Marklin Example: Compute vacuum field in a 3D boundary (NCSX)
In this example we compute the the vacuum magnetic field with a specified flux within a complex 3D toroidal region, the LCFS of NCSX in this case. We then demonstrate tracing the resulting field as well as compute the result of heating with anisotropic thermal conduction aligne to the magnetic field.
import os
import sys
import time
import h5py
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize']=(6,6)
plt.rcParams['font.weight']='bold'
plt.rcParams['axes.labelweight']='bold'
plt.rcParams['lines.linewidth']=2
plt.rcParams['lines.markeredgewidth']=2
%matplotlib inline
%config InlineBackend.figure_format = "retina"
Load Marklin library
To load the Marklin python module we need to tell python where to the module is located. This can be done either through the PYTHONPATH environment variable or using within a script using sys.path.append() as below, where we look for the environement variable OFT_ROOTPATH to provide the path to where the OpenFUSIONToolkit is installed (/Applications/OFT on macOS).
tokamaker_python_path = os.getenv('OFT_ROOTPATH')
if tokamaker_python_path is not None:
sys.path.append(os.path.join(tokamaker_python_path,'python'))
from OpenFUSIONToolkit import OFT_env
Python interface for Marklin force-free ideal MHD equilibrium functionality.
Definition __init__.py:1
Compute vacuum field
Initialize Marklin object
First we create a Marklin instance to use for field calculations.
myOFT = OFT_env(nthreads=4)
taylor_solver = Marklin(myOFT)
#---------------------------------------------- Open FUSION Toolkit Initialized Development branch: Marklin_vacuum Revision id: 1de4a06 Parallelization Info: # of MPI tasks = 1 # of NUMA nodes = 1 # of OpenMP threads = 4 Fortran input file = /var/folders/52/n5qxh27n4w19qxzqygz2btbw0000gn/T/oft_51876/oftpyin XML input file = none Integer Precisions = 4 8 Float Precisions = 4 8 16 Complex Precisions = 4 8 LA backend = native #----------------------------------------------
Load mesh
Now we load a mesh of the desired region generated using Cubit using setup_mesh() and build the required FE spaces using setup().
taylor_solver.setup_mesh(mesh_file='NCSX_plasma.h5',grid_order=2)
taylor_solver.setup(order=2,minlev=1)
**** Loading OFT mesh
Mesh File = NCSX_plasma.h5
**** Generating grid level 1
Generating domain linkage
Generating boundary domain linkage
Mesh statistics:
Volume = 2.971E+00
Surface area = 2.445E+01
# of points = 39405
# of edges = 251752
# of faces = 413201
# of cells = 200854
# of boundary points = 11493
# of boundary edges = 34479
# of boundary faces = 22986
# of boundary cells = 22873
Resolution statistics:
hmin = 2.709E-02
hrms = 5.283E-02
hmax = 1.318E-01
Surface grounded at vertex 16292
WARNING: Removed curvature in 5 cells due to poorly conditioned Jacobians
**** Creating Lagrange FE space
Order = 2
Minlev = 1
**** Creating H(Curl) FE space
Order = 2
Minlev = 1
WARNING: No Lagrange MG smoother settings found:
WARNING: Using default values, which may result in convergence failure.
WARNING: No H(Curl) MG smoother settings found:
WARNING: Using default values, which may result in convergence failure.
Compute vacuum field
In marklin the vacuum field within a multiply connected volume, like a torus, can be computed by specifying the flux thrugh a given cut plane that traverses the mesh. In the case of a topological torus, like NCSX, this cut plane should be a poloidal plane, which we specify using a center point hcpc and unit normal direction hcpv. This defines a circular cut surface, where the amplitude of hcpv set the radius \(r = 1/|hcpv|\), that is used to slice the model.
We then use compute_vac() to compute the vacuum field with unit flux through the specified plane.
- Note
- In general multiple slice planes are allowed for more complex geometry (see Benedett et al. 2021).
nh = 1
hcpc = np.array([[1.5,0.0,0.0],])
hcpv = np.array([[0.0,0.4,0.0],])
taylor_solver.compute_vac(nh,hcpc,hcpv)
**** Creating H^1 FE space
Order = 3
Minlev = 1
**** Creating H(Curl) + Grad(H^1) FE space
Order = 2
Minlev = 1
WARNING: No H^1 MG smoother settings found:
WARNING: Using default values, which may result in convergence failure.
