def test_combine_geometries(self):
geometry1Dmacro = pybamm.Geometry1DMacro()
geometry1Dmicro = pybamm.Geometry1DMicro()
geometry = pybamm.Geometry(geometry1Dmacro, geometry1Dmicro)
self.assertEqual(
set(geometry.keys()),
set(
[
"negative electrode",
"separator",
"positive electrode",
"negative particle",
"positive particle",
"current collector",
]
),
)
# update with custom geometry
whole_cell = ["negative electrode", "separator", "positive electrode"]
x = pybamm.SpatialVariable("x", whole_cell)
custom_geometry = {
"negative electrode": {
"primary": {x: {"min": pybamm.Scalar(1), "max": pybamm.Scalar(2)}}
}
}
geometry = pybamm.Geometry(
geometry1Dmacro, geometry1Dmicro, custom_geometry=custom_geometry
)
self.assertEqual(
geometry["negative electrode"], custom_geometry["negative electrode"]
)
def test_combine_geometries_strings(self):
geometry = pybamm.Geometry("1D macro", "1D micro")
self.assertEqual(
set(geometry.keys()),
set(
[
"negative electrode",
"separator",
"positive electrode",
"negative particle",
"positive particle",
"current collector",
]
),
)
geometry = pybamm.Geometry("3D macro", "1D micro")
self.assertEqual(
set(geometry.keys()),
set(
[
"negative electrode",
"separator",
"positive electrode",
"negative particle",
"positive particle",
"current collector",
]
),
)
def default_geometry(self):
if self.options["dimensionality"] == 0:
return pybamm.Geometry("1D macro", "1+1D micro")
elif self.options["dimensionality"] == 1:
return pybamm.Geometry("1+1D macro", "1+1D micro")
elif self.options["dimensionality"] == 2:
return pybamm.Geometry("2+1D macro", "1+1D micro")
def default_geometry(self):
dimensionality = self.options["dimensionality"]
if dimensionality == 0:
return pybamm.Geometry("1D macro", "1D micro")
elif dimensionality == 1:
return pybamm.Geometry("1+1D macro", "(1+0)+1D micro")
elif dimensionality == 2:
return pybamm.Geometry("2+1D macro", "(2+0)+1D micro")
def test_processed_variable_1D_unknown_domain(self):
x = pybamm.SpatialVariable("x",
domain="SEI layer",
coord_sys="cartesian")
geometry = pybamm.Geometry({
"SEI layer": {
x: {
"min": pybamm.Scalar(0),
"max": pybamm.Scalar(1)
}
}
})
submesh_types = {"SEI layer": pybamm.Uniform1DSubMesh}
var_pts = {x: 100}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
nt = 100
y_sol = np.zeros((var_pts[x], nt))
solution = pybamm.Solution(
np.linspace(0, 1, nt),
y_sol,
pybamm.BaseModel(),
{},
np.linspace(0, 1, 1),
np.zeros((var_pts[x])),
"test",
)
c = pybamm.StateVector(slice(0, var_pts[x]), domain=["SEI layer"])
c.mesh = mesh["SEI layer"]
c_casadi = to_casadi(c, y_sol)
pybamm.ProcessedVariable([c], [c_casadi], solution, warn=False)
def test_extrapolate_on_nonuniform_grid(self):
geometry = pybamm.Geometry("1D micro")
submesh_types = {
"negative particle": pybamm.MeshGenerator(pybamm.Exponential1DSubMesh),
"positive particle": pybamm.MeshGenerator(pybamm.Exponential1DSubMesh),
}
var = pybamm.standard_spatial_vars
rpts = 10
var_pts = {var.r_n: rpts, var.r_p: rpts}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
method_options = {"extrapolation": {"order": "linear", "use bcs": False}}
spatial_methods = {"negative particle": pybamm.FiniteVolume(method_options)}
disc = pybamm.Discretisation(mesh, spatial_methods)
var = pybamm.Variable("var", domain="negative particle")
surf_eqn = pybamm.surf(var)
disc.set_variable_slices([var])
surf_eqn_disc = disc.process_symbol(surf_eqn)
micro_submesh = mesh["negative particle"]
# check constant extrapolates to constant
constant_y = np.ones_like(micro_submesh[0].nodes[:, np.newaxis])
np.testing.assert_array_almost_equal(
surf_eqn_disc.evaluate(None, constant_y), 1
)
# check linear variable extrapolates correctly
linear_y = micro_submesh[0].nodes
y_surf = micro_submesh[0].edges[-1]
np.testing.assert_array_almost_equal(
surf_eqn_disc.evaluate(None, linear_y), y_surf
)
def test_processed_variable_1D_unknown_domain(self):
x = pybamm.SpatialVariable("x",
domain="SEI layer",
coord_sys="cartesian")
