Abstract: The Navier-Stokes (N-S) equation with stream function formulation is used as the governing equation.It has no pressure terms or velocity terms compared with the N-S equations,and no vorticity terms or velocity terms compared with the wrticity-stream function equations,awiding the problems of wrticity boundary conditions.The variable is only the stream function term.Considering the upwindfeature of convective term,the upwind scheme is adopted to simulate the 2-D sudden expansion laminar.The results are basically consistent with the experiment results of the Durst and Hybrid Fnnite Analytic Method.On the basic of series of calculations,it establishes the relation between the characteristic value and the Reynolds number, when the main flow deflects after sudden expansion section.This complements the researches on sudden expansion flow.