This work was carried out under the U.K. Universities Global Atmospheric Modelling Programme funded by the U.K. Natural Environment Research Council.
Boris, J. P., and D. L. Book, 1973: Flux corrected transport. I: SHASTA, a fluid transport algorithm that works. J. Comput. Phys.,11, 38–69.
Crowley, W. P., 1968: Numerical advection experiments. Mon. Wea. Rev.,96, 1–11.
Harten, A., 1983: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys.,49, 357–393.
Hundsdorfer, W., B. Koren, M. van Loon, and J. G. Verwer, 1995: A positive finite-difference advection scheme. J. Comput. Phys.,117, 35–46.
Lax, P. D., and B. Wendroff, 1960: Systems of conservation laws. Commun. Pure Appl. Math.,13, 217–237.
Leonard, B. P., 1979: A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng.,19, 59–98.
——, 1991: The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comput. Methods Appl. Mech. Eng.,88, 17–74.
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.
Sweby, P. K., 1985: High resolution TVD schemes using flux limiters. Lect. Appl. Math.,22, 289–309.
Thuburn, J., 1993: Use of a flux-limited scheme for vertical advection in a GCM. Quart. J. Roy. Meteor. Soc.,119, 469–487.
——, 1996: Multidimensional flux-limited advection schemes. J. Comput. Phys.,123, 74–83.
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.
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.
Zalesak, S. T., 1979: Fully multidimensional flux corrected transport algorithms for fluids. J. Comput. Phys.,31, 335–362.
——, 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.