Adding val-1fa and val-1fb verification cases idaholab#12

Makefile

@@ -31,7 +31,7 @@ CONTACT                     := no
 EXTERNAL_PETSC_SOLVER       := no
 FLUID_PROPERTIES            := no
 FUNCTIONAL_EXPANSION_TOOLS  := no
-HEAT_CONDUCTION             := no
+HEAT_CONDUCTION             := yes
 LEVEL_SET                   := no
 MISC                        := no
 NAVIER_STOKES               := no

doc/config.yml

@@ -1,6 +1,7 @@
 Content:
     - ${ROOT_DIR}/doc/content
     - ${MOOSE_DIR}/framework/doc/content
+    - ${MOOSE_DIR}/modules/heat_conduction/doc/content
 Renderer:
     type: MooseDocs.base.MaterializeRenderer
 Extensions:
@@ -31,6 +32,7 @@ Extensions:
         categories:
             framework: !include ${MOOSE_DIR}/framework/doc/sqa_framework.yml
             tmap: !include ${ROOT_DIR}/doc/sqa_tmap.yml
+            heat_conduction: !include ${MOOSE_DIR}/modules/heat_conduction/doc/sqa_heat_conduction.yml
         repos:
             default: https://github.com/idaholab/TMAP8
         reports: !include ${ROOT_DIR}/doc/sqa_reports.yml

doc/content/verification/bibfile.bib

@@ -4,9 +4,20 @@ @techreport{longhurst1992verification
   year={1992},
   institution={EG and G Idaho, Inc., Idaho Falls, ID (United States)}
 }
+
+@techreport{ambrosek2008verification,
+  title={Verification and Validation of TMAP7},
+  author={Ambrosek, James and Longhurst, GR},
+  year={2008},
+  number = "INEEL/EXT-04-01657",
+  month = "December",
+  publisher = "INL Technical Report",
+  institution = "Idaho National Laboratory"
+}
+
 @article{longhurst2005verification,
 	title={Verification and validation of the tritium transport code TMAP7},
-	author={Longhurst, Glen R and Ambrosek, James},
+	author={Ambrosek, James and Longhurst, Glen R},
 	journal={Fusion science and technology},
 	volume={48},
 	number={1},

doc/content/verification/val-1fa.md

@@ -0,0 +1,34 @@
+# val-1fa
+
+# Heat Conduction with Heat Generation
+
+This heat transfer verification problem is taken from [!cite](longhurst1992verification). In this problem heat conduction through a slab is modeled. The slab has heat generation. One end of the slab is kept at a constant temperature of 300K while the other end acts as an adiabatic surface. The analytical solution for this case is given as:
+
+\begin{equation}
+T = T_s \;+\; \frac{QL^2}{2k} \left(1-\frac{x^2}{L^2}\right)
+\end{equation}
+
+where:
+
+    $Q$ : internal heat generation rate (10,000 W/m$^3$)
+
+    $L$ : length of the slab (1.6 m)
+
+    $k$ : thermal conductivity (10 W/m-K)
+
+    $T_s$ : imposed surface temperature (300 K)
+
+
+The slab is assumed to have a density of 1 kg/m$^3$ and a specific heat capabity of 1 J/kg-K.
+
+Comparison of the temperature computed through TMAP8 and calculated analytically is shown in
+[val-1fa_comparison_temperature]. The TMAP8 code predictions match very well with
+the analytical solution.
+
+!media figures/val-1fa_comparison_temperature.png
+    style=width:60%;margin-bottom:2%
+    id=val-1fa_comparison_temperature
+    caption=Comparison of temperature along the slab calculated
+     through TMAP8 and analytically
+
+!bibtex bibliography

