Add radiation-driven shell to regression tests (#810)

### Description
Adds this problem to the nightly regression test suite. There was also a
bug in the initial conditions in the radiation flux in converting from
spherical to Cartesian flux components (now fixed).

At late times, the simulation still has a slightly discrepancy w.r.t.
the semi-analytic solution (similar to that shown in the original code
paper). This is most likely due to initial shell thickness being quite
significant. (There is not an easy solution to this, since there is no
steady-state solution that satisfies the M1 closure for sufficiently
thin shells.)


![shell_velocity](https://github.com/user-attachments/assets/0473f97c-3506-4d40-94c5-a9b84e2900f0)


https://github.com/user-attachments/assets/8851d7cd-9d92-4de6-ac7e-ab5fef035af5

### Related issues
Closes #743.

### Checklist
_Before this pull request can be reviewed, all of these tasks should be
completed. Denote completed tasks with an `x` inside the square brackets
`[ ]` in the Markdown source below:_
- [x] I have added a description (see above).
- [x] I have added a link to any related issues (if applicable; see
above).
- [x] I have read the [Contributing
Guide](https://github.com/quokka-astro/quokka/blob/development/CONTRIBUTING.md).
- [ ] I have added tests for any new physics that this PR adds to the
code.
- [x] *(For quokka-astro org members)* I have manually triggered the GPU
tests with the magic comment `/azp run`.