WARNING: No H(Curl) + Grad(H^1) MG smoother settings found:
WARNING: Using default values, which may result in convergence failure.
Starting CG solver
0 0.000000E+00 0.000000E+00 5.196134E-01
1 -1.241239E+00 7.558267E+00 1.678812E-01 2.221160E-02
2 -1.592051E+00 1.287183E+01 8.550400E-02 6.642725E-03
3 -1.738624E+00 1.825675E+01 5.840551E-02 3.199119E-03
4 -1.816082E+00 1.892195E+01 5.035339E-02 2.661110E-03
5 -1.866464E+00 1.893167E+01 4.097687E-02 2.164461E-03
6 -1.904393E+00 1.918058E+01 3.258061E-02 1.698625E-03
7 -1.932401E+00 1.967075E+01 2.846816E-02 1.447233E-03
8 -1.952755E+00 2.026996E+01 2.453982E-02 1.210650E-03
9 -1.969077E+00 2.101250E+01 2.169898E-02 1.032670E-03
10 -1.981978E+00 2.186385E+01 1.964990E-02 8.987395E-04
20 -2.042309E+00 2.925770E+01 9.192464E-03 3.141896E-04
30 -2.063302E+00 3.548574E+01 6.431481E-03 1.812413E-04
40 -2.074084E+00 4.090133E+01 4.648587E-03 1.136537E-04
50 -2.080637E+00 4.577368E+01 3.819397E-03 8.344090E-05
60 -2.085032E+00 5.019740E+01 3.099724E-03 6.175069E-05
70 -2.088166E+00 5.425592E+01 2.633178E-03 4.853256E-05
80 -2.089716E+00 5.664190E+01 9.623929E-04 1.699083E-05
90 -2.089797E+00 5.677498E+01 1.540889E-04 2.714028E-06
100 -2.089804E+00 5.678723E+01 1.338724E-04 2.357438E-06
110 -2.089874E+00 5.699665E+01 8.167835E-04 1.433038E-05
120 -2.091188E+00 8.755666E+01 1.575571E-03 1.799487E-05
130 -2.091497E+00 9.899170E+01 5.639781E-04 5.697226E-06
140 -2.091589E+00 1.025464E+02 4.346820E-04 4.238880E-06
150 -2.091632E+00 1.042056E+02 3.752413E-04 3.600970E-06
160 -2.091724E+00 1.078896E+02 2.899037E-04 2.687040E-06
170 -2.091741E+00 1.085676E+02 1.634790E-04 1.505781E-06
180 -2.091747E+00 1.088008E+02 1.173792E-04 1.078845E-06
190 -2.091750E+00 1.089243E+02 5.037487E-05 4.624761E-07
200 -2.091750E+00 1.089379E+02 9.761509E-06 8.960618E-08
210 -2.091750E+00 1.089383E+02 1.314689E-06 1.206820E-08
220 -2.091750E+00 1.089384E+02 2.068677E-07 1.898943E-09
230 -2.091750E+00 1.089384E+02 4.987179E-08 4.577982E-10
240 -2.091750E+00 1.089384E+02 5.640933E-09 5.178097E-11
Injector = INJ1
Vacuum Energy = 28.674593883550340
Trace magnetic field
Get field evaluation object
To trace the magnetic field in python we need to retrieve an interpolation object to enable evaluation of the field at arbitrary points. This can be done using get_binterp(), where the flux is set by the vac_facs argument.
binterp_obj = taylor_solver.get_binterp(vac_facs=np.r_[1.0,])
Define tracer function for ODE integration
def tracer_eval(y, t, interp_obj, fac):
b = interp_obj.eval(y)
if interp_obj.cell.value <= 0:
return [0.0,0.0,0.0]
else:
return b*fac
Perform field line tracing
Now we trace a single field line for [1.5, 0.0, 0.0], where we trace forward and backward along the field line by applying a scale factor of -1.0 in the second case.
