Skip to main content
Have a personal or library account? Click to login
An accurate interpolating scheme for semi-Lagrangian advection on an unstructured mesh for ocean modelling Cover

An accurate interpolating scheme for semi-Lagrangian advection on an unstructured mesh for ocean modelling

Tellus
Volume 49 (1997): Issue 1
By: ,   and    
Open Access
|Jan 1997
References

References

  1. Bates , J. R. and McDonald , A . 1982 . Multiply-upstream, semi-Lagrangian advective schemes: Analysis and application to a multilevel primitive equation model. Mon. Wea. Re v . 112 , 1831 – 1842 .
    Search in Google ScholarBack to article
  2. Baumgardner , J. R. and Frederickson , P. O . 1985 . Icosahedral discretization of the two-sphere . Siam J. Numer. Anal . 22 , 1107 – 1115 .
    Search in Google ScholarBack to article
  3. Bermejo , R . 1990 . On the equivalence of semi-Lagrangian and particle-in-cell finite element methods. Mon. Wea. Re v . 118 , 979 – 987 .
    Search in Google ScholarBack to article
  4. Bespalov , A. , Kuznetsov , Y. , Pironneau , O. and Vallet , M. G . 1992 . Fictitious domains with separable preconditioners versus unstructured adapted meshes . Impact of Computing in Science and Engineering 4 , 217 – 249 .
    Search in Google ScholarBack to article
  5. Christakos , G . 1984 . On the problem of permissible covariance and variogram models . Water Resources Research 20 , 251 – 265 .
    Search in Google ScholarBack to article
  6. Cullen , M. J. P . 1974 . Integration of the primitive equations on a sphere using the finite element method . Quart. J. Roy. Soc . 100 , 555 – 562 .
    Search in Google ScholarBack to article
  7. Daley , R . 1991 . Atmospheric data analysis . Cambridge University Press .
    Search in Google ScholarBack to article
  8. Delfiner , P. and Delhomme , J. P . 1973 . Optimum interpolation by kriging. Proceedings of NATO ASI, Display and analysis of spatial data eds. J. C. Davis and M. J. McCullagh , pp. 96 – 114 , John Wiley, New York.
    Search in Google ScholarBack to article
  9. Delfiner , P . 1979 . The intrinsic model of order k. Notes de cours C-77. Centre de Géostatistique , Ecole des Mines de Paris , Fontainebleau , France .
    Search in Google ScholarBack to article
  10. Dubrule , O . 1981 . Krigeage et spline en cartographie automatique. Application à des exemples pétroliers. Thése de Docteur Ingénieur. Centre de Géostatistique , Ecole des Mines de Paris , Fontainebleau , France .
    Search in Google ScholarBack to article
  11. Gilbert , R. , Carrier , R. , Benoit , C. , Soulié , M. and Schiettekatte , J . 1990 . Applications of dual kriging in human factors engineering. Advances in industrial ergonomics and safety (II) . Biman Das , ed. Taylor & Francis, London.
    Search in Google ScholarBack to article
  12. Heikes , R. and Randall , D. A . 1995a . Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part I: basic design and results of tests. Mon. Wea. Re v . 123 , 1862 – 1880 .
    Search in Google ScholarBack to article
  13. Heikes , R. and Randall , D. A . 1995b . Numerical integration of the shallow-water equations on a twisted icosahedral grid. Part II: a detailed description of the grid and an analysis of numerical accuracy. Mon. Wea. Re v . 123 , 1881 – 1887 .
    Search in Google ScholarBack to article
  14. Journel , A. G. and Huijbregts , C. J . 1978 . Mining geostatistics . Academic Press .
    Search in Google ScholarBack to article
  15. Karpic , S. R . 1994 . A spline-based semi-Lagrangian method for advection-dominated transport equations on triangular meshes. Proceedings, 2nd Annual Conf. of the CFD Society of Canada , Toronto. J. J. Gottlieb and C. R. Ethier (eds.), 91 - 98 .
    Search in Google ScholarBack to article
  16. Krige , D. G . 1951 . A statistical approach to some basic mine valuation problems on the Witwatersrand . J. Chem. Metall. MM. Soc. S. Afr . 52 , 119 – 139 .
    Search in Google ScholarBack to article
  17. Leslie , L. M. and Purser , R. J . 1991 . High-order numerics in a three-dimensional time-split semi-Lagrangian forecast model. Mon. Wea. Re v . 119 , 1612 – 1623 .
    Search in Google ScholarBack to article
  18. Lorenc , A. C . 1986 . Analysis methods for numerical weather prediction . Quart. J. Roy. Soc . 112 , 1177 – 1194 .
    Search in Google ScholarBack to article
  19. Matheron , G . 1973 . The intrinsic random functions and their applications . Adv. Appl. Prob . 5 , 439 – 468 .
    Search in Google ScholarBack to article
  20. Matheron , G . 1980 . Splines et krigeage: leur équivalence formelle . Rapport N-667, Centre de Géostatistique, Ecole des Mines de Paris , Fontainebleau , France .
