**Due May 20, 2005 (3:30 pm, no extensions)**

This is an optional assignment for bonus credit only (10 marks).

Write a 1-D fluid dynamics code using either the Lax scheme or the
two-step Lax-Wendroff scheme (extra credit if you do both!) to solve
the fluid equations in conservative form:

Test your code by solving the classic 1-D ``shock tube'' problem (Sod
1978, *J. Comput. Phys.* **27**, 1). At there is
hot, dense gas with , on the left and cool, rarefied
gas with , on the right. The initial gas
speed is zero throughout (in these units, speed is normalized to the
sound speed , where ). This nonequilibrium situation results in a shock wave propagating
right with a rarefaction wave propagating left. Compare your results
at with those shown in Stone & Norman 1992, *ApJS*
**80**, 753, Fig. 11 (i.e., plot , , , and
as a function of at time ). HINT: let
the number of grid points in be a free parameter, set assuming your domain ranges from 0 to 1 in with the
discontinuity at , and choose to safely satisfy
the Courant condition. Don't forget the boundary conditions! (You
may assume neither wave reaches either boundary during the time
interval simulated.) For what (if any!) do you get a good match
with the Stone & Norman figure?

- BONUS: Make a movie of the results!