The new frontier in the quest for the highest contrast levels in the focal plane of a coronagraph is now the correction of the large diffraction artifacts introduced at the science camera by apertures of increasing complexity. Indeed, the future generation of space- and ground-based coronagraphic instruments will be mounted on on-axis and/or segmented telescopes; the design of coronagraphic instruments for such observatories is currently a domain undergoing rapid progress. One approach consists of using two sequential deformable mirrors (DMs) to correct for aberrations introduced by secondary mirror structures and segmentation of the primary mirror. The coronagraph for the WFIRST-AFTA mission will be the first of such instruments in space with a two-DM wavefront control system. Regardless of the control algorithm for these multiple DMs, they will have to rely on quick and accurate simulation of the propagation effects introduced by the out-of-pupil surface. In the first part of this paper, we present the analytical description of the different approximations to simulate these propagation effects. In Appendix A, we prove analytically that in the special case of surfaces inducing a converging beam, the Fresnel method yields high fidelity for simulations of these effects. We provide numerical simulations showing this effect. In the second part, we use these tools in the framework of the active compensation of aperture discontinuities (ACAD) technique applied to pupil geometries similar to WFIRST-AFTA. We present these simulations in the context of the optical layout of the high-contrast imager for complex aperture telescopes, which will test ACAD on a optical bench. The results of this analysis show that using the ACAD method, an apodized pupil Lyot coronagraph, and the performance of our current DMs, we are able to obtain, in numerical simulations, a dark hole with a WFIRST-AFTA-like. Our numerical simulation shows that we can obtain contrast better than 2×10−9 in monochromatic light and better than 3×10−8 with 10% bandwidth between 5 and 14 λ/D.