import ufl
from festim import k_B
from festim.boundary_conditions import FixedConcentrationBC
def sieverts_law(T, S_0, E_S, pressure):
"""Applies the Sieverts law to compute the concentration at the boundary."""
S = S_0 * ufl.exp(-E_S / k_B / T)
return S * pressure**0.5
[docs]
class SievertsBC(FixedConcentrationBC):
"""Sieverts boundary condition class.
c = S * sqrt(pressure)
S = S_0 * exp(-E_S / k_B / T)
Args:
subdomain (festim.Subdomain): the subdomain where the boundary
condition is applied
species (str): the name of the species
S_0 (float or fem.Constant): the Sieverts constant pre-exponential
factor (H/m3/Pa0.5)
E_S (float or fem.Constant): the Sieverts constant activation energy (eV)
pressure (float or callable): the pressure at the boundary (Pa)
Attributes:
subdomain (festim.Subdomain): the subdomain where the boundary
condition is applied
value (float or fem.Constant): the value of the boundary condition
species (festim.Species or str): the name of the species
S_0 (float or fem.Constant): the Sieverts constant pre-exponential
factor (H/m3/Pa0.5)
E_S (float or fem.Constant): the Sieverts constant activation energy (eV)
pressure (float or callable): the pressure at the boundary (Pa)
Examples:
.. testsetup:: SievertsBC
from festim import SievertsBC, SurfaceSubdomain
my_subdomain = SurfaceSubdomain(id=1)
.. testcode:: SievertsBC
SievertsBC(subdomain=my_subdomain, S_0=1e-6, E_S=0.2, pressure=1e5,
species="H")
SievertsBC(subdomain=my_subdomain, S_0=1e-6, E_S=0.2,
pressure=lambda x: 1e5 + x[0], species="H")
SievertsBC(subdomain=my_subdomain, S_0=1e-6, E_S=0.2,
pressure=lambda t: 1e5 + t, species="H")
SievertsBC(subdomain=my_subdomain, S_0=1e-6, E_S=0.2,
pressure=lambda T: 1e5 + T, species="H")
SievertsBC(subdomain=my_subdomain, S_0=1e-6, E_S=0.2,
pressure=lambda x, t: 1e5 + x[0] + t, species="H")
"""
def __init__(self, subdomain, S_0, E_S, pressure, species) -> None:
# TODO find a way to have S_0 and E_S as fem.Constant
# maybe in create_value()
self.S_0 = S_0
self.E_S = E_S
self.pressure = pressure
value = self.create_new_value_function()
super().__init__(value=value, species=species, subdomain=subdomain)
[docs]
def create_new_value_function(self):
"""Creates a new value function based on the pressure attribute.
Raises:
ValueError: if the pressure function is not supported
Returns:
callable: the value function
"""
if callable(self.pressure):
arg_combinations = {
("x",): lambda T, x=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(x=x)
),
("t",): lambda T, t=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(t=t)
),
("T",): lambda T: sieverts_law(
T, self.S_0, self.E_S, self.pressure(T=T)
),
("t", "x"): lambda T, x=None, t=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(x=x, t=t)
),
("T", "x"): lambda T, x=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(x=x, T=T)
),
("T", "t"): lambda T, t=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(t=t, T=T)
),
("T", "t", "x"): lambda T, x=None, t=None: sieverts_law(
T, self.S_0, self.E_S, self.pressure(x=x, t=t, T=T)
),
}
# get the arguments of the pressure function
args = self.pressure.__code__.co_varnames
key = tuple(sorted(args))
# get the lambda function based on the argument combination
if key not in arg_combinations:
raise ValueError("pressure function not supported")
func = arg_combinations[key]
return func
else:
return lambda T: sieverts_law(T, self.S_0, self.E_S, self.pressure)