doc/content/verification/val-1fb.md

@@ -0,0 +1,48 @@
+# val-1fb
+
+# Thermal Transient in a Slab
+
+This verification problem is taken from [!cite](ambrosek2008verification). In this problem thermal transient in a slab is modeled. The ends of a slab are kept fixed at different temperatures. The temperature distribution in the slab evolves from an initial state to steady-state. The analytical solution for this case is given as:
+
+\begin{equation}
+T(x,t) = T_o \;+\; (T_1-T_o)\Bigg\{1-\frac{x}{L}-\frac{2}{L}\sum_{m=1}^{\infty} \left(\frac{1}{\lambda_m}  \sin(\lambda_m x) \exp(-\alpha \lambda_m^2 t)  \right)\Bigg\}
+\end{equation}
+
+where:
+
+
+    $T$ : temperature in the slab (K)
+
+
+    $x$ : distance across the slab (m)
+
+    $t$ : time (seconds)
+
+    $T_o$ : fixed temperature at one end of the slab (400 K)
+
+    $T_1$ : fixed temperature at the other end of the slab (300 K)
+
+    $L$ : length of the slab (4.0 m)
+
+    $\lambda_m$ : $\frac{m\pi}{L}$
+
+    $\alpha$ : thermal diffusivity (1.0 m$^2$/s) where 
+
+\begin{equation}
+\alpha = \frac{k}{\rho C_p}
+\end{equation}
+
+$k$ is the thermal conductivity, $\rho$ is the density and $C_p$ is the specific heat capacity of the slab material.
+
+# 
+
+
+Comparison of the temperature distribution in the slab, computed through TMAP8 and calculated analytically, is shown in [val-1fb_comparison_temperature]. The TMAP8 code predictions match very well with the analytical solution.
+
+!media figures/val-1fb_comparison_temperature.png
+    style=width:60%;margin-bottom:2%
+    id=val-1fb_comparison_temperature
+    caption=Comparison of temperature distribution in the slab calculated
+     through TMAP8 and analytically
+
+!bibtex bibliography

doc/content/verification/val-list.md

@@ -6,3 +6,5 @@
 | val-1b | [Diffusion Problem with Constant Source Boundary Condition](val-1b.md) |
 | val-1c | [Diffusion Problem with Partially Preloaded Slab](val-1c.md) |
 | val-1d | [Permeation Problem with Trapping](val-1d.md) |
+| val-1fa | [Heat Conduction with Heat Generation](val-1fa.md) |
+| val-1fb | [Thermal Transient](val-1fb.md) |

test/tests/val-1fa/comparison_val-1fa.py

@@ -0,0 +1,36 @@
+import csv
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib import gridspec
+import pandas as pd
+from scipy import special
+
+
+
+fig = plt.figure(figsize=[6.5,5.5])
+gs = gridspec.GridSpec(1,1)
+ax = fig.add_subplot(gs[0])
+
+analytical_x = np.linspace(0.0, 1.6, 40)
+Ts = 300
+k = 10
+L = 1.6
+Q = 10000
+analytical_temp = Ts + Q*L**2 * (1- analytical_x**2/L**2) / (2*k)
+ax.scatter(analytical_x,analytical_temp,label=r"Analytical",c='k', marker='^')
+
+tmap_sol = pd.read_csv("./gold/u_vs_x.csv")
+tmap_x = tmap_sol['id']
+tmap_temp = tmap_sol['temp']
+ax.plot(tmap_x,tmap_temp,label=r"TMAP8",c='tab:gray')
+
+ax.set_xlabel(u'Distance along slab (m)')
+ax.set_ylabel(u"Temperature (K)")
+ax.legend(loc="best")
+#ax.set_xlim(left=0)
+ax.set_ylim(bottom=0)
+plt.grid(visible=True, which='major', color='0.65', linestyle='--', alpha=0.3)
+
+ax.minorticks_on()
+plt.savefig('val-1fa_comparison_temperature.png', bbox_inches='tight');
+plt.close(fig)

