  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.
