Phys. 157 (2000) 371.
14. P.E. Merilees, The pseudospectral approximation applied to the shallow water equations on a sphere, Atmosphere 11 (1973) 13.
15. M. Ranǐć, R.J. Purser, F. Mesinger, A global shallow-water model using an expanded spherical cube: genomic versus conformal coordinates, Quart. J. R. Meteorol. Soc. 122 (1996) 959.
16. J.S. Shang, High-order compact-difference schemes for time-dependent Maxwell equations, J. Comput. Phys. 153 (1999) 312.
17. W.F. Spotz, M.A. Taylor, P.N. Swarztrauber, Fast shallow-water equation solvers in latitude-longitude coordinates, J. Comput. Phys. 145 (1998) 432.
18. S. Sugiura, Fluid calculation on a sphere using combined compact scheme, Master Thesis, Nagoya University, 2000 (in Japanese).
19. D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob-Chien, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211.