Convergence testing for a non-constant conductivity

 make DIM=1 CONDUCTIVITY_DIR=powerlaw -j 20

 ./Castro1d.gnu.ex inputs.1d.powerlaw castro.time_integration_method=2 castro.sdc_order=4 amr.n_cell=64
 mv diffuse_plt00048 diffuse_64
 ./Castro1d.gnu.ex inputs.1d.powerlaw castro.time_integration_method=2 castro.sdc_order=4
 mv diffuse_plt00190 diffuse_128
 ./Castro1d.gnu.ex inputs.1d.powerlaw castro.time_integration_method=2 castro.sdc_order=4 amr.n_cell=256
 mv diffuse_plt00760 diffuse_256
 ./Castro1d.gnu.ex inputs.1d.powerlaw castro.time_integration_method=2 castro.sdc_order=4 amr.n_cell=512
 mv diffuse_plt03040 diffuse_512

 RichardsonConvergenceTest1d.gnu.ex coarFile=diffuse_64 mediFile=diffuse_128 fineFile=diffuse_256 > convergence_diffusion.1d.lo.sdc4.out
 RichardsonConvergenceTest1d.gnu.ex coarFile=diffuse_128 mediFile=diffuse_256 fineFile=diffuse_512 > convergence_diffusion.1d.hi.sdc4.out


This gives (for the lower resolution runs):

Level  L1 norm of Error in Each Component
-----------------------------------------------
Warning: BoxArray lengths are not the same at level 0
  0    Level  L1 norm of Error in Each Component
-----------------------------------------------
Warning: BoxArray lengths are not the same at level 0
  0    \begin{table}[p]
\begin{center}
\begin{tabular}{|cccc|} \hline
Variable & $e_{4h \rightarrow 2h}$ & Order & $e_{2h \rightarrow h}$\\
\hline
density&         0.000000e+00 & ------------ &0.000000e+00 \\
xmom&         0.000000e+00 & ------------ &0.000000e+00 \\
ymom&         0.000000e+00 & ------------ &0.000000e+00 \\
zmom&         0.000000e+00 & ------------ &0.000000e+00 \\
rho_E&         1.111626e-05 & 3.948910124 & 7.198104e-07 \\
rho_e&         1.111626e-05 & 3.948910124 & 7.198104e-07 \\
Temp&         1.063477e-05 & 3.952987539 & 6.866892e-07 \\
rho_X&         0.000000e+00 & ------------ &0.000000e+00 \\
pressure&         7.410837e-06 & 3.948910124 & 4.798736e-07 \\


e.g. we see fourth-order convergence in the temperature



2-d test:

make DIM=2 CONDUCTIVITY_DIR=powerlaw -j 20

 ./Castro2d.gnu.ex inputs.2d.powerlaw castro.time_integration_method=2 castro.sdc_order=4 amr.n_cell=64 64
 mv diffuse_plt00039 diffuse_2d_64
 ./Castro2d.gnu.ex inputs.2d.powerlaw castro.time_integration_method=2 castro.sdc_order=4
 mv diffuse_plt00157 diffuse_2d_128
 ./Castro2d.gnu.ex inputs.2d.powerlaw castro.time_integration_method=2 castro.sdc_order=4 amr.n_cell=256 256
 mv diffuse_plt00626 diffuse_2d_256

 RichardsonConvergenceTest2d.gnu.ex coarFile=diffuse_2d_64 mediFile=diffuse_2d_128 fineFile=diffuse_2d_256 > convergence_diffusion.2d.lo.sdc4.out
