The cost-effectiveness of semi-lagrangian advection

Monthly Weather Review

Volumn 124, Issue 12, 1996, Pages 2883-2897

  Bartello, Peter ^a,b   Thomas, Stephen J ^a  

^a ENVIRONMENT CANADA   (Canada)

^b 2121 Voie de Service Nord   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000016565     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(1996)124<2883:TCEOSL>2.0.CO;2     Document Type: Article

References (54)

1. Anselmet, F., Y. Gagne, E. J. Hopfinger, and R. A. Antonia, 1984: High-order velocity structure functions in turbulent shear flows. J. Fluid Mech., 140, 63-89.
2. Baptista, A. M., 1987: Solution of advection-dominated transport by Eulerian-Lagrangian methods using the backwards method of characteristics. Ph.D thesis, Massachusetts Institute of Technology, 260 pp.
3. Bartello, P., 1995: Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci., 52, 4410-4428.
4. _, and G. Holloway, 1991: Passive scalar transport in β-plane turbulence. J. Fluid Mech., 223, 521-536.
5. Basdevant, C., B. Legras, R. Sadourny, and M. Béland, 1981: A study of barotropic model flows: Intermittency, waves and predictability. J. Amos. Sci., 38, 2305-2326.
6. Bates, J. R., and A. McDonald, 1985: Comments on "Some properties and comparitive performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation." Atmos.-Ocean, 23, 193-194.
7. Bermejo, R., 1990: On the equivalence of semi-Lagrangian schemes and particle-in-cell finite element methods. Mon. Wea. Rev., 118, 979-987.
8. Boukir, K., Y. Maday, and B. Métivet, 1994: A high-order characteristics method for the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng., 116, 211-218.
9. Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28, 1087-1095.
10. Courant, R., K. O. Friedrichs, and H. Levvy, 1928: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Annalen, 100, 32-74.
11. _, E. Isaacson, and H. Rees, 1952: On the solution of nonlinear hyperbolic differential equations by finite differences. Commun. Pure Appl. Math., 5, 243-255.
12. Crowley, W. P., 1968: Numerical advection experiments. Mon. Wea. Rev., 96, 1-11.
13. Douglas, J., and T. F. Russell, 1982: Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal., 19, 871-885.
14. Ewing, R. R., T. F. Russell, and M. F. Wheeler, 1984: Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics. Comput. Methods Appl. Mech. Eng., 47, 73.
15. Fjørtoft, R., 1952: On a numerical method of integrating the barotropic vorticity equation. Tellus, 4, 179-194.
16. Frisch, U., M. Lesieur, and A. Brissaud, 1974: A Markovian random coupling model for turbulence. J. Fluid Mech., 65, 145-152.
17. Gage, K. S., and G. D. Nasttom, 1986: Theoretical interpretations of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft during GASP. J. Atmos. Sci., 43, 729-740.
18. Gear, C. W., 1971: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, 253 pp.
19. Holloway, G., and S. S. Kristmannsson, 1984: Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech., 141, 27-50.
20. Kraichnan, R. H., 1967: Intermittency in the very small scales of turbulence. Phys. Fluids, 10, 2080-2082.
21. _, 1971a: An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech., 47, 513-524.
22. _, 1971b: Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech., 47, 525-535.
23. Kwizak, M., and A. Robert, 1971: A semi-implicit scheme for grid point atmospheric models of the primitive equations. Mon. Wea. Rev., 99, 32-36.
24. Lesieur, M., 1990: Turbulence in Fluids. 2d ed. Kluwer, 412 pp.
25. Leslie, D. C., 1973: Developments in the Theory of Turbulence. Clarendon Press, 368 pp.
26. LeVeque, R. J., 1990: Numerical Methods for Conservation Laws. Birkhaüser, 214 pp.
27. Malevsky, A., 1996: Spline-characteristic methods for simulation of convective turbulence. J. Comput. Phys., 123, 466-475.