geometry = pybamm.Geometry()
geometry.add_domain(
"SEI layer",
{
"primary": {
x: {
"min": pybamm.Scalar(0),
"max": pybamm.Scalar(1)
}
}
},
)
submesh_types = {"SEI layer": pybamm.Uniform1DSubMesh}
var_pts = {x: 100}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
nt = 100
solution = pybamm.Solution(
np.linspace(0, 1, nt),
np.zeros((var_pts[x], nt)),
np.linspace(0, 1, 1),
np.zeros((var_pts[x])),
"test",
)
c = pybamm.StateVector(slice(0, var_pts[x]), domain=["SEI layer"])
c.mesh = mesh["SEI layer"]
pybamm.ProcessedVariable(c, solution)
def default_geometry(self):
var = pybamm.standard_spatial_vars
geometry = {
"current collector": {
var.y: {
"min": 0,
"max": pybamm.geometric_parameters.l_y
},
var.z: {
"min": 0,
"max": pybamm.geometric_parameters.l_z
},
"tabs": {
"negative": {
"y_centre": pybamm.geometric_parameters.centre_y_tab_n,
"z_centre": pybamm.geometric_parameters.centre_z_tab_n,
"width": pybamm.geometric_parameters.l_tab_n,
},
"positive": {
"y_centre": pybamm.geometric_parameters.centre_y_tab_p,
"z_centre": pybamm.geometric_parameters.centre_z_tab_p,
"width": pybamm.geometric_parameters.l_tab_p,
},
},
}
}
return pybamm.Geometry(geometry)
def get_1p1d_mesh_for_testing(
xpts=None, zpts=15, cc_submesh=pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)
):
geometry = pybamm.Geometry("1+1D macro")
return get_mesh_for_testing(
xpts=xpts, zpts=zpts, geometry=geometry, cc_submesh=cc_submesh
)
def default_geometry(self):
geometry = {}
var = pybamm.standard_spatial_vars
if self.options["dimensionality"] == 1:
geometry["current collector"] = {
var.z: {"min": 0, "max": 1},
"tabs": {
"negative": {
"z_centre": pybamm.geometric_parameters.centre_z_tab_n
},
"positive": {
"z_centre": pybamm.geometric_parameters.centre_z_tab_p
},
},
}
elif self.options["dimensionality"] == 2:
geometry["current collector"] = {
var.y: {"min": 0, "max": pybamm.geometric_parameters.l_y},
var.z: {"min": 0, "max": pybamm.geometric_parameters.l_z},
"tabs": {
"negative": {
"y_centre": pybamm.geometric_parameters.centre_y_tab_n,
"z_centre": pybamm.geometric_parameters.centre_z_tab_n,
"width": pybamm.geometric_parameters.l_tab_n,
},
"positive": {
"y_centre": pybamm.geometric_parameters.centre_y_tab_p,
"z_centre": pybamm.geometric_parameters.centre_z_tab_p,
"width": pybamm.geometric_parameters.l_tab_p,
},
},
}
return pybamm.Geometry(geometry)
def get_2p1d_mesh_for_testing(
xpts=None,
ypts=15,
zpts=15,
cc_submesh=pybamm.MeshGenerator(pybamm.ScikitUniform2DSubMesh),
):
geometry = pybamm.Geometry("2+1D macro")
return get_mesh_for_testing(
xpts=xpts, zpts=zpts, geometry=geometry, cc_submesh=cc_submesh
)
def test_combine_geometries_3D(self):
geometry3Dmacro = pybamm.Geometry3DMacro()
geometry1Dmicro = pybamm.Geometry1DMicro()
geometry = pybamm.Geometry(geometry3Dmacro, geometry1Dmicro)
self.assertEqual(
set(geometry.keys()),
set([
"negative electrode",
"separator",
"positive electrode",
"negative particle",
"positive particle",
"current collector",
]),
)
with self.assertRaises(ValueError):
geometry1Dmacro = pybamm.Geometry1DMacro()
geometry = pybamm.Geometry(geometry3Dmacro, geometry1Dmacro)
def get_mesh_for_testing(xpts=None,
rpts=10,
ypts=15,
zpts=15,
geometry=None,
cc_submesh=None):
param = pybamm.ParameterValues(
values={
"Electrode width [m]": 0.4,
"Electrode height [m]": 0.5,
"Negative tab width [m]": 0.1,
"Negative tab centre y-coordinate [m]": 0.1,
"Negative tab centre z-coordinate [m]": 0.0,
"Positive tab width [m]": 0.1,
"Positive tab centre y-coordinate [m]": 0.3,
"Positive tab centre z-coordinate [m]": 0.5,
"Negative electrode thickness [m]": 0.3,
"Separator thickness [m]": 0.3,
"Positive electrode thickness [m]": 0.3,
})
if geometry is None:
geometry = pybamm.Geometry("1D macro", "1D micro")
param.process_geometry(geometry)
submesh_types = {
"negative electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive electrode": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
}
if cc_submesh:
submesh_types["current collector"] = cc_submesh
