Abstract: It is difficult to deal with complex geometric regions for numerical simulation of convections.The auto-adaptive Cartesian grid approach is able to tackle the problem easily.But,up to now,it is mainly applied to solving compressible outer flows of Euler equations and Navier-Stokes equations.This paper simulated two convection cases of incompressible inner flow.The two cases were also simulated by STAR-CD,a commercial CFD code.The simulation results by auto-adaptive Cartesian grid approach and STAR-CD were compared and consistencies were shown.So the auto-adaptive Cartesian grid approach is suitable to be applied to simulating convection problems.