Although for classical models of diffusive shock acceleration (DSA) at supernova remnants (SNRs) it is hard to reach PeV energies, SNRs are still believed to contribute a large amount of the total Galactic cosmic-ray luminosity. Nowadays it is clear that SNRs show a significant temporal evolution of those parameters relevant for the transport and acceleration of CRs within and the escape from them; the magnetic field for example can change from being mainly radial to tangential with increasing age of the SNRs. Thus, for an accurate description of CR acceleration over the lifetime of the source, time-dependent models are required, dropping the assumption of parallel shocks. At regions where the shock is oblique, drifts of CRs have to be taken into account. In the case of strong external magnetic fields, such as at SN 1006, the situation becomes even more interesting, drifts potentially drive CRs to regions where the shock is parallel and where DSA is most efficient.

We utilize a new generalized stochastic differential equation solver based on the open source propagation framework CRPropa to model time-dependent DSA in such potential Galactic cosmic-ray sources. We present models of DSA ranging from parallel to perpendicular spherical SNRs, including complex magnetic background fields. Furthermore, we consider anisotropic diffusion which allows CRs to cross magnetic field lines, facilitating DSA at almost perpendicular shocks at which otherwise shock drift acceleration takes over.