import numpy as np
import ufl
from dolfinx import fem
import festim as F
from festim.subdomain.surface_subdomain import SurfaceSubdomain
[docs]
class FluxBCBase:
"""Flux boundary condition class.
Ensuring the gradient of the solution u at a boundary:
.. math::
-A \\nabla u \\cdot \\mathbf{n} = f
where :math:`A` is some material property (diffusivity for particle flux and thermal
conductivity for heat flux), :math:`\\mathbf{n}` is the outwards normal vector of
the boundary, :math:`f` is a function of space and time.
Args:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the boundary
condition is applied
value (float, fem.Constant, callable): the value of the boundary condition
Attributes:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the boundary
condition is applied
value (float, fem.Constant, callable): the value of the boundary condition
value_fenics (fem.Function or fem.Constant): the value of the boundary
condition in
fenics format
bc_expr (fem.Expression): the expression of the boundary condition that
is used to
update the value_fenics
"""
def __init__(self, subdomain: SurfaceSubdomain, value):
self.subdomain = subdomain
self.value = value
self.value_fenics = None
self.bc_expr = None
@property
def value_fenics(self):
return self._value_fenics
@value_fenics.setter
def value_fenics(self, value):
if value is None:
self._value_fenics = value
return
if not isinstance(
value, fem.Function | fem.Constant | np.ndarray | ufl.core.expr.Expr
):
raise TypeError(
f"Value must be a dolfinx.fem.Function, dolfinx.fem.Constant,"
f" np.ndarray or ufl.core.expr.Expr not {type(value)}"
)
self._value_fenics = value
@property
def time_dependent(self):
if self.value is None:
raise TypeError("Value must be given to determine if its time dependent")
if isinstance(self.value, fem.Constant):
return False
if callable(self.value):
arguments = self.value.__code__.co_varnames
return "t" in arguments
else:
return False
@property
def temperature_dependent(self):
if self.value is None:
return False
if isinstance(self.value, fem.Constant):
return False
if callable(self.value):
arguments = self.value.__code__.co_varnames
return "T" in arguments
else:
return False
[docs]
def create_value_fenics(self, mesh, temperature, t: fem.Constant):
"""Creates the value of the boundary condition as a fenics object and sets it to
self.value_fenics. If the value is a constant, it is converted to a
fenics.Constant. If the value is a function of t, it is converted to a
fenics.Constant. Otherwise, it is converted to a ufl Expression.
Args:
mesh (dolfinx.mesh.Mesh) : the mesh
temperature (float): the temperature
t (dolfinx.fem.Constant): the time
"""
x = ufl.SpatialCoordinate(mesh)
if isinstance(self.value, (int, float)):
self.value_fenics = F.as_fenics_constant(mesh=mesh, value=self.value)
elif callable(self.value):
arguments = self.value.__code__.co_varnames
if "t" in arguments and "x" not in arguments and "T" not in arguments:
# only t is an argument
if not isinstance(self.value(t=float(t)), (float, int)):
raise ValueError(
f"self.value should return a float or an int, not {type(self.value(t=float(t)))} " # noqa: E501
)
self.value_fenics = F.as_fenics_constant(
mesh=mesh, value=self.value(t=float(t))
)
else:
kwargs = {}
if "t" in arguments:
kwargs["t"] = t
if "x" in arguments:
kwargs["x"] = x
if "T" in arguments:
kwargs["T"] = temperature
self.value_fenics = self.value(**kwargs)
[docs]
def update(self, t):
"""Updates the flux bc value.
Args:
t (float): the time
"""
if callable(self.value):
arguments = self.value.__code__.co_varnames
if isinstance(self.value_fenics, fem.Constant) and "t" in arguments:
self.value_fenics.value = self.value(t=t)
[docs]
class ParticleFluxBC(FluxBCBase):
"""Particle flux boundary condition class.
Ensuring the gradient of the solution c at a boundary:
-D * grad(c) * n = f
where D is the material diffusivity, n is the outwards normal vector of the
boundary, f is a function of space and time.
Args:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the
particle flux
is applied
value (float, fem.Constant, callable): the value of the particle flux
species (festim.Species): the species to which the flux is applied
species_dependent_value (dict): a dictionary containing the species
that the value. Example: {"name": species}
where "name" is the variable name in the callable value and species
is a festim.Species object.
