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.
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.