t = np.linspace(0, 40, 1000)
t0 = time.perf_counter()
sol, infodict = odeint(tracer_eval, np.array([1.5,0.0,0.0]), t, args=(binterp_obj,1.0), atol=1.E-9, full_output=True)
sol2, infodict2 = odeint(tracer_eval, np.array([1.5,0.0,0.0]), t, args=(binterp_obj,-1.0), atol=1.E-9, full_output=True)
t1 = time.perf_counter()
print("Time = {0:.3F} [s]".format(t1-t0))
print("Time/step = {0:.2E} [s]".format((t1-t0)/(np.sum(infodict['nfe'])+np.sum(infodict2['nfe']))))
Time = 1.287 [s] Time/step = 1.18E-08 [s]
Plot resulting field lines
fig, ax = plt.subplots(1,3,sharey=True,figsize=(10,4),constrained_layout=True)
ax[0].plot(sol[:,0],sol[:,1])
ax[0].plot(sol2[:,0],sol2[:,1])
ax[0].set_aspect('equal','box')
ax[1].plot(sol[:,0],sol[:,2])
ax[1].plot(sol2[:,0],sol2[:,2])
ax[1].set_aspect('equal','box')
ax[2].plot(sol[:,1],sol[:,2])
ax[2].plot(sol2[:,1],sol2[:,2])
ax[2].set_aspect('equal','box')
Save field for 3D plotting
taylor_solver.setup_io()
taylor_solver.save_field(binterp_obj,'B')
Starting CG solver
0 0.000000E+00 0.000000E+00 2.512636E-02
1 -1.284860E+01 1.074343E+03 2.478268E-03 2.306775E-06
2 -1.432609E+01 1.666399E+03 6.082516E-04 3.650095E-07
3 -1.433662E+01 1.673020E+03 1.065931E-04 6.371296E-08
4 -1.433710E+01 1.672989E+03 4.698798E-05 2.808624E-08
5 -1.433722E+01 1.672883E+03 2.567654E-05 1.534867E-08
6 -1.433726E+01 1.672797E+03 1.396381E-05 8.347583E-09
7 -1.433727E+01 1.672778E+03 7.588359E-06 4.536382E-09
8 -1.433727E+01 1.672777E+03 4.353274E-06 2.602424E-09
9 -1.433727E+01 1.672780E+03 2.485503E-06 1.485852E-09
10 -1.433727E+01 1.672783E+03 1.297498E-06 7.756521E-10
20 -1.433727E+01 1.672790E+03 6.489980E-09 3.879734E-12
Solver parallel diffusion
We now compute a parallel diffusion problem to get the temperature produced in response to uniform heating with anisotropic transport that is slow in the cross-field direction compared to the parallel direction. In this case we use \(\chi_{\parallel}/\chi_{\perp} = 10^5\).
t0 = time.perf_counter()
taylor_solver.compute_par_diff(binterp_obj,1.E-5)
t1 = time.perf_counter()
print('Solver time = {0:.4} [s]'.format(t1-t0))
Starting CG solver
0 0.000000E+00 0.000000E+00 8.084242E-03
1 -9.285216E-04 2.399326E-01 1.170790E-02 4.879660E-02
2 -5.389076E-03 1.618621E+00 2.491258E-02 1.539123E-02
3 -1.544873E-02 4.861987E+00 3.221482E-02 6.625855E-03
4 -2.779872E-02 8.907011E+00 3.337504E-02 3.747053E-03
5 -4.616194E-02 1.499180E+01 4.605103E-02 3.071747E-03
6 -7.104545E-02 2.332810E+01 4.857101E-02 2.082082E-03
7 -9.931607E-02 3.287841E+01 5.062435E-02 1.539744E-03
8 -1.359469E-01 4.533555E+01 6.371587E-02 1.405428E-03
9 -1.796943E-01 6.028997E+01 6.245061E-02 1.035837E-03
10 -2.321670E-01 7.829372E+01 7.044421E-02 8.997428E-04
20 -1.230217E+00 4.257862E+02 1.060530E-01 2.490757E-04
30 -3.193057E+00 1.118217E+03 1.443705E-01 1.291078E-04
40 -6.078533E+00 2.144452E+03 1.713346E-01 7.989668E-05
50 -9.759393E+00 3.461204E+03 1.884273E-01 5.443983E-05