if xpts is None:
xn_pts, xs_pts, xp_pts = 40, 25, 35
else:
xn_pts, xs_pts, xp_pts = xpts, xpts, xpts
var = pybamm.standard_spatial_vars
var_pts = {
var.x_n: xn_pts,
var.x_s: xs_pts,
var.x_p: xp_pts,
var.r_n: rpts,
var.r_p: rpts,
var.y: ypts,
var.z: zpts,
}
return pybamm.Mesh(geometry, submesh_types, var_pts)
def test_multiple_meshes_macro(self):
param = pybamm.ParameterValues(
values={
"Negative electrode thickness [m]": 0.1,
"Separator thickness [m]": 0.2,
"Positive electrode thickness [m]": 0.3,
"Electrode height [m]": 0.4,
"Negative tab centre z-coordinate [m]": 0.0,
"Positive tab centre z-coordinate [m]": 0.4,
})
geometry = pybamm.Geometry("1+1D macro")
param.process_geometry(geometry)
# provide mesh properties
var = pybamm.standard_spatial_vars
var_pts = {var.x_n: 10, var.x_s: 15, var.x_p: 20, var.z: 5}
submesh_types = {
"negative electrode":
pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive electrode":
pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
# check types
self.assertIsInstance(mesh["negative electrode"], list)
self.assertIsInstance(mesh["separator"], list)
self.assertIsInstance(mesh["positive electrode"], list)
self.assertEqual(len(mesh["negative electrode"]), 5)
self.assertEqual(len(mesh["separator"]), 5)
self.assertEqual(len(mesh["positive electrode"]), 5)
for i in range(5):
self.assertIsInstance(mesh["negative electrode"][i],
pybamm.Uniform1DSubMesh)
self.assertIsInstance(mesh["separator"][i],
pybamm.Uniform1DSubMesh)
self.assertIsInstance(mesh["positive electrode"][i],
pybamm.Uniform1DSubMesh)
self.assertEqual(mesh["negative electrode"][i].npts, 10)
self.assertEqual(mesh["separator"][i].npts, 15)
self.assertEqual(mesh["positive electrode"][i].npts, 20)
def test_add_domain(self):
L = pybamm.Parameter("L")
zero = pybamm.Scalar(0)
x = pybamm.SpatialVariable("x", domain=["negative electrode"])
geometry = pybamm.Geometry()
geometry.add_domain("name_of_domain", {"primary": {x: {"min": zero, "max": L}}})
geometry.add_domain("name_of_domain", {"tabs": {"negative": {"z_centre": L}}})
# name must be a string
with self.assertRaisesRegex(ValueError, "name must be a string"):
geometry.add_domain(123, {"primary": {x: {"min": zero, "max": L}}})
# keys of geometry must be either \"primary\" or \"secondary\"
with self.assertRaisesRegex(ValueError, "primary.*secondary"):
geometry.add_domain(
"name_of_domain", {"primaryy": {x: {"min": zero, "max": L}}}
)
# inner dict of geometry must have pybamm.SpatialVariable as keys
with self.assertRaisesRegex(ValueError, "pybamm\.SpatialVariable as keys"):
geometry.add_domain(
"name_of_domain", {"primary": {L: {"min": zero, "max": L}}}
)
# no minimum extents for variable
with self.assertRaisesRegex(ValueError, "minimum"):
geometry.add_domain("name_of_domain", {"primary": {x: {"max": L}}})
# no maximum extents for variable
with self.assertRaisesRegex(ValueError, "maximum"):
geometry.add_domain("name_of_domain", {"primary": {x: {"min": zero}}})
# tabs region must be \"negative\" or \"positive\"
with self.assertRaisesRegex(ValueError, "negative.*positive"):
geometry.add_domain(
"name_of_domain", {"tabs": {"negativee": {"z_centre": L}}}
)
# tabs region params must be \"y_centre\", "\"z_centre\" or \"width\"
with self.assertRaisesRegex(ValueError, "y_centre.*z_centre.*width"):
geometry.add_domain(
"name_of_domain", {"tabs": {"negative": {"z_centree": L}}}
)
def test_read_parameters(self):
L_n = pybamm.geometric_parameters.L_n
L_s = pybamm.geometric_parameters.L_s
L_p = pybamm.geometric_parameters.L_p
L_y = pybamm.geometric_parameters.L_y
L_z = pybamm.geometric_parameters.L_z
tab_n_y = pybamm.geometric_parameters.Centre_y_tab_n
tab_n_z = pybamm.geometric_parameters.Centre_z_tab_n
L_tab_n = pybamm.geometric_parameters.L_tab_n
tab_p_y = pybamm.geometric_parameters.Centre_y_tab_p
tab_p_z = pybamm.geometric_parameters.Centre_z_tab_p
L_tab_p = pybamm.geometric_parameters.L_tab_p
geometry = pybamm.Geometry("2+1D macro", "(2+1)+1D micro")
