Cosmic rays (CR) are important in a number of astrophysical situations, including stellar winds, supernovae, cluster shocks and jets from active galactic nuclei. CR's not only produce observable radiation but also contribute to the energetics. How CRs are accelerated is a topic of great interest for understanding the observed CR spectrum and the contribution of CRs to astrophysical systems. The leading theory, known as Diffusive Shock Acceleration (DSA), invokes Fermi acceleration off of Alfven waves at astrophysical shocks.
The pressure from the CRs can modify the shocks they are accelerated at making a highly non-linear system. Due to the computational costs of solving such a non-linear system current codes work in only one spatial dimension (1-D). 1-D systems suppress effects which are inherently multidimensional, such as instabilities and non-symmetric flows, which occur in astrophysical systems. These multidimensional effects can have a profound effect on the modelled dynamics and hence the observational characteristics of a system.
Multidimensional Adaptive Subcycling Tridiagonal solver (MAST)
A critical part of solving time dependant non-linear DSA is the diffusion of the CRs. Normally diffusion problems can develop unphysical boundary artifacts if the diffusion length is larger than the computational domain. This poses a problem for parallel computation which usually divides the grid into smaller domains. MAST utilizes timestep subcycling to reduce the diffusion length of any given subcycle such that it is less than the size of the domain. Floating boundaries are also utilized to allow information to propagate out from the domain edges without needing to synchronize the domain boundaries every subcycle. This allows every domain to act independently during subcycling permitting parallel computation.
The MAST solver in conjunction with the Coarse-Grained Momentum finite Volume (CGMV)  method has been implemented for solving DSA in both AstroBEAR (Astronomical Boundary Embedded Adaptive Refinement) MHD (Magnetohydrodynamic) code and WOMBAT. With this inclusion of CR feedback, these codes now have the capability to model multidimensional time-dependant DSA for the first time.
A poster on multidimensional DSA was presented at the 214th Meeting of the American Astronomical Society in Pasadena on June 7-11, 2009. The poster is available in PDF format below.
Edmon, P., & Jones, T. W., 2010, in progress
Jones, T. W., & Kang, H., 2005, AstroPart, 24, 75-91 (ADS link)