It was proved numerically that the Domain Decomposition Method (DDM) with one layer overlapping grids is identical to the block iterative method of linear algebra equations. The results obtained using DDM could be in reasonable aggeement with the results of full-domain simulation. With the three dimensional solver developed by the authors, the flow field in a pipe was simulated using the full-domain DDM with one layer overlapping grids and with patched grids respectively. Both of the two cases led to the convergent solution. Further research shows the superiority of the DDM with one layer overlapping grids to the DDM with patched grids. A comparison between the numerical results obtained by the authors and the experimental results given by Enayet[3] shows that the numerical results are reasonable.