From contour plots on a surface having interface boundary, a jump in the value of a variable is observed. Well, this does not happen with interior boundary. So is there any fix for this?
If you are working in fluent, this would mean that the interface has not been defined properly. For continuous flow properties, select the two surfaces at the interface but do not specify any other properties. This would normally define two surface at which all properties and gradients are the same and this make the domain continuous.
you have mesh miss-matching problem at the interface. The mesh resolution as well as the matching boundary condition must be rechecked. Any jump in values show that the conservation laws were been satisfied. At all, I think if you use the Finite volume(if you are) you may have minimum difficulties.
Fluent's guide lines for interface boundaries are followed with specification of "enforce-continuity-after-bc". After doing this Fluent creates new wall at the interfaces which were empty. To realize the problem of discontinuity at the interface, please simulate a simple duct flow with interface boundary. The result at the interface is self explanatory. The problem of discontinuity or jump in flow properties may be inherent in the way the interface is handled by the Fluent or any other commercial software like CFX.