AN IMPROVED SEMI-IMPLICIT TIME DIFFERENCE SCHEME OF SPECTRAL MODEL AND NUMERICAL APPLICATIONS  

作　　者：张朝林 yahoo.com. 郑庆林 宋青丽 

机构地区：[1]Dr.ZHANG Chaolin,Beijing Urban Meteorological Research Institute,Beijing Meteorological Bureau,No.44 Zizhuyuan Road.Haidian District.Beijing 100089,P.R.China,Phone:[phone]-6276.E-mail:c_lzhang [2]Chinese Academy of Meteorological Sciences,Beijing 100081

出　　处：《Acta meteorologica Sinica》2002年第2期180-194,共15页

基　　金：The project is supported by the Beijing New Star Program of Science and Technology of China during 2001-2004 under Grant No.H013610330119.

摘　　要：In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation. Additionally,due to using time difference on two terms at different time.the popular scheme artificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partly using semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.In fact,the popular semi-implicit time difference scheme of spectral model still includes some important linear terms using time explicit difference scheme,and the major terms are directly related to fast internal-and external-gravity waves in the atmospheric forecasting equation. Additionally,due to using time difference on two terms at different time.the popular scheme artificially introduces unbalance between pressure gradient force and Coriolis force terms while numerically computing their small difference between large quantities.According to the computational stability analysis conducted to the linear term time difference scheme in simple harmonic motion equation,one improved semi-implicit time difference scheme is also designed in our study.By adopting a kind of revised time-explicit-difference scheme to these linear terms that still included in spectral model governing equations,the defect of spectral model which only partly using semi-implicit integrating scheme can be overcome effectively.Moreover,besides all spectral coefficients of prognostic equations,especially of Helmholtz divergence equation,can be worked out without any numerical iteration,the time-step (computation stability) can also be enlarged (enhanced) by properly introducing an adjustable coefficient.

关 键 词：spectral model SEMI-IMPLICIT time difference scheme numerical experiment computational stability 

分 类 号：P435[天文地球—大气科学及气象学]