基于Endlich迭代调整的全球流函数和速度势计算及风场分解与重建

摘要

本文将有限区域求解流函数和速度势的Endlich迭代调整方法(E-T方法)推广至全球区域,并与常用Guass-Seidel迭代求解Poisson方程方法(G-P方法)进行了比较.结果表明:ET方法适应于全球流函数和速度势的计算,其由内向外调整,不需严格考虑边界条件,可消除边界对计算结果的影响;E-T方法能准确分解和重建原始风场,而由于极地边界和差分格式影响,G-P方法求得的旋转风和辐散风之和不能准确重建原始风场,尤其是经向为固定边界时,两极地附近重建风场误差非常明显;E-T方法与G-P方法另一重要差异是前者利用流函数和速度势与风场偏微分关系直接进行迭代求解,不需计算涡度和散度,不但保证了重建风场的准确性,还防止了涡度和散度计算误差带来的二次污染.%The method of Endlich iteration and adjustment (E-T method) for computing stream function and velocity potential in the limited area is used to computing the global stream function and velocity potential,which is compared with the method using the Gauss-Seidel iteration to solve the Poisson equations (G-P method).The results show that the E-T method is appropriate to compute global stream function and velocity potential,which makes the adjustment from inner to outer,i.e.using the value of the center grid to adjust that of surrounding grids.Therefore,the E-T method does not need the exact boundary conditions,and eliminates the influence of the boundary on the results.The E-T method can partition and reconstruct the original wind field with an accurate result.However,because of the influences of boundary conditions and difference schemes,the total of the rotational wind field and divergent wind field obtained by the G-P method is different to the original wind field.In particular,when the meridional boundary has a constant value,the error between the reconstructed wind field and the original wind field is very obvious.Another important difference between the E-T method and the G-P method is that the former directly uses the partial differential equation between the stream function,velocity potential and wind field to make iteration and adjustment.It does not need to calculate the divergence and vorticity of the wind field,which not only guarantees the accurate reconstructed wind field,but also avoids the errors produced from the calculation of the divergence and vorticity.