Attributes:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the
particle flux
is applied
value (float or fem.Constant): the value of the particle flux
species (festim.Species): the species to which the flux is applied
value_fenics (fem.Function or fem.Constant): the value of the particle flux in
fenics format
bc_expr (fem.Expression): the expression of the particle flux that is used to
update the value_fenics
species_dependent_value (dict): a dictionary containing the species
that the value. Example: {"name": species}
where "name" is the variable name in the callable value and species
is a festim.Species object.
Examples:
.. testsetup:: ParticleFluxBC
from festim import SurfaceSubdomain, ParticleFluxBC, Species
my_subdomain = SurfaceSubdomain(id=1)
species1 = Species(name="1")
.. testcode:: ParticleFluxBC
ParticleFluxBC(subdomain=my_subdomain, value=1, species="H")
ParticleFluxBC(subdomain=my_subdomain, value=lambda x: 1 + x[0],
species="H")
ParticleFluxBC(subdomain=my_subdomain, value=lambda t: 1 + t, species="H")
ParticleFluxBC(subdomain=my_subdomain, value=lambda T: 1 + T, species="H")
ParticleFluxBC(subdomain=my_subdomain, value=lambda x, t: 1 + x[0]
+ t, species="H")
ParticleFluxBC(subdomain=my_subdomain, value=lambda c1: 2 * c1**2,
species="H", species_dependent_value={"c1": species1})
"""
def __init__(self, subdomain, value, species, species_dependent_value={}):
super().__init__(subdomain=subdomain, value=value)
self.species = species
self.species_dependent_value = species_dependent_value
self._volume_subdomain = None
[docs]
def create_value_fenics(self, mesh, temperature, t: fem.Constant):
"""Creates the value of the boundary condition as a fenics object and sets it to
self.value_fenics. If the value is a constant, it is converted to a
fenics.Constant. If the value is a function of t, it is converted to a
fenics.Constant. Otherwise, it is converted to a ufl Expression.
Args:
mesh (dolfinx.mesh.Mesh) : the mesh
temperature (float): the temperature
t (dolfinx.fem.Constant): the time
"""
x = ufl.SpatialCoordinate(mesh)
if isinstance(self.value, (int, float)):
self.value_fenics = F.as_fenics_constant(mesh=mesh, value=self.value)
elif callable(self.value):
arguments = self.value.__code__.co_varnames
if "t" in arguments and "x" not in arguments and "T" not in arguments:
# only t is an argument
if not isinstance(self.value(t=float(t)), (float, int)):
raise ValueError(
f"self.value should return a float or an int, not {type(self.value(t=float(t)))} " # noqa: E501
)
self.value_fenics = F.as_fenics_constant(
mesh=mesh, value=self.value(t=float(t))
)
else:
kwargs = {}
if "t" in arguments:
kwargs["t"] = t
if "x" in arguments:
kwargs["x"] = x
if "T" in arguments:
kwargs["T"] = temperature
for name, species in self.species_dependent_value.items():
if species.concentration:
kwargs[name] = species.concentration
else: # probably in discontinuous case
kwargs[name] = species.subdomain_to_solution[
self._volume_subdomain
]
self.value_fenics = self.value(**kwargs)
[docs]
class HeatFluxBC(FluxBCBase):
"""Heat flux boundary condition class.
Ensuring the gradient of the solution T at a boundary:
-lambda * grad(T) * n = f
where lambda is the thermal conductivity , n is the outwards normal vector
of the boundary, f is a function of space and time.
Args:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the heat flux
is applied
value (float, callable, fem.Constant): the value of the heat flux
Attributes:
subdomain (festim.SurfaceSubdomain): the surface subdomain where the heat flux
is applied
value (float, callable, fem.Constant): the value of the heat flux
value_fenics (fem.Function or fem.Constant): the value of the heat flux in
fenics format
bc_expr (fem.Expression): the expression of the heat flux that is used to
update the value_fenics
Examples:
.. testsetup:: HeatFluxBC
from festim import SurfaceSubdomain, HeatFluxBC, Species
my_subdomain = SurfaceSubdomain(id=1)
species1 = Species(name="1")
.. testcode:: HeatFluxBC
HeatFluxBC(subdomain=my_subdomain, value=1)
HeatFluxBC(subdomain=my_subdomain, value=lambda x: 1 + x[0])
HeatFluxBC(subdomain=my_subdomain, value=lambda t: 1 + t)
HeatFluxBC(subdomain=my_subdomain, value=lambda x, t: 1 + x[0] + t)
"""
def __init__(self, subdomain, value):
super().__init__(subdomain=subdomain, value=value)