28. McDonald, A., 1987: Accuracy of multiply-upstream, semi-Lagrangian advective schemes II. Mon. Wea. Rev., 115, 1446-1450.
29. McGregor, J. L., 1993: Economical determination of departure points for semi-Lagrangian models. Mon. Wea. Rev., 121, 221-230.
30. Oliveira, A., and A. M. Baptista, 1995: A comparison of integration and interpolation Eulerian-Lagrangian methods. Int. J. Numer. Methods Fluids, 21, 183-204.
31. Ostiguy, L., and J. P. R. Laprise, 1990: On the positivity of mass in commonly used numerical transport schemes. Atmos.-Ocean, 28, 147-161.
32. Pinty, J.-P., R. Benoit, E. Richard, and R. Laprise, 1995: Simple tests of a semi-implicit semi-Lagrangian model on 2D mountain wave problems. Mon. Wea. Rev., 123, 3042-3058.
33. Pironneau, O., 1982: On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. Numer. Math., 38, 309-332.
34. Priestley, A., 1994: Exact projections and the Lagrange-Galerkin method: A realistic alternative to quadrature. J. Comput. Phys., 112, 316-333.
35. Pudykiewicz, J., and A. Staniforth, 1984: Some properties and comparitive performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation. Atmos.-Ocean, 22, 283-308.
36. _, R. Benoit, and A. Staniforth, 1985: Preliminary results from a partial LRTAP model based on an existing meteorological forecast model. Atmos.-Ocean, 23, 267-303.
37. Purser, R. J., and L. M. Leslie, 1991: An efficient interpolation procedure for high-order three-dimensional semi-Lagrangian models. Mon. Wea. Rev., 119, 2492-2498.
38. Rančić, M., 1995: An efficient, conservative, monotonic remapping for semi-Lagrangian transport algorithms. Mon. Wea. Rev., 123, 1213-1217.
39. Ritchie, H., C. Temperton, A. Simmons, M. Hortal, T. Davies, D. Dent, and M. Hamrud, 1995: Implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model. Mon. Wea. Rev., 123, 489-514.
40. Roache, P. J., 1992: A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids, 15, 1259-1275.
41. Robert, A., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proc. of the WMO/IUGG Symp. on NWP, Tokyo, Japan, Japan Meteor. Agency, 19-24.
42. _, 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.-Ocean., 19, 35-46.
43. _, 1993: Bubble convection experiments with a semi-implicit formulation of the Euler equations. J. Atmos. Sci., 50, 1865-1873.
44. Sawyer, J. S., 1963: A semi-Lagrangian method of solving the vorticity advection equation. Tellus, 15, 336-342.
45. Smolarkiewicz, P. K., and G. A. Grell, 1992: A class of monotone interpolation schemes. J. Comput. Phys., 101, 431-440.
46. _, and J. Pudykiewicz, 1992: A class of semi-Lagrangian approximations for fluids. J. Atmos. Sci., 49, 2082-2096.
47. Staniforth, A., and J. Pudykiewicz, 1985: Reply to comments on and addenda to "Some properties and comparitive performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation." Atmos.-Ocean, 23, 195-200.
48. _, and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models - A review. Mon. Wea. Rev., 119, 2206-2223.
49. Süli, E., 1988: Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations. Numer. Math., 53, 459.
50. Tanguay, M., A. Robert, and R. Laprise, 1990: A semi-implicit semi-Lagrangian fully compressible forecast model. Mon. Wea. Rev., 118, 1970-1980.
51. Temperton, C., and A. Staniforth, 1987: An efficient two-time-level semi-Lagrangian semi-implicit integration scheme. Quart. J. Roy. Meteor. Soc., 113, 1025-1039.
52. Thomas, S., and J. Côté, 1995: Massively parallel semi-Lagrangian advection. J. Simulation, Practice and Theory, 3, 223-238.
53. Vreugdenhil, C. B., and B. Koren, 1993: Notes on Numerical Fluid Mechanics. Vol. 45, Numerical Methods for Advection Diffusion Problems, Vieweg, 373 pp.
54. Wiin-Nielson, A., 1959: On the application of trajectory methods in numerical forecasting. Tellus, 11, 180-196.