The monotonic Quartic Spline Method (QSM) for conservative transport problems

Journal of Computational Physics

Volumn 229, Issue 4, 2010, Pages 1150-1166

  Zerroukat, M ^a   Staniforth, A ^a   Wood, N ^a  

^a MET OFFICE   (United Kingdom)

Author keywords

Advection; Conservation; Monotonicity; PPM; PSM; Remapping

Indexed keywords

MASS CONSERVATION; MONOTONICITY; MONOTONICS; PSM; QUARTIC SPLINE; REMAPPING; REMAPPING ALGORITHMS; SPLINE METHODS; SPLITTINGS; TRANSPORT PROBLEMS;

EID: 72049116013     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.10.018     Document Type: Article

References (24)

1. Colella P., and Woodward P. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54 (1984) 174-201
2. Zerroukat M., Wood N., and Staniforth A. SLICE: a semi-Lagrangian inherently conserving and efficient scheme for transport problems. Q. J. Roy. Meteorol. Soc. 128 (2002) 2801-2820
3. Zerroukat M., Wood N., and Staniforth A. SLICE-S: a semi-Lagrangian inherently conserving and efficient scheme for transport problems on the sphere. Q. J. Roy. Meteorol. Soc. 130 (2004) 2649-2664
4. Rančić M. An efficient conservative monotonic remapping for semi-Lagrangian transport algorithms. Mon. Weather Rev. 123 (1995) 1213-1217
5. Laprise J.P.R., and Plante A. A class of semi-Lagrangian integrated mass (SLIM) numerical transport algorithms. Mon. Weather Rev. 123 (1995) 553-565
6. B. Machenhauer, M. Olk, On the development of a cell-integrated semi-Lagrangian shallow water model on the sphere, in: ECMWF Workshop Proceedings: Semi-Lagrangian Methods, ECMWF, Reading, UK, 1996, pp. 213-228.
7. Machenhauer B., and Olk M. The implementation of the semi-implicit cell-integrated semi-Lagrangian models. Atmos.-Ocean 35 (1997) 103-126 (special issue)
8. Xiao F., and Yabe T. Completely conservative and oscillationless semi-Lagrangian schemes for advection transportation. J. Comput. Phys. 170 (2001) 498-522
9. Nair R., and Machenhauer B. The mass conservative cell-integrated semi-Lagrangian advection scheme on the sphere. Mon. Weather Rev. 130 (2002) 649-667
10. Nair R., Scroggs J., and Semazzi F. Efficient conservative global transport schemes for climate and atmospheric chemistry models. Mon. Weather Rev. 130 (2002) 2059-2073
11. Nair R., Scroggs J., and Semazzi F. A forward trajectory global semi-Lagrangian transport scheme. J. Comput. Phys. 190 (2003) 275-294
12. Zerroukat M., Wood N., and Staniforth A. The Parabolic Spline Method (PSM) for conservative transport problems. Int. J. Numer. Meth. Fluid 11 (2006) 1297-1318
13. Zerroukat M., Wood N., and Staniforth A. Application of the Parabolic Spline Method (PSM) to a multi-dimensional conservative transport scheme (SLICE). J. Comput. Phys 225 (2007) 935-948
14. Staniforth A., and Côté J. Semi-Lagrangian integration schemes for atmospheric models - a review. Mon. Weather Rev. 119 (1991) 2206-2223
15. van Leer B. Towards the ultimate conservative difference scheme IV: a new approach to numerical convection. J. Comput. Phys. 23 (1977) 276-299
16. Ahlberg J.H., Nilson E.N., and Walsh J.L. The Theory of Splines and Their Applications. first ed. (1967), Academic Press, London
17. Press W., Teukolsky S., Vetterling W., and Flannery B. Numerical Recipes in FORTRAN: The Art of Scientific Computing. second ed. (1992), Cambridge University Press, Cambridge, UK
18. Zerroukat M., Wood N., and Staniforth A. A monotonic and positive-definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme. Q. J. Roy. Meteorol. Soc. 131 (2005) 2923-2936
19. M. Zerroukat, N. Wood, A. Staniforth, Erratum for: a monotonic and positive-definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme, Q. J. Roy. Meteorol. Soc. 131, 2923-2936, Q. J. Roy. Meteorol. Soc. 134 (2008) 280.
20. White L., and Adcroft A. A high-order finite volume remapping scheme for nonuniform grids: the piecewise quartic method (PQM). J. Comput. Phys. 227 (2008) 7394-7422
21. 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. J. Comput. Phys. 102 (1992) 211-224
22. Hadj A.D.A., and Elouafi M. A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix. Appl. Math. Comput. 202 (2008) 441-445
23. Lin S.J., and Rood R.B. Multidimensional flux-form semi-Lagrangian transport schemes. Mon. Weather Rev. 124 (1996) 2046-2070
24. Lauritzen P.H., and Nair R.D. Monotone and conservative cascade remapping between spherical grids (CaRS): regular latitude-longitude and cubed-sphere grids. Mon. Weather Rev. 136 (2008) 1416-1432