    Search in Google ScholarBack to article
  21. Mcdonald , A . 1984 . Accuracy of multiply-upstream semi-Lagrangian advective schemes. Mon. Wea. Re v . 112 , 1267 – 1275 .
    Search in Google ScholarBack to article
  22. McDonald , A . 1987 . Accuracy of multiply-upstream semi-Lagrangian advective schemes (II). Mon. Wea. Re v . 115 , 1446 – 1450 .
    Search in Google ScholarBack to article
  23. McDonald , A. and Bates , J. R . 1987 . Improving the estimate of the departure point position in a two-time level semi-Lagrangian and semi-implicit scheme. Mon. Wea. Re v . 115 , 737 – 739 .
    Search in Google ScholarBack to article
  24. Morton , K. W . 1985 . Generalized Galerkin methods for hyperbolic problems . Comp. Meth. Appl. Mech. Eng . 52 , 847 – 871 .
    Search in Google ScholarBack to article
  25. Pudykiewicz , J. and Staniforth , A . 1984 . Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation . Atmos. Ocean . 22 , 283 – 308 .
    Search in Google ScholarBack to article
  26. Pudykiewicz , J. , Benoit , R. and Staniforth , A . 1985 . Preliminary results from a partial LRTAP model based on an existing meteorological forecast model . Atmos. Ocean . 23 , 267 – 303 .
    Search in Google ScholarBack to article
  27. Pumell , D. K . 1976 . Solution of the advective equation by upstream interpolation with a cubic spline. Mon. Wea. Re v . 104 , 42 – 48 .
    Search in Google ScholarBack to article
  28. Purser , R. J. and Leslie , L. M . 1988 . A semi-implicit semi-Lagrangian finite-difference scheme using high order spatial differencing on a nonstaggered grid. Mon. Wea. Re v . 116 , 2069 – 2080 .
    Search in Google ScholarBack to article
  29. Raviart , P. A . 1985 . An analysis of particle methods. Numerical methods of fluid dynamics, vol 1127, F. Brezzi , ed. Springer-Verlag , 324 pp.
    Search in Google ScholarBack to article
  30. Robert , A . 1981 . A stable numerical integration scheme for the primitive meteorological equations . Atmos. Ocean . 19 , 35 – 46 .
    Search in Google ScholarBack to article
  31. Robert , A . 1982 . A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations . Jpn. Meteor. Soc . 60 , 319 – 325 .
    Search in Google ScholarBack to article
  32. Robert , A. , Henderson , J. and Turnbull , C . 1972 . An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Re v . 100 , 329 – 335 .
    Search in Google ScholarBack to article
  33. Sadourny , R. , Arakawa , A. and Mintz. 1968 . Integration of the non-divergent barotropic vorticity equations with an icosahedral-hexagonal grid for the sphere. Mon. Wea. Re v . 96 , 351 – 356 .
    Search in Google ScholarBack to article
  34. Sadoumy , R . 1972 . Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Re v . 100 , 136 – 144 .
    Search in Google ScholarBack to article
  35. Staniforth , A. and Pudykiewicz , J . 1985 . Reply to comments on and addenda to some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation . Atmos. Ocean . 23 , 195 – 200 .
    Search in Google ScholarBack to article
  36. Staniforth , A. and Temperton , C . 1986 . Semi-implicit semi-Lagrangian integration schemes for a barotropic finite-element regional model. Mon. Wea. Re v . 114 , 2078 – 2090 .
    Search in Google ScholarBack to article
  37. Staniforth , A. and Côté , J . 1991 . Semi-Lagrangian integration schemes for atmospheric models: a review. Mon. Wea. Re v . 119 , 2206 – 2223 .
    Search in Google ScholarBack to article
  38. 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 .
    Search in Google ScholarBack to article
  39. Trochu , F . 1993 . A contouring program based on dual kriging interpolation . Engineering with Computers 9 , 160 – 177 .
    Search in Google ScholarBack to article
  40. Williamson , D. L . 1968 . Integration of the barotropic vorticity equation on a spherical geodesic grid . Tellus . 20 , 642 – 653 .
    Search in Google ScholarBack to article
  41. Williamson , D. L . 1970 . Integration of the primitive barotropic model over a spherical geodesic grid. Mon. Wea. Re v . 98 , 512 – 520 .
    Search in Google ScholarBack to article
DOI: https://doi.org/10.3402/tellusa.v49i1.12216 | Journal eISSN: 3035-9554
Journal RSS Feed
Language: English
Page range: 119 - 138
Submitted on: Jul 27, 1995
Accepted on: Apr 9, 1996
Published on: Jan 1, 1997
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services

© 1997 Daniel Y. Le Roux, Charles A. Lin, Andrew Staniforth, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 49 (1997): Issue 1
Previous article
Next article