Incorporation of cosmic ray transport into the ZEUS MHD code. Application for studies of Parker instability in the ISM

We present a numerical algorithm for the incorporation of the active cosmic ray transport into the ZEUS-3D mag- netohydrodynamical code. The cosmic ray transport is described by the diusion-advection equation. The applied form of the diusion tensor allows for anisotropic diusion of cosmic rays along and across the magnetic field direction, which is con- trolled by two parameters: the parallel and perpendicular diusion coecients. The implemented numerical algorithm is tested by comparison of the diusive transport of cosmic rays to analytical solutions of the diusion equation. Our method is numeri- cally stable for a wide range of diusion coecients, including the realistic values inferred from the observational data for the Milky Way of about 6 10 28 cm 2 s 1 . The presented algorithm is applied for exemplary simulations of the Parker instability triggered by cosmic rays injected by a single SN remnant.