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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 &amp; Giddings. Following Kang &amp; 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.

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