A comparative study of high-order, quasi-conservative, semi-Lagrangian, and Eulerian advection schemes

Journal of Applied Meteorology

Volumn 36, Issue 5, 1997, Pages 599-613

  Huang, Ching Yuang ^a  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; ATMOSPHERIC POLLUTION; EULERIAN SCHEME; FLOW; LAGRANGIAN SCHEME;

ADVECTION; EULERIAN SCHEMES; FLOW MODELLING; SEMI-LAGRANGIAN SCHEMES;

EID: 0030733831     PISSN: 08948763     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0450(1997)036<0599:ACSOHO>2.0.CO;2     Document Type: Review

References (40)

1. Bermejo, R., 1990: On the equivalence of semi-Lagrangian schemes and particle-in-cell finite element method. Mon. Wea. Rev., 118, 979-987.
2. _, and A. Staniforth, 1992: The conversion of semi-Lagrangian advection schemes to quasi-monotone schemes. Mon. Wea. Rev., 120, 2622-2632.
3. Bott, A., 1989a: A positive definite advection scheme obtained by nonlinear renormalization of the advection flux. Mon. Wea. Rev., 117, 1006-1015.
4. _, 1989b: Reply. Mon. Wea. Rev., 117, 2633-2636.
5. _, 1992: Monotone flux limitation in the area-preserving fluxform advection algorithm. Mon. Wea. Rev., 120, 2592-2602.
6. Carpenter, R. L., Jr., K. K. Drogemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the piecewise parabolic method to meteorological modeling. Mon. Wea. Rev., 118, 586-612.
7. Chlond, A., 1994: Locally modified version of Bott's advection scheme. Mon. Wea. Rev., 122, 111-125.
8. Colella, P., and P. R. Woodward, 1984: The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys., 54, 174-201.
9. Crowley. W. P., 1968: Numerical advection experiments. Mon. Wea. Rev., 96, 1-11.
10. Easter, R. C., 1993: Two modified versions of Bott's positive-definite numerical advection scheme. Mon. Wea. Rev., 121, 297-304.
11. Emde, V. D., 1992: Solving conservation laws with parabolic and cubic splines. Mon. Wea. Rev.. 120, 482-492.
12. Gravel, S., and A. Staniforth, 1992: Variable resolution and robustness. Mon. Wea. Rev., 120, 2633-2640.
13. _, and _, 1994: A mass-conserving semi-Lagrangian scheme for the shallow-water equations. Mon. Wea. Rev., 122, 243-248.
14. Huang, C. Y., 1993: A study of high-order advection schemes in variable resolution. Terr. Atmos. Ocean, 4, 421-440.
15. _, 1994: Semi-Lagrangian advection schemes and Eulerian WKL algorithms. Mon. Wea. Rev., 122, 1647-1658.
16. _, and S. Raman, 1991: A comparative study of numerical advection schemes featuring a one-step modified WKL algorithm. Mon. Wea. Rev., 119, 2900-2918.
17. Krishnamurti, T. N., 1962: Numerical integration of primitive equations by a quasi-Lagrangian advection scheme. J. Appl. Meteor., 1, 508-521.
18. Lin, S.-J., W. C. Chao, Y. C. Sud, and G. K. Waker, 1994: A class of the van Leer-type transport schemes and its application to the moisture transport in a general circulation model. Mon. Wea. Rev., 122, 1575-1593.
19. Long, P. E., Jr., and D. W. Pepper, 1981: An examination of some simple numerical schemes for calculating scalar advection. J. Appl. Meteor., 20, 146-156.
20. Makar, P. A., and S. R. Karpik, 1996: Basis-spline interpolation on the sphere: Applications to semi-Lagrangian advection. Mon. Wea. Rev., 124, 182-199.
21. McGregor, J. L., 1993: Economical determination of departure points for semi-Lagrangian models. Mon. Wea. Rev., 121, 221-230.
22. Navon, I. M., 1981: Implementation of a posteriori methods for enforcing conservation of potential enstrophy and mass in discretized shallow-water equations. Mon. Wea. Rev., 109, 946-958.
23. Priestley, A., 1993: A quasi-conservative version of the semi-Lagrangian advection scheme. Mon. Wea. Rev., 121, 621-629.
24. Pudykiewicz, J., and A. Staniforth, 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.
25. Purnell, D. K., 1976: Solution of the advective equation by upstream interpolation with a cubic spline. Mon. Wea. Rev., 104, 42-48.
26. Rasch, P. J., and D. L. Williamson, 1990: On shape-preserving interpolation and semi-Lagrangian transport. SIAM J. Sci. Stat. Comput., 11, 656-687.
27. Smolarkiewicz, P. K., 1982: The multidimensional Crowley advection scheme. Mon. Wea. Rev., 110, 1968-1983.
28. _, 1983: A simple positive definite advection scheme with small implicit diffusion. Mon. Wea. Rev., 111, 479-486.
29. _, 1984: A full multidimensional positive definite advection algorithm with small implicit diffusion. J. Comput. Phys., 54, 325-362.
30. _, 1989: Comment on "A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes." Mon. Wea. Rev., 117, 2626-2636.
31. _, and T. L. Clark, 1986: A full multidimensional positive definite advection algorithm: Further development and applications. J. Comput. Phys., 67, 396-438.
32. _, and P. J. Rasch, 1991: Monotone advection on the sphere: An Eulerian versus semi-Lagrangian approach. J. Atmos. Sci., 48, 793-810.
33. Staniforth, A., and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models - A review. Mon. Wea. Rev., 119, 2206-2223.
34. _, _, and J. Pudykiewicz, 1987: Comments on "Smolarkiewicz's deformation flow." Mon. Wea. Rev., 115, 894-900.
35. Tremback, C. J., J. Powell, W. R. Cotton, and R. A. Pielke, 1987: The forward-in-time upstream advection scheme: Extension to higher orders. Mon. Wea. Rev., 115, 540-555.
36. van Leer, B., 1977: Toward the ultimate conservative difference scheme. IV: A new approach to numerical convection. J. Comput. Phys., 23, 276-299.
37. _, 1979: Toward the ultimate conservative difference scheme. V: A second order sequel to Godunov's method. J. Comput. Phys., 32, 101-136.
38. Williamson, D. L., and P. J. Rasch, 1989: Two-dimensional semi-Lagrangian transport with shape preserving interpolation. Mon. Wea. Rev., 117, 102-129.
39. _, and _, 1994: Water vapor transport in the NCAR CCM2. Tellus, 46A, 34-51.
40. Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31, 335-362.