60 -1.396066E+01 4.971270E+03 1.862839E-01 3.747208E-05
70 -1.854914E+01 6.627302E+03 1.917667E-01 2.893586E-05
80 -2.326522E+01 8.335759E+03 1.961009E-01 2.352526E-05
90 -2.810087E+01 1.009348E+04 2.030224E-01 2.011421E-05
100 -3.286027E+01 1.182920E+04 2.006930E-01 1.696589E-05
110 -3.779363E+01 1.363417E+04 1.983027E-01 1.454454E-05
120 -4.282691E+01 1.548161E+04 1.978018E-01 1.277657E-05
130 -4.789572E+01 1.734783E+04 2.019026E-01 1.163849E-05
140 -5.296782E+01 1.922087E+04 2.039880E-01 1.061284E-05
150 -5.801541E+01 2.109047E+04 2.005173E-01 9.507483E-06
160 -6.295441E+01 2.292524E+04 2.004233E-01 8.742476E-06
170 -6.807987E+01 2.483464E+04 2.010571E-01 8.095835E-06
180 -7.332373E+01 2.679353E+04 2.037142E-01 7.603113E-06
190 -7.845546E+01 2.871560E+04 2.023288E-01 7.045954E-06
200 -8.344817E+01 3.059046E+04 2.040172E-01 6.669310E-06
210 -8.868165E+01 3.256069E+04 2.026573E-01 6.223986E-06
220 -9.396546E+01 3.455503E+04 1.992571E-01 5.766372E-06
230 -9.899818E+01 3.645941E+04 1.977490E-01 5.423813E-06
240 -1.038456E+02 3.829820E+04 1.959239E-01 5.115747E-06
250 -1.085983E+02 4.010532E+04 1.967606E-01 4.906098E-06
260 -1.133609E+02 4.192055E+04 1.934334E-01 4.614285E-06
270 -1.182610E+02 4.379282E+04 1.940754E-01 4.431673E-06
280 -1.232682E+02 4.571078E+04 2.006070E-01 4.388614E-06
290 -1.282015E+02 4.760504E+04 1.990014E-01 4.180259E-06
300 -1.329790E+02 4.944376E+04 1.924321E-01 3.891939E-06
310 -1.374797E+02 5.117983E+04 1.857469E-01 3.629298E-06
320 -1.418889E+02 5.288412E+04 1.839861E-01 3.479042E-06
330 -1.463273E+02 5.460329E+04 1.872483E-01 3.429249E-06
340 -1.507946E+02 5.633734E+04 1.950016E-01 3.461321E-06
350 -1.555481E+02 5.818643E+04 1.958532E-01 3.365961E-06
360 -1.603755E+02 6.006857E+04 1.921326E-01 3.198554E-06
370 -1.651157E+02 6.192092E+04 1.916756E-01 3.095491E-06
380 -1.699443E+02 6.381195E+04 1.999347E-01 3.133185E-06
390 -1.751009E+02 6.583604E+04 2.065047E-01 3.136651E-06
400 -1.805068E+02 6.796317E+04 2.096949E-01 3.085420E-06
410 -1.861286E+02 7.018084E+04 2.085657E-01 2.971833E-06
420 -1.917360E+02 7.239841E+04 2.132674E-01 2.945746E-06
430 -1.974552E+02 7.466551E+04 2.161157E-01 2.894452E-06
440 -2.032915E+02 7.698453E+04 2.129400E-01 2.766010E-06
450 -2.088021E+02 7.917929E+04 2.068580E-01 2.612526E-06
460 -2.141420E+02 8.131069E+04 2.019501E-01 2.483684E-06
470 -2.194201E+02 8.342186E+04 2.042136E-01 2.447963E-06
480 -2.246370E+02 8.551309E+04 2.044780E-01 2.391190E-06
490 -2.298206E+02 8.759524E+04 2.033146E-01 2.321069E-06
500 -2.350834E+02 8.971349E+04 2.051138E-01 2.286321E-06
510 -2.405465E+02 9.191684E+04 2.057239E-01 2.238153E-06
520 -2.460561E+02 9.414330E+04 2.086550E-01 2.216356E-06
530 -2.514995E+02 9.634760E+04 2.099178E-01 2.178755E-06
540 -2.569605E+02 9.856330E+04 2.107038E-01 2.137751E-06
550 -2.627114E+02 1.009014E+05 2.146772E-01 2.127595E-06
560 -2.688318E+02 1.033952E+05 2.213365E-01 2.140684E-06
570 -2.751712E+02 1.059842E+05 2.270489E-01 2.142289E-06
