Multi-material problem: initial trap distribution and diffusion barrier

User Support
1

Hi, all!

Assume a multi-material problem (for example, W-Cu) with traps defined within one material only. There are two points that I’d like to discuss.

1.If the initial condition for traps is provided with a float, then the traps are initialised within the whole geometry rather than within one material. Consider the following MWE:

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

model = F.Simulation()

vertices = np.linspace(0, 1, num=1000)

model.mesh = F.MeshFromVertices(vertices)

tungsten = F.Material(id=1, D_0=1, E_D=0, S_0=1, E_S=0, borders=[0, 0.5])
copper = F.Material(id=2, D_0=1, E_D=0, S_0=1, E_S=0, borders=[0.5, 1])

model.materials = [tungsten, copper]

trap_1 = F.Trap(
    k_0=1,
    E_k=0,
    p_0=2,
    E_p=0,
    density=1,
    materials=tungsten,
)

model.traps = [trap_1]

model.initial_conditions = [
    F.InitialCondition(field="1", value=5),
]

model.boundary_conditions = [F.DirichletBC(surfaces=[1, 2], value=0, field=0)]

model.T = 300

model.dt = F.Stepsize(
    initial_value=0.1,
    stepsize_change_ratio=1.1,
    max_stepsize=1,
    dt_min=1,
)

model.settings = F.Settings(
    absolute_tolerance=1e10,
    relative_tolerance=1e-10,
    final_time=0,
    chemical_pot=True,
    traps_element_type="DG",
)

model.initialise()

f.plot(model.h_transport_problem.traps[0].previous_solution)

plt.ylabel("Trap concentration")
plt.xlabel("x")
plt.show()

it produces:
image

I suppose a workaround is to use sp.Piecewise for the initial condition (or maybe I miss something?). If so, isn’t it confusing?

2.The second point concerns the material interface. If I suppose that hydrogen cannot diffuse from the first material into the second (e.g., there is another thin layer between these materials: W-CuO/CuO2-Cu, that prevents hydrogen migration into copper), what’d be a better option to simulate such a case?

2

Yes this is a current limitation. You could use Piecewise in 1D but it wouldn’t be applicable to complex 3D problems for instance.

Ideally we would have a volume argument to InitialCondition.
Btw this would require the traps element type to be DG.

You could either

  • simulate this interlayer explicitely with a very low diffusivity
  • if H cannot diffuse through the interface (I guess it’s similar to having a solubility approaching zero? then only simulate the W part and have a non-flux BC on the boundary
1 Like
3

Thank you for the response.

You could either

  • simulate this interlayer explicitely with a very low diffusivity
  • if H cannot diffuse through the interface (I guess it’s similar to having a solubility approaching zero? then only simulate the W part and have a non-flux BC on the boundary

If I need both materials to simulate “realistic” temperature evolution in the composite geometry, then I end up with the first approach.

4

This approach isn’t really appropriate for a 2D/3D geometry since you potentially have a very small inter-layer. But ok for 1D I suppose

you could have a heat transfer transient solve on one side and then only read the temperature in the part you want. But that would require a bit of tinkering.

In the fenicsx branch, when we add the interface conditions this will not be an issue since it will be possible to define a mobile species in one subdomain only.