Time Evolution of Cosmic-Ray Modified Plane Shocks
  We have developed a novel computer code designed to follow the evolution of cosmic-ray modified shocks, including the full momentum dependence of the particles for a realistic diffusion coefficient model. In this form the problem is technically very difficult, because one needs to cover a wide range of diffusive scales, beginning with those slightly larger than the physical shock thickness. With most finite difference schemes for Euler's equations the numerical shock thickness is at least one zone across, so this provides a lower bound on the physical scale for diffusive transport computation. Our code uses sub-zone shock tracking and multi-level adaptive mesh refinement to provide enhanced spatial resolution around shocks at modest cost compared to the coarse grid and vastly improved cost effectiveness compared to a uniform, highly refined grid. We present and discuss the implications from our initial results. 
Hyesung Kang, T.W. Jones, R.J. LeVeque, and K.M. Shyue