A matching method is proposed to connect the computational fluid dynamics (CFD) source region to the computational aeroacoustics propagation region of rotor–stator interaction sound produced in a turbofan engine. The method is based on a modal decomposition across three neighbouring axial interfaces adjacent to the matching interface. The modal amplitudes are determined by a least-squares fit. When slowly varying modes are taken, the interface may be positioned in a duct section of varying cross section. Furthermore, the spurious reflections back into the CFD domain, which result from imperfect reflection-free CFD boundary conditions, can be filtered out by including both left- and right-running modes in the matching. Although the method should be applicable to a wider range of acoustic models, it is implemented and favourably tested for the recently available relatively simple case of slowly varying modes in homentropic potential flow in lined ducts. Homentropic potential flow is a very relevant model for the inlet side and a good model for the bypass side if swirl or other types of vorticity are not dominant in the mean flow. By matching with density or pressure perturbations, any contamination of residual nonacoustical vorticity is avoided.