Computation of the Finite Difference Quotient in Longitude on a Uniform Longitude-latitude Grid in High-latitudes
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摘要: 针对在高纬地区计算纬向差商时,常须把时间步长取得很小,或采取Fourier滤波的问题,提出了可以避免这些困难的差分格式。这种格式可以根据任何给定的、稳定的差分格式构造。在形式上它和后者相同,但要求调整网格距,使之可以取和中纬地区同样大的时间步长,并满足计算稳定性条件。在计算中它很有用,也很方便,几乎没有额外的运算量。而且,如果所根据的格式具有质量或能量守恒性质,新格式也同样具有。Abstract: In consideration of small time step or Fourier filtering having to be taken in the integration of thee grid model in high-latitudes due to the convergence of the grid points near the poles, a difference scheme has been presented, which can avoid such difficulties mentioned above. The scheme can be constructed on the basis of any given finite difference scheme. It is the same as the latter in form, but requires that the grid-length used should be adjusted so as to let the time step to be as large as the one used in midlatitudes and the computational stability criterion to be satisfied. In computation it is convenient and there is nearly no extra operational amount. Furthermore, if the original scheme is mass-or-energy-conserving, the new scheme also has such a property.
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