Numerical schemes
PMML has developed a new forward-in-time semi-Lagrangian advection scheme. The one-dimensional cubic splines are applied to transform the values and locations between Euler coordinates and Lagrangian coordinates in a 2-D or 3-D domain. This method is more accurate than the conventional semi-Lagrangian advection schemes. This scheme is positive-definite and mass conserved when the variational principle is used to control the total mass. (Sun et al. 1996, Sun and Yeh 1997, Sun and Sun 2004).
Illustrations
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Numerical simulation and vertical profiles of analytic solution (dashed line) and numerical result (solid line) of Doswell’s idealized cyclogenesis after 16 time steps with CN = 4.243, revolution = 4.386 and δ = 2.0 with mass correction Ms + ge but without internet filter. (Sun and Sun 2004) |
Publications
Sun, W. Y. and M. T. Sun, 2004: Mass Correction Applied to Semi-Lagrangian Advection Scheme. Mon. Wea. Rev. 132, 4, 975–984.
Sun, W. Y., 2002: Numerical modeling in the atmosphere. J. Korean Meteorol. Soc. 38, 3, 237–251.
Chen, S. H., and W. Y. Sun, 2002: The applications of the multigrid method and a flexible hybrid coordinate in a nonhydrostatic model. Mon. Wea. Rev. 129, 2660–2676.
Hsu, W.-R., and W. Y. Sun, 2001: A time-split, forward-backward numerical model for solving a nonhydrostatic and compressible system of equations. Tellus 53A, 279–299.
Sun, W. Y., and K. S. Yeh., 1997: A general semi-Lagrangian advection scheme employing forward trajectories. Q. J. R. Meteorol. Soc. 123, 2463–2476.
Sun, W. Y., K. S. Yeh, and R. Y. Sun, 1996: A simple Semi-Lagrangian Scheme for advection equation. Q. J. R. Meteorol. Soc. 122, 1211–1226.
Sun, W. Y., 1995: Pressure gradient in a sigma coordinate. Terrestrial, Atmospheric and Oceanic Sciences 4, 579–590.
Sun, W. Y., 1993: Numerical experiments for advection equation. J. of Comput. Phys. 108, 264–271.
Sun, W. Y., 1993: Comments on “A comparative study of numerical advection scheme featuring a one-step modified WKL algorithm.” Mon. Wea. Rev. 121, 310–311.
Sun, W. Y., 1984a: Numerical analysis for hydrostatic and nonhydrostatic equations of inertial-internal Gravity Waves. Mon. Wea. Rev. 112, 259–268.
Sun, W. Y., 1982: A comparison of two explicit time integration schemes applied to the transient heat equation. Mon. Wea. Rev. 110, 1645–1652.
Sun, W. Y., 1980: A forward-backward time integration scheme to treat internal gravity waves. Mon. Wea. Rev. 108, 402–407.