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:

- Given the fraction of the mesh points to be used for the first and second degree variation of the chosen adaptive function, and , calculate and through Eq.(5) and (6).
- Calculate the weight function
**W**using updated values (time ) of the chosen adaptive function. - Compute new mesh points, and mesh speeds, by Eq.(3) and (8).
- Solve the governing equations for time .
- Set up the new time step.
- Repeat steps.

Time step control is done by fixing the CFL number globally. The compressible flow CFL number is typically defined [6] 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.

Thu Mar 21 14:48:13 EST 1996