self.assertEqual(
set([x.name for x in geometry.parameters]),
set(
[
x.name
for x in [
L_n,
L_s,
L_p,
L_y,
L_z,
tab_n_y,
tab_n_z,
L_tab_n,
tab_p_y,
tab_p_z,
L_tab_p,
]
]
),
)
self.assertTrue(
all(isinstance(x, pybamm.Parameter) for x in geometry.parameters)
)
def test_multiple_meshes(self):
param = pybamm.ParameterValues(
values={
"Negative electrode thickness [m]": 0.1,
"Separator thickness [m]": 0.2,
"Positive electrode thickness [m]": 0.3,
})
geometry = pybamm.Geometry("1+1D micro")
param.process_geometry(geometry)
# provide mesh properties
var = pybamm.standard_spatial_vars
var_pts = {var.x_n: 10, var.x_p: 10, var.r_n: 5, var.r_p: 6}
submesh_types = {
"negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
# check types
self.assertIsInstance(mesh["negative particle"], list)
self.assertIsInstance(mesh["positive particle"], list)
self.assertEqual(len(mesh["negative particle"]), 10)
self.assertEqual(len(mesh["positive particle"]), 10)
for i in range(10):
self.assertIsInstance(mesh["negative particle"][i],
pybamm.Uniform1DSubMesh)
self.assertIsInstance(mesh["positive particle"][i],
pybamm.Uniform1DSubMesh)
self.assertEqual(mesh["negative particle"][i].npts, 5)
self.assertEqual(mesh["positive particle"][i].npts, 6)
"positive interface current"] = pybamm.interface.CurrentForInverseButlerVolmer(
model.param, "Positive", "lithium-ion main")
model.submodels[
"electrolyte diffusion"] = pybamm.electrolyte_diffusion.ConstantConcentration(
model.param)
model.submodels[
"electrolyte conductivity"] = pybamm.electrolyte_conductivity.LeadingOrder(
model.param)
model.submodels["negative sei"] = pybamm.sei.NoSEI(model.param, "Negative")
model.submodels["positive sei"] = pybamm.sei.NoSEI(model.param, "Positive")
# build model
model.build_model()
# create geometry
geometry = pybamm.Geometry("1D macro", "1D micro")
# process model and geometry
param = model.default_parameter_values
param.process_model(model)
param.process_geometry(geometry)
# set mesh
# Note: li-ion base model has defaults for mesh and var_pts
mesh = pybamm.Mesh(geometry, model.default_submesh_types,
model.default_var_pts)
# discretise model
# Note: li-ion base model has default spatial methods
disc = pybamm.Discretisation(mesh, model.default_spatial_methods)
disc.process_model(model)
def battery_geometry(include_particles=True, current_collector_dimension=0):
"""
A convenience function to create battery geometries.
Parameters
----------
include_particles : bool
Whether to include particle domains
current_collector_dimensions : int, default
The dimensions of the current collector. Should be 0 (default), 1 or 2
Returns
-------
:class:`pybamm.Geometry`
A geometry class for the battery
"""
var = pybamm.standard_spatial_vars
geo = pybamm.geometric_parameters
l_n = geo.l_n
l_s = geo.l_s
geometry = {
"negative electrode": {
var.x_n: {
"min": 0,
"max": l_n
}
},
"separator": {
var.x_s: {
"min": l_n,
"max": l_n + l_s
}
},
"positive electrode": {
var.x_p: {
"min": l_n + l_s,
"max": 1
}
},
}
# Add particle domains
if include_particles is True:
geometry.update({
"negative particle": {
var.r_n: {
"min": 0,
"max": 1
}
},
"positive particle": {
var.r_p: {
"min": 0,
"max": 1
}
},
})
if current_collector_dimension == 0:
geometry["current collector"] = {var.z: {"position": 1}}
elif current_collector_dimension == 1:
geometry["current collector"] = {
var.z: {
"min": 0,
"max": 1
},
"tabs": {
"negative": {
"z_centre": geo.centre_z_tab_n
},
"positive": {
"z_centre": geo.centre_z_tab_p
},
},
}
elif current_collector_dimension == 2:
geometry["current collector"] = {
var.y: {
"min": 0,
"max": geo.l_y
},
var.z: {
"min": 0,
"max": geo.l_z
},
"tabs": {
"negative": {
"y_centre": geo.centre_y_tab_n,
"z_centre": geo.centre_z_tab_n,
"width": geo.l_tab_n,
},
"positive": {
"y_centre": geo.centre_y_tab_p,
"z_centre": geo.centre_z_tab_p,
"width": geo.l_tab_p,
},
},
}
else:
raise pybamm.GeometryError(
"Invalid current collector dimension '{}' (should be 0, 1 or 2)".