580 -2.818387E+02 1.087136E+05 2.355162E-01 2.166391E-06
590 -2.888737E+02 1.116006E+05 2.417875E-01 2.166543E-06
600 -2.967113E+02 1.148250E+05 2.522076E-01 2.196452E-06
610 -3.054883E+02 1.184458E+05 2.692960E-01 2.273581E-06
620 -3.151728E+02 1.224525E+05 2.830180E-01 2.311248E-06
630 -3.256657E+02 1.268063E+05 2.948753E-01 2.325399E-06
640 -3.368209E+02 1.314488E+05 3.020209E-01 2.297632E-06
650 -3.489256E+02 1.365012E+05 3.082571E-01 2.258273E-06
660 -3.615391E+02 1.417812E+05 3.176325E-01 2.240300E-06
670 -3.742082E+02 1.470988E+05 3.172435E-01 2.156669E-06
680 -3.868360E+02 1.524123E+05 3.167199E-01 2.078047E-06
690 -3.990993E+02 1.575841E+05 3.056200E-01 1.939409E-06
700 -4.103337E+02 1.623317E+05 2.859263E-01 1.761371E-06
710 -4.203348E+02 1.665656E+05 2.730295E-01 1.639171E-06
720 -4.292400E+02 1.703415E+05 2.586672E-01 1.518522E-06
730 -4.367287E+02 1.735208E+05 2.297524E-01 1.324063E-06
740 -4.428973E+02 1.761429E+05 2.114690E-01 1.200554E-06
750 -4.482341E+02 1.784143E+05 1.953763E-01 1.095071E-06
760 -4.528450E+02 1.803788E+05 1.873019E-01 1.038381E-06
770 -4.569084E+02 1.821119E+05 1.738554E-01 9.546627E-07
780 -4.604453E+02 1.836220E+05 1.624571E-01 8.847364E-07
790 -4.637790E+02 1.850467E+05 1.579209E-01 8.534113E-07
800 -4.668799E+02 1.863729E+05 1.528750E-01 8.202637E-07
810 -4.698241E+02 1.876333E+05 1.513892E-01 8.068354E-07
820 -4.726523E+02 1.888452E+05 1.484178E-01 7.859230E-07
830 -4.754318E+02 1.900376E+05 1.461979E-01 7.693103E-07
840 -4.781931E+02 1.912235E+05 1.460056E-01 7.635341E-07
850 -4.809631E+02 1.924144E+05 1.503804E-01 7.815445E-07
860 -4.838243E+02 1.936459E+05 1.511148E-01 7.803665E-07
870 -4.867497E+02 1.949066E+05 1.545231E-01 7.928059E-07
880 -4.898662E+02 1.962515E+05 1.572273E-01 8.011520E-07
890 -4.930800E+02 1.976402E+05 1.603535E-01 8.113408E-07
900 -4.964587E+02 1.991020E+05 1.647495E-01 8.274628E-07
910 -4.999499E+02 2.006147E+05 1.663727E-01 8.293149E-07
920 -5.032994E+02 2.020679E+05 1.599561E-01 7.915961E-07
930 -5.064931E+02 2.034557E+05 1.552855E-01 7.632399E-07
940 -5.095302E+02 2.047774E+05 1.521282E-01 7.428955E-07
950 -5.123892E+02 2.060234E+05 1.476118E-01 7.164811E-07
960 -5.150592E+02 2.071885E+05 1.429703E-01 6.900492E-07
970 -5.174853E+02 2.082486E+05 1.341213E-01 6.440441E-07
980 -5.196887E+02 2.092127E+05 1.273201E-01 6.085677E-07
990 -5.216895E+02 2.100894E+05 1.223762E-01 5.824960E-07
1000 -5.234673E+02 2.108692E+05 1.155270E-01 5.478607E-07
1010 -5.249907E+02 2.115382E+05 1.043402E-01 4.932452E-07
1020 -5.262836E+02 2.121063E+05 9.853688E-02 4.645636E-07
1030 -5.274794E+02 2.126322E+05 9.411708E-02 4.426285E-07
1040 -5.285883E+02 2.131203E+05 9.278545E-02 4.353664E-07
1050 -5.296160E+02 2.135730E+05 8.837837E-02 4.138087E-07
1060 -5.305470E+02 2.139833E+05 8.283644E-02 3.871164E-07
1070 -5.313747E+02 2.143483E+05 7.819004E-02 3.647803E-07
1080 -5.321448E+02 2.146882E+05 7.536860E-02 3.510607E-07
1090 -5.328513E+02 2.150003E+05 7.392464E-02 3.438350E-07
