The relaxation methods (Richardson method and accelerated Liebmann method) and the harmonic-cosine series expansion (H-C) approach to compute the stream function and velocity potential in a limited domain were compared. Theoretical derivations show that the H-C approach takes consideration of the boundary conditions by computing a separate component. It not only has solid physical meanings, but also avoids missing weather systems near boundaries. In addition, this approach can reconstruct the wind field accurately and has much higher computational efficiency than the other two methods. The diagnostic analysis of the rainfall enhancement of typhoon Bilis shows that the following: 1) the horizontal wind cannot be recovered fully by the two relaxation methods, while the H-C approach gives much more accurate and efficient results and preserves the influences of monsoon surge at the southern boundary; 2) the H-C approach presents strong convergent signals previous to the abrupt rainfall enhancement. Therefore, the partitioned non-divergent and irrotational wind obtained from the H-C approach can be used in deeper dynamic studies of weather systems in the future.