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A simple and efficient locally mass conserving semi-Lagrangian transport scheme Cover

A simple and efficient locally mass conserving semi-Lagrangian transport scheme

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Open Access
|Jan 2008

References

  1. Arakawa , A. and Lamb , V. 1977 . Computational design and the basic dynamical processes of the UCLA general circulation model . Methods Comput. Phys . 17 , 173 265 .
  2. Bates , J. R. , Moorthi , S. and Higgins , R. W. 1993 . A global multilevel atmospheric model using a vector semi-lagrangian finite-difference scheme. part I: adiabatic formulation . Mon. Wea. Rev . 121 , 244 263 .
  3. Cotter , C. J. , Frank , J. and Reich , S . 2007 . The remapped particle-mesh semi-lagrangian advection scheme. Quart. J. Roy. Meteor Soc . 133 , 251 - 260 .
  4. Doswell , C. A. 1994 . A kinematic analysis of frontogenesis associated with a nondivergent vortex . J. Atmos. Sci . 41 , 1242 1248 .
  5. Durran , D. R. and Reinecke , P. A. 2004 . Instability in a class of explicit two-time-level semi-lagrangian schemes . Quart. J. Roy. Meteor Soc . 130 , 365 369 .
  6. Hólm , E. 1995 . A fully two-dimensional, nonoscillatory advection scheme for momentum and scalar transport equations . Mon. Wea. Rev . 123 , 536 552 .
  7. Jóckel , P. , von Kuhlman , R. , Lawrence , M. G. , Steil , B. , Brenninkmei-jer , C. A. M. , and co-authors. 2001. On a fundamental problem in implementing flux-form advection schemes for tracer transport in 3-dimensional general circulation and chemistry transport models. Quart. J. Roy. Meteor. Soc . 127 , 1035 - 1052 .
  8. Kaas , E. , Guldberg , A. and Lopez , P. 1997 . A lagrangian advection scheme using tracer points. In: Numerical Methods in Atmospheric and Oceanic Modelling-The Andre J. Robert Memorial Volume (eds C. Lin , R. Laprise and H. Ritchie ), pp. 171 - 194. CMOS/NRC Re-search Press (Companion volume to Atmosphere-Ocean), Canada .
  9. Laprise , L. P. R. and Plante , A. 1995 . A class of semi-lagrangian integrated-mass (SLIM) numerical transport algorithm . Mon. Wea. Rev . 123 , 553 565 .
  10. Lauritzen , P. H. 2005 . An Inherently Mass-Conservative Semi-Implicit Semi-Lagrangian Model. PhD Thesis, COGCI, University of Copen-hagen, Niels Bohr Institute, Juliane Manes Vej 30, DK-2100 Copen-hagen Denmark.
  11. Lauritzen , P. H. , Koos , E. and Machenhauer , B . 2006 . A mass-conservative semi-implicit, semi-lagrangian limited-area shallow wa-ter model on the sphere. Mon. Wea. Rev . 134 , 1196 - 1212 .
  12. Leonard , B. P. , Lock , A. P. and Macvean , M. K. 1996 . Conservative explicit unrestricted time step multidimensional constancy-preserving advection schemes. Mon. Wea. Rev . 124 , 2588 - 2606 .
  13. Leslie , M. L. and Purser , R. J. 1995 . Three-dimensional mass-conserving semi-lagrangian scheme employing forward trajectories . Mon. Wea. Rev . 123 , 2551 2566 .
  14. Lin , S.-J. 2004 . A “vertically lagrangian” finite-volume dynamical core for global models . Mon. Wea. Rev . 132 , 2293 2307 .
  15. Lin , S.-J. and Rood , R. B. 1996 . Multidimensional flux-form semi-lagrangian transport schemes . Mon. Wea. Rev . 124 , 2064 2070 .
  16. Lindberg , K. and Alexeev , V. A. 2000 . A study of the spurious orographic resonance in semi-implicit semi-lagrangian models . Mon. Wea. Rev . 128 , 1982 1989 .
  17. Machenhauer , B. and Olk , M. 1997 . The implementation of the semi-implicit scheme in cell-integrated semi-lagrangian models. In: Numerical Methods in Atmospheric and Oceanic Modelling-The Andre J. Robert Memorial Volume, (eds C. Lin , R. Laprise and H. Ritchie ), 103-126. CMOS/NRC Research Press (Companion volume to Atmosphere-Ocean), Canada.
