update readme and some input file

Author: zhichen3

Exec/unit_tests/diffusion_test/README.md

@@ -63,6 +63,29 @@ analytic solution, giving:
  (256, 512)          2.437072009e-05
 ```
 
+## 2-d Spherical Geometry
+
+An analytic convergence test with 2D spherical geometry is done
+using the initial condition constructed with spherical-bessel function
+and legendre polynomial, which tests both radial and theta dependence.
+Run with:
+
+```
+./Castro2d.gnu.MPI.ex inputs.2d.sph.bessel amr.n_cell=64 64
+./Castro2d.gnu.MPI.ex inputs.2d.sph.bessel amr.n_cell=128 128
+./Castro2d.gnu.MPI.ex inputs.2d.sph.bessel amr.n_cell=256 256
+```
+
+After each run, the norm of the errror against the analytic solution
+shows 2nd order accuracy:
+
+```
+ base resolution      L-inf error
+ (64 ,  64)          0.0008168088258
+ (128, 128)          0.0002035772451
+ (256, 256)          5.109916938e-05
+```
+
 
 ## SDC-4 in 1-d
 
@@ -252,3 +275,72 @@ Temp&         1.770452e-06 & 3.966033724 & 1.132894e-07 \\
 ```
 
 e.g. we see fourth-order convergence in the temperature
+
+
+## 2-d spherical geometry (with AMR)
+
+We use a non-center Gaussian initial condition to test
+resolution convergence and AMR for 2D spherical geometry.
+
+First compile with power law conductivity:
+
+```
+make DIM=2 CONDUCTIVITY_DIR=powerlaw -j 20
+```
+
+Now run using:
+
+```
+./Castro2d.gnu.MPI.ex inputs.2d.sph.gaussian amr.plot_per = 0.001 amr.n_cell=32 32 castro.fixed_dt=3.2e-6
+mv diffuse_plt00314 diffuse_sph_32
+./Castro2d.gnu.MPI.ex inputs.2d.sph.gaussian amr.plot_per = 0.001 amr.n_cell=64 64 castro.fixed_dt=1.6e-6
+mv diffuse_plt00626 diffuse_sph_64
+./Castro2d.gnu.MPI.ex inputs.2d.sph.gaussian amr.plot_per = 0.001 amr.n_cell=128 128 castro.fixed_dt=8.e-7
+mv diffuse_plt01251 diffuse_sph_128
+./Castro2d.gnu.MPI.ex inputs.2d.sph.gaussian amr.plot_per = 0.001 amr.n_cell=256 256 castro.fixed_dt=4.e-7
+mv diffuse_plt02501 diffuse_sph_256
+```
+
+Now use the RichardsonConvergence Script:
+
+```
+./RichardsonConvergenceTest2d.gnu.ex coarFile=diffuse_sph_32 mediFile=diffuse_sph_64  fineFile=diffuse_sph_128 > convergence_diffusion.2d.lo.out
+./RichardsonConvergenceTest2d.gnu.ex coarFile=diffuse_sph_64 mediFile=diffuse_sph_128 fineFile=diffuse_sph_256 > convergence_diffusion.2d.hi.out
+```
+
+For the lower resolution runs, e.g. `convergence_diffusion.2d.lo.out`:
+
+```
+Level  L1 norm of Error in Each Component
+-----------------------------------------------
+                   rho_E        2.681136e-04       1.811933   7.636120e-05
+                   rho_e        2.681136e-04       1.811933   7.636120e-05
+                    Temp        2.681136e-04       1.811933   7.636120e-05
+                pressure        1.787424e-04       1.811933   5.090747e-05
+              soundspeed        1.458607e+00       1.797880   4.194908e-01
+                 entropy        2.867059e+04       1.786225   8.312456e+03
+            thermal_cond        6.322558e-04       1.841497   1.764196e-04
+              diff_coeff        6.322558e-04       1.841497   1.764196e-04
+               diff_term        2.631251e-01       1.915835   6.973300e-02
+```
+
+For the higher resolution run, e.g. `convergence_diffusion.2d.hi.out`:
+
+```
+Level  L1 norm of Error in Each Component
+-----------------------------------------------
+Warning: BoxArray lengths are not the same at level 0
+level: 0
+Warning: BoxArray lengths are not the same at level 1
+level: 1
+Warning: BoxArray lengths are not the same at level 0
+                   rho_E        7.636120e-05       2.046783   1.848118e-05
+                   rho_e        7.636120e-05       2.046783   1.848118e-05
+                    Temp        7.636120e-05       2.046783   1.848118e-05
+                pressure        5.090747e-05       2.046783   1.232079e-05
+              soundspeed        4.194908e-01       2.034310   1.024081e-01
+                 entropy        8.312456e+03       2.020431   2.048891e+03
+            thermal_cond        1.764196e-04       2.066769   4.211021e-05
+              diff_coeff        1.764196e-04       2.066769   4.211021e-05
+               diff_term        6.973300e-02       1.903361   1.864102e-02
+```