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

extern/dust_shell/initial_conditions.txt

@@ -1,32 +1,32 @@
 # r_over_r0 reduced_flux Erad_cgs Frad_cgs
-1.000000000000000048e-04 3.755101031908026650e-05 5.849260643223253650e-07 6.584810833497746207e-01
-1.441718602973596219e-03 5.413927440706735881e-04 5.849081618804471932e-07 9.493378914228637555e+00
-2.704299640581599162e-02 1.013562762624721503e-02 5.846128128060447862e-07 1.776395559784417060e+02
-5.264427420865838703e-02 1.961668425674432600e-02 5.840360439316570708e-07 3.434677422808198344e+02
-7.824555201150078243e-02 2.888029728914901992e-02 5.830889736094660357e-07 5.048439908936409779e+02
-1.038468298143431778e-01 3.783067358743209818e-02 5.817195410834095839e-07 6.597485279428594822e+02
-1.779956739478935068e-01 6.114121918945376183e-02 5.759656028151289446e-07 1.055726310902443856e+03
-2.521445180814438358e-01 7.899856349142272971e-02 5.696285693863173242e-07 1.349061225503343167e+03
-3.262933622149941648e-01 9.023184801610512062e-02 5.638115733303117799e-07 1.525156961640026111e+03
-4.062237502412902046e-01 9.486076267381476912e-02 5.588646660393681869e-07 1.589329583582680470e+03
-4.861541382675862444e-01 9.293464799427836320e-02 5.553646422860039258e-07 1.547307347592608494e+03
-5.660845262938822842e-01 8.651743901096156653e-02 5.525405597518683318e-07 1.433139683424766645e+03
-6.460149143201783239e-01 7.823584123424670578e-02 5.460810899423697447e-07 1.280806719571427266e+03
-6.807459332032566035e-01 7.481212301298670320e-02 5.394891460892043165e-07 1.209972204515023122e+03
-7.154769520863348831e-01 7.186691853201436497e-02 5.286291820213997449e-07 1.138940038957400475e+03
-7.502079709694131626e-01 6.968198530201698271e-02 5.117644526806205409e-07 1.069082781484670022e+03
-7.849389898524914422e-01 6.855134780844877873e-02 4.872960447401361441e-07 1.001450729546252319e+03
-8.196700087355697217e-01 6.879633527401403381e-02 4.542155802142597972e-07 9.368024854275187181e+02
-8.521778939234854189e-01 7.061262999568297671e-02 4.154382001870662751e-07 8.794466892024265690e+02
-8.846857791114011160e-01 7.438479746469706111e-02 3.701317120995621678e-07 8.253937649803749537e+02
-9.171936642993168132e-01 8.066352339760292367e-02 3.203808828403107721e-07 7.747551733282971327e+02
-9.497015494872325103e-01 9.020744304431384253e-02 2.690248161789397429e-07 7.275375597170433366e+02
-1.003030219610614449e+00 1.158923399574568469e-01 1.891775328524417536e-07 6.572717886984859206e+02
-1.024463928995228423e+00 1.311152943576374130e-01 1.606398288646572669e-07 6.314330214299012596e+02
-1.045897638379842398e+00 1.499304699665272855e-01 1.350219548090641344e-07 6.068970081536025418e+02
-1.067331347764456373e+00 1.729284538875688892e-01 1.125730104992235057e-07 5.836082760506781142e+02
-1.088765057149070348e+00 2.007054354675900376e-01 9.332050127159230878e-08 5.615092306215482267e+02
-1.118146872845352524e+00 2.474951844047469651e-01 7.184122515985754712e-08 5.330417009732285578e+02
+1.000000000000000048e-04 3.755101032144143522e-05 5.849260642855459238e-07 6.584810833497746207e-01
+1.441718602968267149e-03 5.413927440846509056e-04 5.849081618524834593e-07 9.493378914019864112e+00
+2.704299640580912212e-02 1.013562762624422263e-02 5.846128128060968788e-07 1.776395559784050988e+02
+5.264427420864997709e-02 1.961668425674107166e-02 5.840360439316672352e-07 3.434677422807688458e+02
+7.824555201149083206e-02 2.888029728914537353e-02 5.830889736094605300e-07 5.048439908935724816e+02
+1.038468298143316870e-01 3.783067358742812220e-02 5.817195410834083134e-07 6.597485279427886553e+02
+1.779956739478792960e-01 6.114121918944982748e-02 5.759656028151295798e-07 1.055726310902377008e+03
+2.521445180814269049e-01 7.899856349141945455e-02 5.696285693863187006e-07 1.349061225503290416e+03
+3.262933622149745139e-01 9.023184801610305283e-02 5.638115733303131563e-07 1.525156961639994961e+03
+4.062237502412764378e-01 9.486076267381457483e-02 5.588646660393688221e-07 1.589329583582679106e+03
+4.861541382675783618e-01 9.293464799427880729e-02 5.553646422860042435e-07 1.547307347592616679e+03
+5.660845262938802858e-01 8.651743901096177469e-02 5.525405597518682259e-07 1.433139683424769828e+03
+6.460149143201822097e-01 7.823584123424630332e-02 5.460810899423690035e-07 1.280806719571418853e+03
+6.807459332032604893e-01 7.481212301298635625e-02 5.394891460892032577e-07 1.209972204515015164e+03
+7.154769520863387688e-01 7.186691853201411517e-02 5.286291820213980508e-07 1.138940038957392744e+03
+7.502079709694170484e-01 6.968198530201683005e-02 5.117644526806179998e-07 1.069082781484662291e+03