  18. McGregor , J. L. 1993 . Economical determination of departure points for semi-lagrangian models . Mon. Wea. Rev . 121 , 221 230 .
  19. Nair , R. D. , Cote , J. and Staniforth , A. 1999 . Monotonic cascade inter-polation for semi-lagrangian advection. Quart. J. Roy. Meteor Soc . 125 , 197 - 212 .
  20. Nair , R. D. and Machenhauer , B. 2002 . The mass-conservative cell-integrated semi-lagrangian advection scheme on the sphere . Mon. Wea. Rev . 130 , 649 667 .
  21. Nair , R. D. , Scroggs , J. S. and Semazzi , E H. M. 2002. Efficient conser-vative global transport schemes for climate and atmospheric chemistry models. Mon. Wea. Rev . 130 , 2059 - 2073 .
  22. Ranèié , M. 1995 . An efficient, conservative, monotone remapping for semi-lagrangian transport algorithms . Mon. Wea. Rev . 123 , 1213 1217 .
  23. Rasch , P. J. and Williamson , D. L. 1990 . Computational aspects of mois-ture transport in global models of the atmosphere . Quart. J. Roy. Me-teor Soc . 116 , 1071 1090 .
  24. Reich , S. 2007 . An explicit and conservative remapping strategy for semi-lagrangian advection . Atm. Sci. Let . 8 , 58 68 .
  25. Rivest , C. , Staniforth , A. and Robert , A. 1994 . Spurious resonant re-sponse of semi-lagrangian discretizations to orographic forcing: Di-agnosis and solution . Mon. Wea. Rev . 122 , 366 376 .
  26. Robert , A. 1981 . A stable numerical integration scheme for the primitive meteorological equations . Atmos.-Ocean 19 , 35 46 .
  27. Robert , A. 1982 . A semi-lagrangian and semi-implicit numerical inte-gration scheme for the primitive meteorological equations . J. Meteor Soc. Japan 60 , 319 325 .
  28. Robert , A. , Henderson , J. and Turnbull , C. 1972 . An implicit time inte-gration scheme for baroclinic models of the atmosphere . Mon. Wea. Rev . 100 , 329 335 .
  29. Staniforth , A. and Cote , J. 1991 . Semi-lagrangian integration schemes for atmospheric models - a review . Mon. Wea. Rev . 119 , 2206 2223 .
  30. Temperton , C. and Staniforth , A. 1987 . An efficient two-time-level semi-lagrangian semi-implicit integration scheme . Quart. J. Roy. Meteor Soc . 113 , 1025 1039 .
  31. Xiao , F. , Yabe , T. , Peng , X. and Kobayashi , H. 2002 . Conservative and oscillation-less atmospheric transport schemes based on rational func-tions . J. Geophys. Res . 107 ( D22 ), 4609 .
  32. Zalezak , S. T. 1979 . Fully multidimensional flux-corrected transport al-gorithms for fluid . J. Comput. Phys . 31 , 335 362 .
  33. Zerroukat , M. , Wood , N. and Staniforth , A. 2002 . SLICE: A semi-lagrangian inherently conserving and efficient scheme for transport problems . Quart. J. Roy. Meteor Soc . 128 , 801 820 .
  34. Zerroukat , M. , Wood , N. and Staniforth , A. 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 .
  35. Zerroukat , M. , Wood , N. and Staniforth , A. 2006 . The parabolic spline method (PSM) for conservative transport problems . Int. J. Numer Meth. Fluid 11 , 1297 1318 .
  36. Zerroukat , M. , Wood , N. and Staniforth , A. 2007 . Application of the parabolic spline method (PSM) to a multi-dimensional conservative semi-lagrangian transport scheme (SLICE) . J. Comput. Phys . 225 ( 1 ) 935 948 .
Language: English
Page range: 305 - 320
Submitted on: Aug 7, 2007
Accepted on: Nov 5, 2007
Published on: Jan 1, 2008
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 2008 Eigil Kaas, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.