1100 -5.335225E+02 2.152971E+05 7.299909E-02 3.390621E-07
1110 -5.341732E+02 2.155851E+05 6.939676E-02 3.218997E-07
1120 -5.347641E+02 2.158467E+05 6.640660E-02 3.076563E-07
1130 -5.353302E+02 2.160975E+05 6.612955E-02 3.060172E-07
1140 -5.358668E+02 2.163353E+05 6.473975E-02 2.992565E-07
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3640 -5.396644E+02 2.180260E+05 1.474641E-06 6.763603E-12
3650 -5.396644E+02 2.180260E+05 1.469951E-06 6.742091E-12
3660 -5.396644E+02 2.180260E+05 1.471925E-06 6.751142E-12
3670 -5.396644E+02 2.180260E+05 1.436946E-06 6.590712E-12
3680 -5.396644E+02 2.180260E+05 1.379960E-06 6.329337E-12
3690 -5.396644E+02 2.180260E+05 1.324893E-06 6.076764E-12
3700 -5.396644E+02 2.180260E+05 1.309612E-06 6.006678E-12
3710 -5.396644E+02 2.180260E+05 1.277566E-06 5.859695E-12
3720 -5.396644E+02 2.180260E+05 1.211118E-06 5.554927E-12
3730 -5.396644E+02 2.180260E+05 1.170161E-06 5.367071E-12
3740 -5.396644E+02 2.180260E+05 1.146008E-06 5.256292E-12
3750 -5.396644E+02 2.180260E+05 1.121992E-06 5.146140E-12
3760 -5.396644E+02 2.180260E+05 1.062787E-06 4.874591E-12
3770 -5.396644E+02 2.180260E+05 1.022602E-06 4.690277E-12
3780 -5.396644E+02 2.180259E+05 9.903733E-07 4.542456E-12
3790 -5.396644E+02 2.180259E+05 9.843979E-07 4.515050E-12
3800 -5.396644E+02 2.180259E+05 9.451360E-07 4.334970E-12
3810 -5.396644E+02 2.180259E+05 8.927438E-07 4.094668E-12
3820 -5.396644E+02 2.180259E+05 8.679767E-07 3.981071E-12
3830 -5.396644E+02 2.180259E+05 9.046617E-07 4.149331E-12
3840 -5.396644E+02 2.180259E+05 9.356462E-07 4.291445E-12
3850 -5.396644E+02 2.180259E+05 9.540483E-07 4.375848E-12
3860 -5.396644E+02 2.180259E+05 9.591111E-07 4.399069E-12
3870 -5.396644E+02 2.180259E+05 1.005154E-06 4.610252E-12
3880 -5.396644E+02 2.180259E+05 1.019483E-06 4.675972E-12
3890 -5.396644E+02 2.180259E+05 1.074991E-06 4.930564E-12
3900 -5.396644E+02 2.180259E+05 1.125973E-06 5.164399E-12
3910 -5.396644E+02 2.180259E+05 1.181946E-06 5.421129E-12
3920 -5.396644E+02 2.180259E+05 1.239271E-06 5.684054E-12
3930 -5.396644E+02 2.180259E+05 1.303684E-06 5.979493E-12
3940 -5.396644E+02 2.180259E+05 1.343222E-06 6.160839E-12
3950 -5.396644E+02 2.180259E+05 1.370319E-06 6.285121E-12
3960 -5.396644E+02 2.180259E+05 1.410070E-06 6.467443E-12
3970 -5.396644E+02 2.180258E+05 1.447067E-06 6.637135E-12
3980 -5.396644E+02 2.180258E+05 1.491198E-06 6.839546E-12
3990 -5.396644E+02 2.180258E+05 1.475149E-06 6.765938E-12
4000 -5.396644E+02 2.180258E+05 1.472710E-06 6.754753E-12
4010 -5.396644E+02 2.180258E+05 1.501561E-06 6.887078E-12
4020 -5.396644E+02 2.180258E+05 1.568121E-06 7.192367E-12
4030 -5.396644E+02 2.180258E+05 1.590689E-06 7.295876E-12
4040 -5.396644E+02 2.180258E+05 1.622512E-06 7.441837E-12
4050 -5.396644E+02 2.180257E+05 1.685263E-06 7.729650E-12
4060 -5.396644E+02 2.180257E+05 1.742688E-06 7.993036E-12
4070 -5.396644E+02 2.180257E+05 1.782199E-06 8.174260E-12
4080 -5.396644E+02 2.180257E+05 1.794154E-06 8.229094E-12