format(current_collector_dimension))
return pybamm.Geometry(geometry)
def default_geometry(self):
return pybamm.Geometry("2D current collector")
def get_p2d_mesh_for_testing(xpts=None, rpts=10):
geometry = pybamm.Geometry("1D macro", "1+1D micro")
return get_mesh_for_testing(xpts=xpts, rpts=rpts, geometry=geometry)
def default_geometry(self):
return pybamm.Geometry("1D macro", "1+1D micro")
def half_cell_geometry(
include_particles=True, current_collector_dimension=0, working_electrode="positive"
):
"""
A convenience function to create battery geometries.
Parameters
----------
include_particles : bool
Whether to include particle domains
current_collector_dimensions : int, default
The dimensions of the current collector. Should be 0 (default), 1 or 2
current_collector_dimensions : string
The electrode taking as working electrode. Should be "positive" or "negative"
Returns
-------
:class:`pybamm.Geometry`
A geometry class for the battery
"""
var = half_cell_spatial_vars
geo = pybamm.geometric_parameters
if working_electrode == "positive":
l_w = geo.l_p
elif working_electrode == "negative":
l_w = geo.l_n
else:
raise ValueError(
"The option 'working_electrode' should be either 'positive'"
" or 'negative'"
)
l_Li = geo.l_Li
l_s = geo.l_s
geometry = {
"lithium counter electrode": {var.x_Li: {"min": 0, "max": l_Li}},
"separator": {var.x_s: {"min": l_Li, "max": l_Li + l_s}},
"working electrode": {var.x_w: {"min": l_Li + l_s, "max": l_Li + l_s + l_w}},
}
# Add particle domains
if include_particles is True:
geometry.update({"working particle": {var.r_w: {"min": 0, "max": 1}}})
if current_collector_dimension == 0:
geometry["current collector"] = {var.z: {"position": 1}}
elif current_collector_dimension == 1:
geometry["current collector"] = {
var.z: {"min": 0, "max": 1},
"tabs": {
"negative": {"z_centre": geo.centre_z_tab_n},
"positive": {"z_centre": geo.centre_z_tab_p},
},
}
elif current_collector_dimension == 2:
geometry["current collector"] = {
var.y: {"min": 0, "max": geo.l_y},
var.z: {"min": 0, "max": geo.l_z},
"tabs": {
"negative": {
"y_centre": geo.centre_y_tab_n,
"z_centre": geo.centre_z_tab_n,
"width": geo.l_tab_n,
},
"positive": {
"y_centre": geo.centre_y_tab_p,
"z_centre": geo.centre_z_tab_p,
"width": geo.l_tab_p,
},
},
}
else:
raise pybamm.GeometryError(
"Invalid current collector dimension '{}' (should be 0, 1 or 2)".format(
current_collector_dimension
)
)
return pybamm.Geometry(geometry)
def __init__(self, param=None):
# Set fixed parameters here
if param is None:
param = pybamm.ParameterValues({
"Far-field concentration of S(soln) [mol cm-3]":
1e-6,
"Diffusion Constant [cm2 s-1]":
7.2e-6,
"Faraday Constant [C mol-1]":
96485.3328959,
"Gas constant [J K-1 mol-1]":
8.314459848,
"Electrode Area [cm2]":
0.07,
"Temperature [K]":
273.0,
"Voltage frequency [rad s-1]":
9.0152,
"Voltage start [V]":
0.4,
"Voltage reverse [V]":
-0.4,
"Voltage amplitude [V]":
0.0, # 0.05,
"Scan Rate [V s-1]":
0.05,
"Electrode Coverage [mol cm2]":
6.5e-12,
})
# Create dimensional fixed parameters
D = pybamm.Parameter("Diffusion Constant [cm2 s-1]")
F = pybamm.Parameter("Faraday Constant [C mol-1]")
R = pybamm.Parameter("Gas constant [J K-1 mol-1]")
a = pybamm.Parameter("Electrode Area [cm2]")
T = pybamm.Parameter("Temperature [K]")
omega_d = pybamm.Parameter("Voltage frequency [rad s-1]")
E_start_d = pybamm.Parameter("Voltage start [V]")
E_reverse_d = pybamm.Parameter("Voltage reverse [V]")
deltaE_d = pybamm.Parameter("Voltage amplitude [V]")
v = pybamm.Parameter("Scan Rate [V s-1]")