+7.849389898524953280e-01 6.855134780844875098e-02 4.872960447401328619e-07 1.001450729546245043e+03
+8.196700087355736075e-01 6.879633527401417259e-02 4.542155802142554032e-07 9.368024854275116695e+02
+8.521778939234886385e-01 7.061262999568328202e-02 4.154382001870618282e-07 8.794466892024209983e+02
+8.846857791114036695e-01 7.438479746469750520e-02 3.701317120995581444e-07 8.253937649803708609e+02
+9.171936642993187006e-01 8.066352339760342327e-02 3.203808828403075957e-07 7.747551733282942905e+02
+9.497015494872337316e-01 9.020744304431432825e-02 2.690248161789377312e-07 7.275375597170417450e+02
+1.003030219610615559e+00 1.158923399574575547e-01 1.891775328524401654e-07 6.572717886984843290e+02
+1.024463928995229312e+00 1.311152943576380792e-01 1.606398288646561817e-07 6.314330214299002364e+02
+1.045897638379843064e+00 1.499304699665278962e-01 1.350219548090634198e-07 6.068970081536018597e+02
+1.067331347764456817e+00 1.729284538875693888e-01 1.125730104992230822e-07 5.836082760506776594e+02
+1.088765057149070570e+00 2.007054354675903429e-01 9.332050127159211025e-08 5.615092306215478857e+02
+1.118146872845352524e+00 2.474951844047470206e-01 7.184122515985753388e-08 5.330417009732285578e+02
 1.147446050287565411e+00 3.040530980337316502e-01 5.557934245197780048e-08 5.066214110713187893e+02
 1.176745227729778298e+00 3.688774428023082197e-01 4.358752202844885829e-08 4.820199144752725715e+02
 1.206044405171991185e+00 4.385500681459409411e-01 3.491927786461010067e-08 4.590977238732691035e+02
@@ -58,14 +58,20 @@
 1.546576247924941638e+00 8.636240495720141075e-01 1.079436353580702643e-08 2.794746821838933784e+02
 1.596404594890389994e+00 8.791200480310583654e-01 9.952498041173527408e-09 2.623016290403775201e+02
 1.646232941855838350e+00 8.916142219547158465e-01 9.227997027531266418e-09 2.466636400124249064e+02
-1.734375178853998056e+00 9.091912467741695147e-01 8.153162862422567086e-09 2.222296828330790390e+02
-1.822517415852157763e+00 9.224110306819669480e-01 7.277792911337121628e-09 2.012541684514484359e+02
+1.734375178853998056e+00 9.091912467741694037e-01 8.153162862422568740e-09 2.222296828330790390e+02
+1.822517415852157763e+00 9.224110306819671701e-01 7.277792911337119974e-09 2.012541684514484359e+02
 1.910659652850317469e+00 9.323283560477764187e-01 6.551368291360504820e-09 1.831140256663184118e+02
-1.998801889848477176e+00 9.400305847321852593e-01 5.937260295798599041e-09 1.673203545558839949e+02
-2.086944126846637104e+00 9.463952883490297507e-01 5.409702260886093429e-09 1.534852463072307103e+02
-2.272433441672774723e+00 9.563968807764520186e-01 4.514889045582422516e-09 1.294511568363405729e+02
-2.457922756498912342e+00 9.638255901339627396e-01 3.829417015942469982e-09 1.106501019861635768e+02
-2.643412071325049961e+00 9.695659269448310136e-01 3.291247133925901363e-09 9.566620401136817975e+01
-2.828901386151187580e+00 9.740199695318354500e-01 2.860645873254432982e-09 8.353195821790863818e+01
-3.195695155395610776e+00 9.804830097508788755e-01 2.226880004038710651e-09 6.545722516738128149e+01
-3.500000000000000000e+00 9.840687773348448797e-01 1.849720182475050407e-09 5.456977847985999830e+01
+1.998801889848477176e+00 9.400305847321853703e-01 5.937260295798599041e-09 1.673203545558839949e+02
+2.086944126846637104e+00 9.463952883490298618e-01 5.409702260886092602e-09 1.534852463072307103e+02
+2.272433441672772059e+00 9.563968807762568414e-01 4.514889045583355576e-09 1.294511568363408855e+02
+2.457922756498907013e+00 9.638255901347262400e-01 3.829417015939454081e-09 1.106501019861640600e+02
+2.643412071325041968e+00 9.695659269473928532e-01 3.291247133917225065e-09 9.566620401136876239e+01
+2.828901386151176922e+00 9.740199695356472898e-01 2.860645873243259426e-09 8.353195821790926345e+01
+3.195695155818024880e+00 9.804830097539137812e-01 2.226880003443110004e-09 6.545722515007672371e+01
+3.562488925484872837e+00 9.847259406867946430e-01 1.784206642841335117e-09 5.267217275611908178e+01
+3.929282695151720795e+00 9.876556558038823708e-01 1.462296600552641392e-09 4.329739107983610324e+01
+4.570182323792682411e+00 9.908450535180021168e-01 1.077444177193692332e-09 3.200525022874398928e+01
+5.211081952433644027e+00 9.929357294822037661e-01 8.269716695772742945e-10 2.461684964939163933e+01
+5.851981581074605643e+00 9.944685441777345591e-01 6.547426396019746781e-10 1.952011529386182431e+01
+6.492881209715567259e+00 9.956025175470230026e-01 5.312594591625017127e-10 1.585672027136650897e+01
+7.000000000000000000e+00 9.962532121817468944e-01 4.567744063764533480e-10 1.364244461996499957e+01

