Description

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Description#

The Crown

A complex geometry has been constructed and meshed in SALOME and the resulting .med file is located in the challenge_D folder. You will need to first convert this med file to .xdmf, the file format readable by FEniCS, a function has been provided for this, which will also produce the correspondance dictionary, providing the ids for each tagged volume and surface.

The geometry has only one volume subdomain but several surfaces.

The material of the problem is Gold.

The temperature field is to be solved within FESTIM. Consider a thermal conductivity \(315 \ \mathrm{W \ m^{-1}\ K^{-1}}\) and boundary conditions of a fixed temperature of \(600 \ \mathrm{K}\) on \(\Gamma_{\text{inner boundary}}\) and a convective heat flux on \(\Gamma_{\text{outer boundary}}\), with a heat transfer coefficient of \(10^{4} \ \mathrm{W \ m^{-2} \ K^{-1}}\) and outer temperature of \(300\ \text{K}\).

For the hydrogen transport problem, consider an implantation flux of \(10^{19} \ \mathrm{m^{2} s^{-1}}\) with an implantation depth of \(3 \ \mathrm{nm}\) on \(\Gamma_{\text{inner boundary}}\) and a fixed concentration of \(0\) on \(\Gamma_{\text{outer boundary}}\).

📖 Tasks:

  • Evaluate the time to reach 99% of the equilibrium

  • Evaluate the outwards flux

  • Evaluate the hydrogen inventory at steady state

  • Plot the temporal evolution of the outwards flux (on \(\Gamma_{\text{outer boundary}}\)) and hydrogen inventory

  • Plot steady state temperature and mobile concentration fields

  • Bonus: try and inspect the generated XDMF mesh files in Paraview

The transport properties for the geometry’s material can be found below:

import h_transport_materials as htm

D_gold = htm.diffusivities.filter(material="gold")[0]

print(f"Diffusivity of material: \n {D_gold}")

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Cell In[1], line 1
----> 1 import h_transport_materials as htm
      2 
      3 D_gold = htm.diffusivities.filter(material="gold")[0]
      4 

File ~/checkouts/readthedocs.org/user_builds/festim-workshop/conda/festim1/lib/python3.11/site-packages/h_transport_materials/__init__.py:25
     22 Rg = 8.314 * ureg.Pa * ureg.m**3 * ureg.mol**-1 * ureg.K**-1
     23 avogadro_nb = 6.022e23 * ureg.particle * ureg.mol**-1
---> 25 from pybtex.database import parse_file
     26 from pathlib import Path
     28 bib_database = parse_file(str(Path(__file__).parent) + "/references.bib")

File ~/checkouts/readthedocs.org/user_builds/festim-workshop/conda/festim1/lib/python3.11/site-packages/pybtex/database/__init__.py:44
     42 from pybtex.errors import report_error
     43 from pybtex.py3compat import fix_unicode_literals_in_doctest, python_2_unicode_compatible
---> 44 from pybtex.plugin import find_plugin
     47 # for python2 compatibility
     48 def indent(text, prefix):

File ~/checkouts/readthedocs.org/user_builds/festim-workshop/conda/festim1/lib/python3.11/site-packages/pybtex/plugin/__init__.py:26
      2 # Copyright (c) 2006-2021  Andrey Golovizin
      3 # Copyright (c) 2014  Matthias C. M. Troffaes
      4 #
   (...)     21 # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
     22 # SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
     25 import os.path  # splitext
---> 26 import pkg_resources
     28 from pybtex.exceptions import PybtexError
     31 class Plugin(object):

ModuleNotFoundError: No module named 'pkg_resources'

💡Hint: to visualise the fields produced by FESTIM, you can either export to XDMF using the XDMFExport class and then open the files in Paraview. Alternatively, you can visualise it in python with the fenics.plot function:

import fenics as f
import festim as F
import matplotlib.pyplot as plt

my_model = F.Simulation(.....)
my_model.initialise()
my_model.run()

plt.figure()
c_mobile = my_model.h_transport_problem.mobile.mobile_concentration()
f.plot(c_mobile)

plt.figure()
T = my_model.T.T
f.plot(T)

import meshio


def convert_med_to_xdmf(
    med_file,
    cell_file="mesh_domains.xdmf",
    facet_file="mesh_boundaries.xdmf",
    cell_type="tetra",
    facet_type="triangle",
):
    """Converts a MED mesh to XDMF
    Args:
        med_file (str): the name of the MED file
        cell_file (str, optional): the name of the file containing the
            volume markers. Defaults to "mesh_domains.xdmf".
        facet_file (str, optional): the name of the file containing the
            surface markers.. Defaults to "mesh_boundaries.xdmf".
        cell_type (str, optional): The topology of the cells. Defaults to "tetra".
        facet_type (str, optional): The topology of the facets. Defaults to "triangle".
    Returns:
        dict, dict: the correspondance dict, the cell types
    """
    msh = meshio.read(med_file)

    correspondance_dict = msh.cell_tags

    cell_data_types = msh.cell_data_dict["cell_tags"].keys()

    for mesh_block in msh.cells:
        if mesh_block.type == cell_type:

            meshio.write_points_cells(
                cell_file,
                msh.points,
                [mesh_block],
                cell_data={"f": [-1 * msh.cell_data_dict["cell_tags"][cell_type]]},
            )
        elif mesh_block.type == facet_type:
            meshio.write_points_cells(
                facet_file,
                msh.points,
                [mesh_block],
                cell_data={"f": [-1 * msh.cell_data_dict["cell_tags"][facet_type]]},
            )

    return correspondance_dict, cell_data_types


mesh_file = "challenge_D/challenge_mesh.med"

correspondance_dict, cell_data_types = convert_med_to_xdmf(
    mesh_file,
    cell_type="triangle",
    facet_type="line",
    cell_file="challenge_D/mesh_domains.xdmf",
    facet_file="challenge_D/mesh_boundaries.xdmf",
)

print("This is the correspondance dict:")
print(correspondance_dict)

This is the correspondance dict:
{np.int64(-6): ['solid'], np.int64(-7): ['inner_boundary'], np.int64(-8): ['outer_boundary']}

Your answer#

import festim as F

# YOUR CODE GOES HERE ...
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