A Full 'Particle-ln-CeN' Numerical Integration Method Tested for the Shallow Water Equations.

摘要

Most modern atmospheric general circulation models (GCMs) include liquid water as a prognostic variable. The process of advection is in the same models treated by different methods that are usually only considered feasible for relatively smooth varying fields such as wind and mass. The most commonly used schemes are Eulerian centered difference schemes in grid point models, Eulerian spectral schemes using transform method (see Machenhauer 1979) and semi-Lagrangian schemes (see Staniforth and Cote 1991). When a discontinous or sharply varying field such as liquid water content is advected using these schemes, numerical dispersion and diffusion become a serious problem. In spectral models where no numerical dispersion is present, a diffusion with the effect of smoothing is usually needed to prevent non-linear instabilities. Even if the diffusion is avoided for e.g. liquid water content, the spectral truncation will still lead to unphysical "over and under-shootings" - the so called Gibbs phenomenon - near spatial discontinuities generated in the physical parameterization routines.