Exec/unit_tests/diffusion_test/inputs.2d.sph.bessel

@@ -23,6 +23,7 @@ castro.hi_bc       =  1   3
 castro.do_hydro = 0
 castro.diffuse_temp = 1
 castro.do_react = 0
+castro.diffuse_use_amrex_mlmg = 0
 
 # TIME STEP CONTROL
 
@@ -43,16 +44,6 @@ amr.regrid_int      = 2       # how often to regrid
 amr.blocking_factor = 8       # block factor in grid generation
 amr.max_grid_size   = 32
 
-amr.refinement_indicators = temperr tempgrad
-
-amr.refine.temperr.value_greater = 1.1
-amr.refine.temperr.field_name = Temp
-amr.refine.temperr.max_level = 3
-
-amr.refine.tempgrad.gradient = 0.1
-amr.refine.tempgrad.field_name = Temp
-amr.refine.tempgrad.max_level = 3
-
 # CHECKPOINT FILES
 amr.check_file      = diffuse_chk     # root name of checkpoint file
 amr.check_int       = 1000     # number of timesteps between checkpoints
@@ -81,7 +72,6 @@ problem.gaussian_init = 0
 
 # CONDUCTIVITY
 conductivity.const_conductivity = 10.0
-castro.diffuse_use_amrex_mlmg = 0
 
 # EOS
 eos.eos_assume_neutral = 1

Exec/unit_tests/diffusion_test/inputs.2d.sph.gaussian

@@ -5,9 +5,9 @@ stop_time = 0.001
 # PROBLEM SIZE & GEOMETRY
 geometry.is_periodic = 0    0
 geometry.coord_sys   = 2    # 2 = SPHERICAL
-geometry.prob_lo     = 0.1       0.0
+geometry.prob_lo     = 0.2       0.0
 geometry.prob_hi     = 1.0       3.141592653589793238
-amr.n_cell           = 64        64
+amr.n_cell           = 32        32
 
 castro.allow_non_unit_aspect_zones = 1
 
@@ -23,6 +23,7 @@ castro.hi_bc       =  2   3
 castro.do_hydro = 0
 castro.diffuse_temp = 1
 castro.do_react = 0
+castro.diffuse_use_amrex_mlmg = 0
 
 # TIME STEP CONTROL
 
@@ -37,7 +38,7 @@ amr.v                 = 1       # verbosity in Amr.cpp
 #amr.grid_log         = grdlog  # name of grid logging file
 
 # REFINEMENT / REGRIDDING
-amr.max_level       = 0       # maximum level number allowed
+amr.max_level       = 1       # maximum level number allowed
 amr.ref_ratio       = 2 2 2 2 # refinement ratio
 amr.regrid_int      = 2       # how often to regrid
 amr.blocking_factor = 8       # block factor in grid generation
@@ -59,8 +60,8 @@ amr.check_int       = 1000     # number of timesteps between checkpoints
 
 # PLOTFILES
 amr.plot_file       = diffuse_plt
-#amr.plot_int        = 10
-amr.plot_per        = 0.0001
+amr.plot_int        = -1
+amr.plot_per        = 0.001
 amr.derive_plot_vars=ALL
 
 # PROBLEM PARAMETERS
@@ -79,11 +80,13 @@ problem.diff_coeff = 1.0
 # Note that changing problem::center only works with gaussian initial condition,
 # i.e. problem.gaussian_init=1
 
-problem.center = 0.5 1.57079632679 0
+problem.center = 0.6 1.57079632679 0
 
 # CONDUCTIVITY
 conductivity.const_conductivity = 10.0
-castro.diffuse_use_amrex_mlmg = 0
 
+# For powerlaw conductivity of form k_th = k_th0 T^v
+conductivity.cond_coeff=1
+conductivity.cond_exponent=2
 # EOS
 eos.eos_assume_neutral = 1