Steady axisymmetric source-sink flows of a compressible viscous fluid in a rotating cylinder is simulated numerically. The source and the sink are, respectively, the feed and the dischargo slits at the end plates of the cylinder. Compressibility of the fluid is taken into account in the form of steady-state density stratification in the radial direction formed by rigid body rotatation in the absence of the source and sink. Stream function-vorticity formulation is chosen for this study. Stability problem ocurring at high angular speed is overcome by using upwind difference scheme.
The solution techniques used for the resulting finite difference equations are SOR and SIP（Strongly Implicit Procedure）, and the latter is found to be more efficient for this set of equations. Additionally, when using SIP, we adopted the method devised by Jacobs (1974) to compensate for the error due to the artificial viscosity.
The simulation results give streamlines and axial velocity profiles for the flows through the detached shear layer and the Stewartson layer near the side wall
To check the results of numerical simulation. A model cylinder was driven at an angular velocity of 200-500r.p.m. The air containing paraffine mist as a tracers is fed into the cylinder through the inlet slit at the upper end plate and is withdrawn through the outlet slits at the upper and lower plates.
Values of axial velocity from the present numerical simulation were compared with those from experiments.