TVD schemes, positive schemes, and the universal limiter

Monthly Weather Review

Volumn 125, Issue 8, 1997, Pages 1990-1993

  Thuburn, John ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000079179     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(1997)125<1990:TSPSAT>2.0.CO;2     Document Type: Article

References (15)

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3. Harten, A., 1983: High resolution schemes for hyperbolic conservalion laws. J. Comput. Phys., 49, 357-393.
4. Hundsdorfer, W., B. Koren, M. van Loon, and J. G. Verwer, 1995: A positive finite-difference advection scheme. J. Comput. Phys., 117, 35-46.
5. Lax, P. D., and B. Wendroff, 1960: Systems of conservation laws. Commun. Pure Appl. Math., 13, 217-237.
6. Leonard, B. P., 1979: A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng., 19, 59-98.
7. _, 1991: The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput. Methods Appl. Mech. Eng., 88, 17-74.
8. Roe, P. L., and M. J. Baines, 1983: Asymptotic behaviour of some non-linear schemes for linear advection. Proceedings of the 5th GAMM Conference on Numerical Methods in Fluid Mechanics, M. Pandolfi and R. Piva, Eds., Vieweg, 283-290.
9. Sweby, P. K., 1985: High resolution TVD schemes using flux limiters. Lect. Appl. Math., 22, 289-309.
10. Thuburn, J., 1993: Use of a flux-limited scheme for vertical advection in a GCM. Quart. J. Roy. Meteor. Soc., 119, 469-487.
11. _, 1996: Multidimensional flux-limited advection schemes. J. Comput. Phys., 123, 74-83.
12. 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.
13. van Leer, B., 1974: Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second order scheme. J. Comput. Phys., 14, 361-370.
14. Zalesak, S. T., 1979: Fully multidimensional flux corrected transport algorithms for fluids. J. Comput. Phys., 31, 335-362.
15. _, 1987: A preliminary comparison of modern shock-capturing schemes: Linear advection. Advances in Computer Methods for Partial Differential Equations VI, R. Vichnevetsky and R. S. Stapleton, Eds., IMACS, 15-22.