Gamma = pybamm.Parameter("Electrode Coverage [mol cm2]")
# Create dimensional input parameters
E0_d = pybamm.InputParameter("Reversible Potential [V]")
k0_d = pybamm.InputParameter("Redox Rate [s-1]")
kcat_d = pybamm.InputParameter("Catalytic Rate [cm3 mol-l s-1]")
alpha = pybamm.InputParameter("Symmetry factor [non-dim]")
Cdl_d = pybamm.InputParameter("Capacitance [F]")
Ru_d = pybamm.InputParameter("Uncompensated Resistance [Ohm]")
# Create scaling factors for non-dimensionalisation
E_0 = R * T / F
T_0 = E_0 / v
I_0 = F * a * Gamma / T
L_0 = pybamm.sqrt(D * T_0)
# Non-dimensionalise parameters
E0 = E0_d / E_0
k0 = k0_d * T_0
kcat = kcat_d * Gamma * L_0 / D
Cdl = Cdl_d * a * E_0 / (I_0 * T_0)
Ru = Ru_d * I_0 / E_0
omega = 2 * np.pi * omega_d * T_0
E_start = E_start_d / E_0
E_reverse = E_reverse_d / E_0
t_reverse = E_start - E_reverse
deltaE = deltaE_d / E_0
# Input voltage protocol
Edc_forward = -pybamm.t
Edc_backwards = pybamm.t - 2 * t_reverse
Eapp = E_start + \
(pybamm.t <= t_reverse) * Edc_forward + \
(pybamm.t > t_reverse) * Edc_backwards + \
deltaE * pybamm.sin(omega * pybamm.t)
# create PyBaMM model object
model = pybamm.BaseModel()
# Create state variables for model
theta = pybamm.Variable("O(surf) [non-dim]")
c = pybamm.Variable("S(soln) [non-dim]", domain="solution")
i = pybamm.Variable("Current [non-dim]")
# Effective potential
Eeff = Eapp - i * Ru
# Faridaic current (Butler Volmer)
i_f = k0 * ((1 - theta) * pybamm.exp(
(1 - alpha) * (Eeff - E0)) - theta * pybamm.exp(-alpha *
(Eeff - E0)))
c_at_electrode = pybamm.BoundaryValue(c, "left")
# Catalytic current
i_cat = kcat * c_at_electrode * (1 - theta)
# ODE equations
model.rhs = {
theta: i_f + i_cat,
i: 1 / (Cdl * Ru) * (i_f + Cdl * Eapp.diff(pybamm.t) - i - i_cat),
c: pybamm.div(pybamm.grad(c)),
}
# algebraic equations (none)
model.algebraic = {}
# Boundary and initial conditions
model.boundary_conditions = {
c: {
"right": (pybamm.Scalar(1), "Dirichlet"),
"left": (i_cat, "Neumann"),
}
}
model.initial_conditions = {
theta: pybamm.Scalar(1),
i: Cdl * Eapp.diff(pybamm.t),
c: pybamm.Scalar(1),
}
# set spatial variables and solution domain geometry
x = pybamm.SpatialVariable('x', domain="solution")
model.geometry = pybamm.Geometry({
"solution": {
x: {
"min": pybamm.Scalar(0),
"max": pybamm.Scalar(20)
}
}
})
model.var_pts = {x: 100}
# Using Finite Volume discretisation on an expanding 1D grid
model.submesh_types = {
"solution":
pybamm.MeshGenerator(pybamm.Exponential1DSubMesh, {'side': 'left'})
}
model.spatial_methods = {"solution": pybamm.FiniteVolume()}
# model variables
model.variables = {
"Current [non-dim]": i,
"O(surf) [non-dim]": theta,
"S(soln) at electrode [non-dim]": c_at_electrode,
"Applied Voltage [non-dim]": Eapp,
}
# --------------------------------
# Set model parameters
param.process_model(model)
geometry = model.geometry
param.process_geometry(geometry)
# Create mesh and discretise model
mesh = pybamm.Mesh(geometry, model.submesh_types, model.var_pts)
disc = pybamm.Discretisation(mesh, model.spatial_methods)
disc.process_model(model)
# Create solver
model.convert_to_format = 'python'
solver = pybamm.ScipySolver(method='BDF', rtol=1e-6, atol=1e-6)
#solver = pybamm.CasadiSolver(mode='fast', rtol=1e-8, atol=1e-10)
# Store discretised model and solver
self._model = model
self._param = param
self._solver = solver
self._omega_d = param.process_symbol(omega_d).evaluate()
self._I_0 = param.process_symbol(I_0).evaluate()
self._T_0 = param.process_symbol(T_0).evaluate()
