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 pro blem 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 provid es a lower bound on the physical scale for diffusive transport computation. Our code uses subzone shock tracking and multilevel adaptive mesh refineme nt to provide enhanced spatial resolution around shocks at a modest cost co mpared to the coarse grid and vastly improved cost effectiveness compared t o a uniform, highly refined grid. We present and discuss the implications f rom our initial results.