Conservative explicit unrestricted-time-step multidimensional constancy-preserving advection schemes

Monthly Weather Review

Volumn 124, Issue 11, 1996, Pages 2588-2626

  Leonard, B P ^a,c   Lock, A P ^b   Macvean, M K ^b  

^a UNIVERSITY OF AKRON   (United States)

^b MET OFFICE   (United Kingdom)

^c The University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000553762     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(1996)124<2588:ceutsm>2.0.co;2     Document Type: Article

References (25)

1. Dukowicz, J. K., and J. D. Ramshaw, 1979: Tensor viscosity method for convection in numerical fluid dynamics. J. Comput. Phys., 32, 71-79.
2. Easter, R. C., 1993: Two modified versions of Bott's positive-definite numerical advection scheme. Mon. Wea. Rev., 121, 297-304.
3. Ekebjærg, L., and P. Justesen, 1991: An explicit scheme for advection-diffusion modelling in two dimensions. Comp. Meth. Appl. Mech. Eng., 88, 287-297.
4. Hólm, E. V., 1995: A fully two-dimensional, nonoscillatory advection scheme for momentum and scalar transport equations. Mon. Wea. Rev., 123, 536-551.
5. Hundsdorfer, W., and E. J. Spee, 1995: An efficient horizontal advection scheme for modeling of global transport of constituents. Mon. Wea. Rev., 123, 3554-3564.
6. Lax, P. D., and B. Wendroff, 1960: Systems of conservation laws. Comm. Pure Appl. Math., 13, 217-237.
7. Leith, C. E., 1965: Numerical simulation of the earth's atmosphere. Meth. Comput. Phys., 4, 1-28.
8. Leonard, B. P., 1991: The ULTIMATE conservative difference scheme applied to one-dimensional advection. Comp. Meth. Appl. Mech. Eng., 88, 17-74.
9. _, 1994: Note on the von Neumann stability of explicit one-dimensional advection schemes. Comp. Meth. Appl. Mech Eng., 118, 29-46.
10. _, and M. K. MacVean, 1995: Grid-refinement study of a benchmark problem using the flux-integral method. Quantification of Uncertainty in Computational Fluid Dynamics, R. W. Johnson and E. D. Hughes, Eds., American Society of Mechanical Engineers, 40-50.
11. _, _, and A. P. Lock, 1993: Positivity-preserving numerical schemes for multidimensional advection. NASA TM 106055, ICOMP-93-05, Lewis Research Center, Cleveland, OH, 62 pp.
12. _, A. P. Lock, and M. K. MacVean, 1995a: The NIRVANA scheme applied to one-dimensional advection. Int. J. Numer. Methods Heat Fluid Flow, 5, 341-377.
13. _, M. K. MacVean, and A. P. Lock, 1995b: The flux integral method for multidimensional convection and diffusion. Appl. Math. Modelling, 19, 333-342.
14. _, A. P. Lock, and M. K. MacVean, 1995c: Extended numerical integration for genuinely multidimensional advective transport insuring conservation. Numerical Methods in Laminar and Turbulent Flow, Vol. 9, C. Taylor and P. Durbetaki, Eds., Pineridge Press, 1-12.
15. Lin, S. J., and R. B. Rood, 1996: Multidimensional flux-form semi-Lagrangian transport schemes. Mon. Wea. Rev., 124, 2046-2070.
16. Rasch, P. J., 1994: Conservative shape-preserving two-dimensional transport on a spherical reduced grid. Mon. Wea. Rev. 122, 1337-1350.
17. Roache, P. J., 1992: A flux-based modified method of characteristics. Int. J. Numer. Methods Fluids, 15, 1259-1275.
18. Smolarkiewicz, P. K., 1982: The multi-dimensional Crowley advection scheme. Mon. Wea. Rev., 110, 1968-1983.
19. _, 1984: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comput. Phys., 54, 325-362.
20. _, and P. J. Rasch, 1991: Monotone advection on the sphere: An Eulerian versus semi-Lagrangian approach. J. Atmos. Sci., 48, 793-810.
21. Staniforth, A., and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models - A review. Mon. Wea. Rev., 119, 2206-2223.
22. _, _, and J. Pudykiewicz, 1987: Comments on "Smolarkiewicz's deformational flow." Mon. Wea. Rev., 115, 894-900.
23. Strang, G., 1968: On the construction and comparison of difference schemes. SIAM J. Numer. Anal., 5, 506-517.
24. Thuburn, J., 1996: Multidimensional flux-limited advection schemes. J. Comput. Phys., 123, 74-83.
25. Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31, 335-362.