test/tests/val-1fa/gold/u_vs_x.csv

@@ -0,0 +1,41 @@
+id,temp,x,y,z
+0,1579.9999253845,0,0,0
+0.041025641025641,1578.3588998614,0.041025641025641,0,0
+0.082051282051282,1576.553771786,0.082051282051282,0,0
+0.12307692307692,1571.630695216,0.12307692307692,0,0
+0.16410256410256,1566.3794135412,0.16410256410256,0,0
+0.20512820512821,1558.1742859222,0.20512820512821,0,0
+0.24615384615385,1549.4768506453,0.24615384615385,0,0
+0.28717948717949,1537.9896719737,0.28717948717949,0,0
+0.32820512820513,1525.8460830905,0.32820512820513,0,0
+0.36923076923077,1511.0768533612,0.36923076923077,0,0
+0.41025641025641,1495.4871108659,0.41025641025641,0,0
+0.45128205128205,1477.4358300725,0.45128205128205,0,0
+0.49230769230769,1458.3999339575,0.49230769230769,0,0
+0.53333333333333,1437.0666020922,0.53333333333333,0,0
+0.57435897435897,1414.5845523486,0.57435897435897,0,0
+0.61538461538462,1389.9691694025,0.61538461538462,0,0
+0.65641025641026,1364.0409660198,0.65641025641026,0,0
+0.6974358974359,1336.1435319825,0.6974358974359,0,0
+0.73846153846154,1306.7691749489,0.73846153846154,0,0
+0.77948717948718,1275.5896898089,0.77948717948718,0,0
+0.82051282051282,1242.7691791112,0.82051282051282,0,0
+0.86153846153846,1208.307642856,0.86153846153846,0,0
+0.9025641025641,1172.0409784799,0.9025641025641,0,0
+0.94358974358974,1134.2973910957,0.94358974358974,0,0
+0.98461538461538,1094.5845730256,0.98461538461538,0,0
+1.025641025641,1053.5589344981,1.025641025641,0,0
+1.0666666666667,1010.3999627174,1.0666666666667,0,0
+1.1076923076923,966.09227303116,1.1076923076923,0,0
+1.1487179487179,919.48714752242,1.1487179487179,0,0
+1.1897435897436,871.8974066612,1.1897435897436,0,0
+1.2307692307692,821.84612740614,1.2307692307692,0,0
+1.2717948717949,770.97433535315,1.2717948717949,0,0
+1.3128205128205,717.47690233283,1.3128205128205,0,0
+1.3538461538462,663.32305907068,1.3538461538462,0,0
+1.3948717948718,606.37947226561,1.3948717948718,0,0
+1.4358974358974,548.94357777648,1.4358974358974,0,0
+1.4769230769231,488.55383716672,1.4769230769231,0,0
+1.5179487179487,427.83589143245,1.5179487179487,0,0
+1.5589743589744,363.99999699781,1.5589743589744,0,0
+1.6,300,1.6,0,0

test/tests/val-1fa/tests

@@ -0,0 +1,11 @@
+[Tests]
+  design = 'HeatConduction.md HeatConductionTimeDerivative.md HeatSource.md'
+  issues = '#12'
+  [heat_conduction_generation]
+    type = Exodiff
+    input = val-1fa.i
+    exodiff = val-1fa_out.e
+    requirement = 'The system shall be able to model heat conduction in a slab that has heat generation'
+    verification = 'val-1fa.md'
+  []
+[]

test/tests/val-1fa/val-1fa.i

@@ -0,0 +1,96 @@
+[Mesh]
+  type = GeneratedMesh
+  dim = 1
+  xmax = 1.6
+  nx = 20
+[]
+
+[Variables]
+  [./temp]
+    initial_condition = 300.0
+  [../]
+[]
+
+[Kernels]
+  [./heat]
+    type = HeatConduction
+    variable = temp
+  [../]
+  [./heatsource]
+    type = HeatSource
+    function = volumetric_heat
+    variable = temp
+  [../]
+  [./HeatTdot]
+    type = HeatConductionTimeDerivative
+    variable = temp
+  [../]
+[]
+
+[BCs]
+  [./lefttemp]
+    type = DirichletBC
+    boundary = right
+    variable = temp
+    value = 300
+  [../]
+  [./rightflux]
+    type = NeumannBC
+    boundary = left
+    variable = temp
+    value = 0
+  [../]
+[]
+
+[Materials]
+  [./density]
+    type = GenericConstantMaterial
+    prop_names = 'density  thermal_conductivity specific_heat'
+    prop_values = '1.0 10.0 1.0'
+  [../]
+[]
+
+[Functions]
+  [./volumetric_heat]
+     type = ParsedFunction
+     value = 1.0e4
+  [../]
+[]
+
+[Preconditioning]
+  [./SMP]
+    type = SMP
+    full = true
+  [../]
+[]
+
+[Executioner]
+  type = Transient
+  scheme = bdf2
+  solve_type = PJFNK
+  petsc_options_iname = '-pc_type -ksp_grmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
+  petsc_options_value = 'asm         101   preonly   ilu      1'
+  nl_rel_tol = 1e-8
+  nl_abs_tol = 1e-10
+  l_tol = 1e-4
+  dt = 1
+  end_time = 10
+  automatic_scaling = true
+[]
+
+[VectorPostprocessors]
+  [line]
+    type = LineValueSampler
+    start_point = '0 0 0'
+    end_point = '1.6 0 0'
+    num_points = 40
+    sort_by = 'x'
+    variable = temp
+  []
+[]
+
+[Outputs]
+  execute_on = FINAL
+  exodus = false
+  csv = true
+[]