4090 -5.396644E+02 2.180257E+05 1.795581E-06 8.235640E-12
4100 -5.396644E+02 2.180257E+05 1.828009E-06 8.384377E-12
4110 -5.396644E+02 2.180256E+05 1.851565E-06 8.492417E-12
4120 -5.396644E+02 2.180256E+05 1.822607E-06 8.359599E-12
4130 -5.396644E+02 2.180256E+05 1.802900E-06 8.269211E-12
4140 -5.396644E+02 2.180256E+05 1.858533E-06 8.524380E-12
4150 -5.396644E+02 2.180256E+05 1.910846E-06 8.764321E-12
4160 -5.396644E+02 2.180255E+05 1.978002E-06 9.072341E-12
4170 -5.396644E+02 2.180255E+05 2.074200E-06 9.513564E-12
4180 -5.396644E+02 2.180255E+05 2.154071E-06 9.879905E-12
4190 -5.396644E+02 2.180255E+05 2.253803E-06 1.033734E-11
4200 -5.396644E+02 2.180254E+05 2.306821E-06 1.058051E-11
4210 -5.396644E+02 2.180254E+05 2.400985E-06 1.101241E-11
4220 -5.396644E+02 2.180254E+05 2.460289E-06 1.128441E-11
4230 -5.396644E+02 2.180253E+05 2.534493E-06 1.162477E-11
4240 -5.396644E+02 2.180253E+05 2.695311E-06 1.236238E-11
4250 -5.396644E+02 2.180252E+05 2.834994E-06 1.300305E-11
4260 -5.396644E+02 2.180252E+05 2.951130E-06 1.353573E-11
4270 -5.396644E+02 2.180251E+05 3.054316E-06 1.400901E-11
4280 -5.396644E+02 2.180251E+05 3.171028E-06 1.454433E-11
4290 -5.396644E+02 2.180250E+05 3.290885E-06 1.509407E-11
4300 -5.396644E+02 2.180250E+05 3.353101E-06 1.537944E-11
4310 -5.396644E+02 2.180249E+05 3.326756E-06 1.525861E-11
4320 -5.396644E+02 2.180248E+05 3.339137E-06 1.531540E-11
4330 -5.396644E+02 2.180247E+05 3.440156E-06 1.577874E-11
4340 -5.396644E+02 2.180247E+05 3.432760E-06 1.574482E-11
4350 -5.396644E+02 2.180246E+05 3.357542E-06 1.539983E-11
4360 -5.396644E+02 2.180245E+05 3.274152E-06 1.501736E-11
4370 -5.396644E+02 2.180245E+05 3.147188E-06 1.443502E-11
4380 -5.396644E+02 2.180244E+05 3.025615E-06 1.387741E-11
4390 -5.396644E+02 2.180244E+05 2.805633E-06 1.286844E-11
4400 -5.396644E+02 2.180243E+05 2.621747E-06 1.202502E-11
4410 -5.396644E+02 2.180243E+05 2.427410E-06 1.113367E-11
4420 -5.396644E+02 2.180243E+05 2.312439E-06 1.060634E-11
4430 -5.396644E+02 2.180242E+05 2.132083E-06 9.779111E-12
4440 -5.396644E+02 2.180242E+05 1.958372E-06 8.982361E-12
4450 -5.396644E+02 2.180242E+05 1.795685E-06 8.236171E-12
4460 -5.396644E+02 2.180242E+05 1.676551E-06 7.689747E-12
4470 -5.396644E+02 2.180242E+05 1.563136E-06 7.169555E-12
4480 -5.396644E+02 2.180241E+05 1.466907E-06 6.728187E-12
4490 -5.396644E+02 2.180241E+05 1.375123E-06 6.307206E-12
4500 -5.396644E+02 2.180241E+05 1.267005E-06 5.811306E-12
4510 -5.396644E+02 2.180241E+05 1.185994E-06 5.439737E-12
4520 -5.396644E+02 2.180241E+05 1.115024E-06 5.114226E-12
4530 -5.396644E+02 2.180241E+05 1.035057E-06 4.747443E-12
4540 -5.396644E+02 2.180241E+05 9.411736E-07 4.316833E-12
4550 -5.396644E+02 2.180241E+05 8.754156E-07 4.015225E-12
4560 -5.396644E+02 2.180241E+05 8.035740E-07 3.685712E-12
4570 -5.396644E+02 2.180241E+05 7.286020E-07 3.341842E-12
4580 -5.396644E+02 2.180241E+05 6.697544E-07 3.071929E-12
4590 -5.396644E+02 2.180241E+05 6.248171E-07 2.865817E-12
