The "zonal grid method" is widely used to alleviate the difficulties for flow field calculations with complex geometry. In the present study, a patched grid method is employed in the computation of flow fields behind a two-ring flameholder which forms a multiple-connected region. A standard K - ε model is used to close the system. The calculation is performed by using a SIMPLE type algorithm in two subdomains in a body-fitted coordinate system With nonstaggered grid arrangements. The concept of conservative interpolation technique is applied to treat the flux conservation across the interface. The effect of the distance between these two rings on the flow pattern is studied. It is found the distance of the rings either in the axial direction or in the radial direction does not change the strength of the recirculation zone, but alters the flow pattern. The predicted streamlines, the turbulence kinetic energy K, and the reverse mass flow rate are presented. / Master of Science