Two applications were chosen to demonstrate the adaptive hydrodynamics scheme. The first examines how the grid redistribution handles severe discontinuities. In the second, we compare our plasma channel simulations with those found by a lagrangian multigroup radiation diffusion scheme. A list of the major steps that our numerical procedure follows to update the equations on an adaptive mesh from time to is given below:
Time step control is done by fixing the CFL number globally. The compressible flow CFL number is typically defined  for a fixed mesh system as
where a is the local sound speed. For an adaptive scheme we can define the CFL number as follows
where ; and being the right and left edge velocities.