A test with nodal source term

The purpose of this benchmark is to test the source term type of NodalSourceTerm being applied to the hydraulic equation in the computations with the Taylor-Hood elements, e.g., the pressure interpolation using linear shape function, and the displacement interpolation using quadratic shape function.

The problem is solved on a rectangular domain $2m \times 1m$. Nodal fluid flux is applied on the left boundary nodes with a value of 0.001 $kg/s$ via the property of NodalSourceTerm. The pore pressure on the right boundary is equal to the initial pore pressure of $10⁵$ $Pa$. The displacement in the normal direction of all boundaries except the left one is fixed.

Fluid and solid are incompressible.

All involved parameters are listed in the following tables:

The time period of 86400s (1 day) is discretised into 100 steps.

# importing libraries
import os
from pathlib import Path

import matplotlib.pyplot as plt
import ogstools as ot
from ogstools.meshlib import MeshSeries

# creating output path if it doesn't exist already.
out_dir = Path(os.environ.get("OGS_TESTRUNNER_OUT_DIR", "_out"))
out_dir.mkdir(parents=True, exist_ok=True)

# Initiate the OGS
model = ot.Project(
    input_file="nodal_source_test.prj", output_file="nodal_source_test.prj"
)

# Run the simulation
model.run_model(logfile=Path(out_dir) / "log.txt")

Project file written to output.
Simulation: nodal_source_test.prj
Status: finished successfully.
Execution took 0.8262348175048828 s

The distributions of pressure and displacement at the end time are shown in the following figure:

# Plotting
mesh = MeshSeries("HM_NodalSourceTem.pvd").mesh(20)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(20, 6))

mesh.plot_contourf(
    ot.variables.pressure.replace(data_name="pressure_interpolated"),
    fig=fig,
    ax=ax1,
    fontsize=15,
)
mesh.plot_contourf(ot.variables.displacement, fig=fig, ax=ax2, fontsize=15)

plt.subplots_adjust(wspace=0.3)  # increase horizontal space
plt.tight_layout()
plt.show()