Simulation of the acoustics of coupled rooms is an important problem not only in architectural acoustics but also in immersive audio applications that require acoustic simulation at interactive rates. Requirements for such applications are less demanding for accuracy but more demanding for computational cost. Scattering delay network (SDN) is a real-time, interactive room acoustics simulator for cuboid rooms. SDN affords an exact simulation of first-order early reflections, a gracefully degrading simulation of second and higher-order specular reflections and an accurate simulation of the statistical properties of the late reverberation. We propose coupled-volume SDN (CV-SDN) as an extension of the SDN model to simulate acoustics of coupled volumes. The proposed model retains the desirable characteristics of the original SDN model while allowing the simulation of double-slope decays with direct control over the simulated aperture size. The double-slope characteristics of room impulse responses simulated with CV-SDN agree well with those of measured impulse responses from a scale model and state-of-the-art room acoustics simulation software.