def test_combine_submeshes(self):
param = pybamm.ParameterValues(
values={
"Negative electrode thickness [m]": 0.1,
"Separator thickness [m]": 0.2,
"Positive electrode thickness [m]": 0.3,
})
geometry = pybamm.Geometry("1D macro", "1D micro")
param.process_geometry(geometry)
# provide mesh properties
var = pybamm.standard_spatial_vars
var_pts = {
var.x_n: 10,
var.x_s: 10,
var.x_p: 12,
var.r_n: 5,
var.r_p: 6
}
submesh_types = {
"negative electrode":
pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"separator": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive electrode":
pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"negative particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"positive particle": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh),
"current collector": pybamm.MeshGenerator(pybamm.SubMesh0D),
}
mesh_type = pybamm.Mesh
# create mesh
mesh = mesh_type(geometry, submesh_types, var_pts)
# create submesh
submesh = mesh.combine_submeshes("negative electrode", "separator")
self.assertEqual(submesh[0].edges[0], 0)
self.assertEqual(submesh[0].edges[-1], mesh["separator"][0].edges[-1])
np.testing.assert_almost_equal(
submesh[0].nodes - np.concatenate([
mesh["negative electrode"][0].nodes, mesh["separator"][0].nodes
]),
0,
)
np.testing.assert_almost_equal(submesh[0].internal_boundaries,
[0.1 / 0.6])
with self.assertRaises(pybamm.DomainError):
mesh.combine_submeshes("negative electrode", "positive electrode")
# test errors
geometry = {
"negative electrode": {
"primary": {
var.x_n: {
"min": pybamm.Scalar(0),
"max": pybamm.Scalar(0.5)
}
}
},
"negative particle": {
"primary": {
var.r_n: {
"min": pybamm.Scalar(0.5),
"max": pybamm.Scalar(1)
}
}
},
}
param.process_geometry(geometry)
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
with self.assertRaisesRegex(pybamm.DomainError, "trying"):
mesh.combine_submeshes("negative electrode", "negative particle")
with self.assertRaisesRegex(
ValueError, "Submesh domains being combined cannot be empty"):
mesh.combine_submeshes()
def test_1D_different_domains(self):
# Negative electrode domain
var = pybamm.Variable("var", domain=["negative electrode"])
x = pybamm.SpatialVariable("x", domain=["negative electrode"])
disc = tests.get_discretisation_for_testing()
disc.set_variable_slices([var])
x_sol = disc.process_symbol(x).entries[:, 0]
var_sol = disc.process_symbol(var)
t_sol = [0]
y_sol = np.ones_like(x_sol)[:, np.newaxis] * 5
sol = pybamm.Solution(t_sol, y_sol)
pybamm.ProcessedSymbolicVariable(var_sol, sol)
# Particle domain
var = pybamm.Variable("var", domain=["negative particle"])
r = pybamm.SpatialVariable("r", domain=["negative particle"])
disc = tests.get_discretisation_for_testing()
disc.set_variable_slices([var])
r_sol = disc.process_symbol(r).entries[:, 0]
var_sol = disc.process_symbol(var)
t_sol = [0]
y_sol = np.ones_like(r_sol)[:, np.newaxis] * 5
sol = pybamm.Solution(t_sol, y_sol)
pybamm.ProcessedSymbolicVariable(var_sol, sol)
# Current collector domain
var = pybamm.Variable("var", domain=["current collector"])
z = pybamm.SpatialVariable("z", domain=["current collector"])
disc = tests.get_1p1d_discretisation_for_testing()
disc.set_variable_slices([var])
z_sol = disc.process_symbol(z).entries[:, 0]
var_sol = disc.process_symbol(var)
t_sol = [0]
y_sol = np.ones_like(z_sol)[:, np.newaxis] * 5
sol = pybamm.Solution(t_sol, y_sol)
pybamm.ProcessedSymbolicVariable(var_sol, sol)
# Other domain
var = pybamm.Variable("var", domain=["line"])
