MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration

We present a new code aimed at the simulation of diffusive shock acceleration (DSA), and discuss various test cases which demonstrate its ability to study DSA in its full time-dependent and non-linear developments. We present the numerical methods implemented, coupling the hydrodynamical evolution of a parallel shock (in one space dimension) and the kinetic transport of the cosmic-ray (CR) distribution function (in one momentum dimension), as first done by Falle & Giddings. Following Kang & Jones and collaborators, we show how the adaptive mesh refinement technique greatly helps accommodating the extremely demanding numerical resolution requirements of realistic (Bohm-like) CR diffusion coefficients. We also present the parallelization of the code, which allows us to run many successive shocks at the cost of a single shock, and thus to present the first direct numerical simulations of linear and non-linear multiple DSA, a mechanism of interest in various astrophysical environments such as superbubbles, galaxy clusters and early cosmological flows.