Impact Factor:1.847
DOI number:10.1002/fld.1947
Journal:International Journal for Numerical Methds in Fluids
Abstract:To investigate the potential of the fourth-order compact difference scheme within the specific context of numerical atmospheric models, a linear baroclinic adjustment system is discretized, using a variety of candidates for practically meaningful staggered 3D grids. A unified method is introduced to derive the dispersion relationship of the baroclinic geostrophic adjustment process. Eight popular 3D grids are obtained by combining contemporary horizontal staggered grids, such as the Arakawa C and Eliassen grids, with optimal vertical grids, such as the Lorenz and Charney-Phillip (CP) grids, and their time-staggered versions. The errors produced on the 3D grids in describing the baroclinic geostrophic adjustment process relative to the differential case are compared in terms of frequency and group velocity components with the elimination of implementation error. The results show that by utilizing the fourth-order compact difference scheme with high precision, instead of the conventional second-order centered difference scheme, the errors in describing baroclinic geostrophic adjustment process decrease but only when using the combinations of the horizontally staggered Arakawa C grid and the vertically staggered CP or the C/CP grid, the time-horizontally staggered Eliassen (EL) and and vertically staggered CP or the EL/CP grid, the C grid and the vertically time-staggered versions of Lorenz (LTS) grid or C/LTS grid, EL grid and LTS grid or EL/LTS grid. The errors were found to increase for specific waves on the rest grids. It can be concluded that errors produced on the chosen 3D grids do not universally decrease when using the fourth-order compact difference scheme; hence, care should be taken when implementing the fourth-order compact difference scheme, otherwise, the expected benefits may be offset by increased errors.
Volume:61
Issue:1
Page Number:106-118
Translation or Not:no
Included Journals:SCI
Date of Publication:2008-10-29