extern/dust_shell/matplotlibrc

@@ -1,7 +1,7 @@
 # Set the backend, otherwise the figure won't show up. Note that this will 
 # depend on your system setup; to see which backend is the default,
 # run "matplotlib.get_backend()" in the Python interpreter.
-backend                 :  GTK3Agg    
+backend                 :  Agg    
 
 # Increase the default DPI, and change the file type from png to pdf 
 savefig.dpi             :   300

extern/dust_shell/solution.py

@@ -112,7 +112,7 @@ def func_M1(t, y):
 
     # solve for critical point
     def g(r):
-        return 3.0*r_0*dlnF_dr(r*r_0) + (4.0/r) + 2.0*sqrt(3.0)*r_0*rho(r*r_0)*kappa0
+        return float(3.0*r_0*dlnF_dr(r*r_0) + (4.0/r) + 2.0*sqrt(3.0)*r_0*rho(r*r_0)*kappa0)
 
     #plt.figure()
     #r_arr = np.linspace(1.0e-3, 2.0, 100)
@@ -139,7 +139,7 @@ def solve_branch(f0, r0, r1):
 
     # solve right branch
     r_start = r_crit + eps
-    r_end = 3.5  # in units of r_0
+    r_end = 7.0  # in units of r_0
     f_start = f_crit + eps * df_dr_crit
     print(f"r_crit = {r_crit}; r_start = {r_start}")
     print(f"f_crit = {f_crit}; f_start = {f_start}")
@@ -166,7 +166,8 @@ def solve_branch(f0, r0, r1):
 
     plt.xlabel('radius r (dimensionless)')
     plt.ylabel('reduced flux f (dimensionless)')
-    plt.xlim(0., 3.5)
+    #plt.xlim(0., 3.5)
+    plt.xlim(0., 7.0)
     plt.ylim(0., 1.)
     plt.savefig('solution.pdf')
 

regression/quokka-tests.ini

@@ -123,3 +123,19 @@ doVis = 1
 visVar = temperature
 testSrcTree = .
 ignore_return_code = 0
+
+[RadhydroShell-GPU]
+buildDir = .
+target = test_radhydro3d_shell
+inputFile = tests/radhydro_shell_regression.in
+link1File = extern/dust_shell/initial_conditions.txt
+dim = 3
+cmakeSetupOpts = -DAMReX_GPU_BACKEND=CUDA
+restartTest = 0
+useMPI = 1
+numprocs = 1
+compileTest = 0
+doVis = 1
+visVar = gasDensity
+testSrcTree = .
+ignore_return_code = 0

src/problems/RadhydroShell/CMakeLists.txt

@@ -4,4 +4,6 @@ if (AMReX_SPACEDIM EQUAL 3)
     if(AMReX_GPU_BACKEND MATCHES "CUDA")
         setup_target_for_cuda_compilation(test_radhydro3d_shell)
     endif()
+
+    add_test(NAME RadhydroShell COMMAND test_radhydro3d_shell radhydro_shell.in ${QuokkaTestParams} WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}/tests)
 endif()