Within our Galaxy, supernova remnants are believed to be the major sources of cosmic rays up to the knee. However important questions remain regarding the share of the hadronic and leptonic components, and the fraction of the supernova energy channelled into these components. We address such question by the means of numerical simulations that combine a hydrodynamic treatment of the shock wave with a kinetic treatment of particle acceleration. Performing 3D simulations allows us to produce synthetic projected maps and spectra of the thermal and non-thermal emission, that can be compared with multi-wavelength observations (in radio, X-rays, and gamma-rays). Supernovae come in different types, and although their energy budget is of the same order, their remnants have different properties, and so may contribute in different ways to the pool of Galactic cosmic-rays. Our first simulations were focused on thermonuclear supernovae, like Tychos SNR, that usually occur in a mostly undisturbed medium. Here we present our 3D simulations of core-collapse supernovae, like the Cas A SNR, that occur in a more complex medium bearing the imprint of the wind of the progenitor star.