test/tests/val-1fb/comparison_val-1fb.py

@@ -0,0 +1,65 @@
+import csv
+import matplotlib.pyplot as plt
+import numpy as np
+from matplotlib import gridspec
+import pandas as pd
+from scipy import special
+
+
+
+fig = plt.figure(figsize=[6.5,5.5])
+gs = gridspec.GridSpec(1,1)
+ax = fig.add_subplot(gs[0])
+
+num_summation_terms = 10
+
+def summation_terms(n, x, t, alph):
+    sum = 0.0
+    for m in range(1, n):
+        lambdaa = m * np.pi / L
+        sum += np.sin(lambdaa * x) * np.exp(-1 * alph * lambdaa**2 * t) / lambdaa
+    return sum
+
+analytical_x = np.linspace(0.0, 4.0, 40)
+To = 300
+T1 = 400
+alpha = 1.0
+L = 4.0
+time = [0.1, 0.5, 1.0, 5.0]
+
+analytical_temp =[]
+for i in range(len(time)):
+    analytical_temp.append(To + (T1-To) * (1 - (analytical_x/L) - (2/L) * summation_terms(num_summation_terms, analytical_x, time[i], alpha)))
+
+ax.scatter(analytical_x,analytical_temp[0],label=r"Analytical 0.1 seconds",c='k', marker='^')
+ax.scatter(analytical_x,analytical_temp[1],label=r"Analytical 0.5 seconds",c='r', marker='^')
+ax.scatter(analytical_x,analytical_temp[2],label=r"Analytical 1.0 seconds",c='b', marker='^')
+ax.scatter(analytical_x,analytical_temp[3],label=r"Analytical 5.0 seconds",c='c', marker='^')
+
+tmap_temp = []
+tmap_sol = pd.read_csv("./gold/u_vs_x_0pt1sec.csv")
+tmap_x = tmap_sol['id']
+tmap_temp.append(tmap_sol['temp'])
+tmap_sol = pd.read_csv("./gold/u_vs_x_0pt5sec.csv")
+tmap_temp.append(tmap_sol['temp'])
+tmap_sol = pd.read_csv("./gold/u_vs_x_1pt0sec.csv")
+tmap_temp.append(tmap_sol['temp'])
+tmap_sol = pd.read_csv("./gold/u_vs_x_5pt0sec.csv")
+tmap_temp.append(tmap_sol['temp'])
+
+ax.plot(tmap_x,tmap_temp[0],label=r"TMAP8 0.1 seconds",c='k')
+ax.plot(tmap_x,tmap_temp[1],label=r"TMAP8 0.5 seconds",c='r')
+ax.plot(tmap_x,tmap_temp[2],label=r"TMAP8 1.0 seconds",c='b')
+ax.plot(tmap_x,tmap_temp[3],label=r"TMAP8 5.0 seconds",c='c')
+
+
+ax.set_xlabel(u'Distance along slab (m)')
+ax.set_ylabel(u"Temperature (K)")
+ax.legend(loc="best")
+#ax.set_xlim(left=0)
+ax.set_ylim(bottom=300)
+plt.grid(visible=True, which='major', color='0.65', linestyle='--', alpha=0.3)
+
+ax.minorticks_on()
+plt.savefig('val-1fb_comparison_temperature.png', bbox_inches='tight');
+plt.close(fig)