(Ref. idaholab#12)

doc/content/verification_and_validation/index.md

@@ -24,7 +24,7 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how
 | ver-1ha | [Convective Gas Outflow Problem](ver-1ha.md)                                                      |
 | ver-1ja | [Radioactive Decay of Mobile Tritium in a Slab](ver-1ja.md)                                       |
 | ver-1jb | [Radioactive Decay of Mobile Tritium in a Slab with a Distributed Trap Concentration](ver-1jb.md) |
-
+| ver-1ka | [Simple Volumetric Source](ver-1ka.md)
 
 # List of benchmarking cases
 

doc/content/verification_and_validation/ver-1ka.md

@@ -0,0 +1,33 @@
+# ver-1ka
+
+# Simple Volumetric Source
+
+## General Case Description
+
+This problem involves two enclosures connected by a diffusive membrane that follows Sieverts law for diffusion. Both enclosures contain hydrogen (H$_2$), deuterium (T$_2$), and hydrogen deuteride (HT). In the first enclosure, there is an initial inventory of only hydrogen (H$_2$) along with a constant volumetric source rate of deuterium (T$_2$). The second enclosure starts out empty.
+
+## Case Set up
+
+This verification problem is taken from [!cite](longhurst1992verification). 
+The rise in pressure of T$_2$ molecules in the first enclosure can be monitored by using a non-flow type membrane between the two enclosures. Consequently, the rate of pressure increase can be expressed as:
+
+\begin{equation}
+\frac{dP_{T_2}}{dt} = \frac{S}{V} kT
+\end{equation}
+
+where $S$ represents the volumetric source rate, $V$ is the volume of the enclosure, $k$ is the Boltzmann constant, and $T$ is the temperature of the enclosure.
+
+Comparison of the TMAP8 results and the analytical solution is shown in
+[ver-1ka_comparison_time] as a function of time. The TMAP8 code predictions match very well with the analytical solution.
+
+!media figures/ver-1ka_comparison_time.png
+    style=width:50%;margin-bottom:2%
+    id=ver-1ka_comparison_time
+    caption=Comparison of T$_2$ partial pressure in an enclosure with no loss pathways as function of time calculated through TMAP8 and analytically
+
+## Input files
+
+!style halign=left
+The input file for this case can be found at [/ver-1ka.i], which is also used as tests in TMAP8 at [/ver-1ka/tests].
+
+!bibtex bibliography

test/tests/ver-1ka/comparison_ver-1ka.py

@@ -0,0 +1,27 @@
+import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+df = pd.read_csv('./gold/ver-1ka_out.csv')
+
+S = 1e20 # m^-3 * s^-1
+V = 1 # m^3
+kb = 1.380649e-23 # Boltzmann constant (J/K)
+T = 500 # K
+
+t_csv = df['time']
+v = df['v']
+t = np.arange(0, 10801, 540)
+
+expression = (S / V) * kb * T * t
+
+plt.plot(t_csv/3600, v, linestyle='-', color='magenta', label='TMAP8', linewidth=3)
+plt.plot(t/3600, expression, marker='+', linestyle='', color='black', label=r"theory", markersize=10)
+
+plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.1e}'.format(val)))
+
+plt.xlabel('Time (hr)')
+plt.ylabel('Pressure (Pa)')
+plt.legend()
+plt.grid(True)
+plt.savefig('ver-1ka_comparison_time.png', bbox_inches='tight')