4600 -5.396644E+02 2.180241E+05 5.796301E-07 2.658560E-12
4610 -5.396644E+02 2.180241E+05 5.370226E-07 2.463134E-12
4620 -5.396644E+02 2.180241E+05 4.980684E-07 2.284465E-12
4630 -5.396644E+02 2.180241E+05 4.581379E-07 2.101318E-12
4640 -5.396644E+02 2.180241E+05 4.205173E-07 1.928766E-12
4650 -5.396644E+02 2.180241E+05 3.842384E-07 1.762367E-12
4660 -5.396644E+02 2.180241E+05 3.467590E-07 1.590462E-12
4670 -5.396644E+02 2.180241E+05 3.175526E-07 1.456502E-12
4680 -5.396644E+02 2.180241E+05 2.936576E-07 1.346904E-12
4690 -5.396644E+02 2.180241E+05 2.823710E-07 1.295137E-12
4700 -5.396644E+02 2.180241E+05 2.632305E-07 1.207346E-12
4710 -5.396644E+02 2.180241E+05 2.427430E-07 1.113377E-12
4720 -5.396644E+02 2.180241E+05 2.272742E-07 1.042427E-12
4730 -5.396644E+02 2.180241E+05 2.210411E-07 1.013838E-12
4740 -5.396644E+02 2.180241E+05 2.149177E-07 9.857524E-13
4750 -5.396644E+02 2.180241E+05 1.993747E-07 9.144620E-13
4760 -5.396644E+02 2.180241E+05 1.852978E-07 8.498963E-13
4770 -5.396644E+02 2.180241E+05 1.766885E-07 8.104082E-13
4780 -5.396644E+02 2.180241E+05 1.716925E-07 7.874936E-13
4790 -5.396644E+02 2.180241E+05 1.627248E-07 7.463619E-13
4800 -5.396644E+02 2.180241E+05 1.505463E-07 6.905030E-13
4810 -5.396644E+02 2.180241E+05 1.386298E-07 6.358465E-13
4820 -5.396644E+02 2.180241E+05 1.317582E-07 6.043286E-13
4830 -5.396644E+02 2.180241E+05 1.217387E-07 5.583726E-13
4840 -5.396644E+02 2.180241E+05 1.096427E-07 5.028926E-13
4850 -5.396644E+02 2.180241E+05 1.020248E-07 4.679520E-13
4860 -5.396644E+02 2.180241E+05 9.671664E-08 4.436054E-13
4870 -5.396644E+02 2.180241E+05 9.116814E-08 4.181563E-13
4880 -5.396644E+02 2.180241E+05 8.477911E-08 3.888521E-13
4890 -5.396644E+02 2.180241E+05 7.879421E-08 3.614015E-13
4900 -5.396644E+02 2.180241E+05 7.558195E-08 3.466679E-13
4910 -5.396644E+02 2.180241E+05 7.318538E-08 3.356757E-13
4920 -5.396644E+02 2.180241E+05 6.914066E-08 3.171240E-13
Solver time = 24.04 [s]
Plot temperature on clipped volume using pyvista
Finally we plot the temperature on a clipped volume showing nested temperature contours from the wall to the core using pyvista.
Load data from plot files
To plot the fields we must load in the mesh from the plot files.
- Note
- In the future this will be handled by dedicated python functions, but we show it here at the moment for demonstration purposes.
import pyvista
plot_data = taylor_solver.build_XDMF()
grid = plot_data['marklin']['vmesh'].get_pyvista_grid()
T = plot_data['marklin']['vmesh'].get_field('T')
grid["scalars"] = T
slice_x = grid.clip(normal='x')
p = pyvista.Plotter()
p.add_mesh(slice_x, cmap="Reds", scalar_bar_args={'title': "T", "vertical": True, "position_y":0.25, "position_x": 0.0})
p.camera.position = (7.0,2.0,0.0)
p.show(jupyter_backend='static')
Removing old Xdmf files
Removed 2 files
Creating output files: oft_xdmf.XXXX.h5
Found Group: marklin
Found Mesh: smesh
# of blocks: 1
Found Mesh: vmesh
# of blocks: 1