x = pybamm.SpatialVariable("x", domain=["line"])
geometry = pybamm.Geometry(
{"line": {x: {"min": pybamm.Scalar(0), "max": pybamm.Scalar(1)}}}
)
submesh_types = {"line": pybamm.MeshGenerator(pybamm.Uniform1DSubMesh)}
var_pts = {x: 10}
mesh = pybamm.Mesh(geometry, submesh_types, var_pts)
disc = pybamm.Discretisation(mesh, {"line": pybamm.FiniteVolume()})
disc.set_variable_slices([var])
x_sol = disc.process_symbol(x).entries[:, 0]
var_sol = disc.process_symbol(var)
t_sol = [0]
y_sol = np.ones_like(x_sol)[:, np.newaxis] * 5
sol = pybamm.Solution(t_sol, y_sol)
pybamm.ProcessedSymbolicVariable(var_sol, sol)
# 2D fails
var = pybamm.Variable(
"var",
domain=["negative particle"],
auxiliary_domains={"secondary": "negative electrode"},
)
r = pybamm.SpatialVariable(
"r",
domain=["negative particle"],
auxiliary_domains={"secondary": "negative electrode"},
)
disc = tests.get_p2d_discretisation_for_testing()
disc.set_variable_slices([var])
r_sol = disc.process_symbol(r).entries[:, 0]
var_sol = disc.process_symbol(var)
t_sol = [0]
y_sol = np.ones_like(r_sol)[:, np.newaxis] * 5
sol = pybamm.Solution(t_sol, y_sol)
with self.assertRaisesRegex(NotImplementedError, "Shape not recognized"):
pybamm.ProcessedSymbolicVariable(var_sol, sol)
def __init__(self, n=100, max_x=10, param=None):
# Set fixed parameters here
if param is None:
param = pybamm.ParameterValues({
"Far-field concentration of A [mol cm-3]":
1e-6,
"Diffusion Constant [cm2 s-1]":
7.2e-6,
"Faraday Constant [C mol-1]":
96485.3328959,
"Gas constant [J K-1 mol-1]":
8.314459848,
"Electrode Area [cm2]":
0.07,
"Temperature [K]":
297.0,
"Voltage frequency [rad s-1]":
9.0152,
"Voltage start [V]":
0.5,
"Voltage reverse [V]":
-0.1,
"Voltage amplitude [V]":
0.08,
"Scan Rate [V s-1]":
0.08941,
})
# Create dimensional fixed parameters
c_inf = pybamm.Parameter("Far-field concentration of A [mol cm-3]")
D = pybamm.Parameter("Diffusion Constant [cm2 s-1]")
F = pybamm.Parameter("Faraday Constant [C mol-1]")
R = pybamm.Parameter("Gas constant [J K-1 mol-1]")
S = pybamm.Parameter("Electrode Area [cm2]")
T = pybamm.Parameter("Temperature [K]")
E_start_d = pybamm.Parameter("Voltage start [V]")
E_reverse_d = pybamm.Parameter("Voltage reverse [V]")
deltaE_d = pybamm.Parameter("Voltage amplitude [V]")
v = pybamm.Parameter("Scan Rate [V s-1]")
# Create dimensional input parameters
E0 = pybamm.InputParameter("Reversible Potential [non-dim]")
k0 = pybamm.InputParameter("Reaction Rate [non-dim]")
alpha = pybamm.InputParameter("Symmetry factor [non-dim]")
Cdl = pybamm.InputParameter("Capacitance [non-dim]")
Ru = pybamm.InputParameter("Uncompensated Resistance [non-dim]")
omega_d = pybamm.InputParameter("Voltage frequency [rad s-1]")
E0_d = pybamm.InputParameter("Reversible Potential [V]")
k0_d = pybamm.InputParameter("Reaction Rate [s-1]")
alpha = pybamm.InputParameter("Symmetry factor [non-dim]")
Cdl_d = pybamm.InputParameter("Capacitance [F]")
Ru_d = pybamm.InputParameter("Uncompensated Resistance [Ohm]")
# Create scaling factors for non-dimensionalisation
E_0 = R * T / F
T_0 = E_0 / v
L_0 = pybamm.sqrt(D * T_0)
I_0 = D * F * S * c_inf / L_0
# Non-dimensionalise parameters
E0 = E0_d / E_0
k0 = k0_d * L_0 / D
Cdl = Cdl_d * S * E_0 / (I_0 * T_0)
Ru = Ru_d * I_0 / E_0
omega = 2 * np.pi * omega_d * T_0
E_start = E_start_d / E_0
E_reverse = E_reverse_d / E_0
t_reverse = E_start - E_reverse
deltaE = deltaE_d / E_0
# Input voltage protocol
Edc_forward = -pybamm.t
Edc_backwards = pybamm.t - 2 * t_reverse
Eapp = E_start + \
(pybamm.t <= t_reverse) * Edc_forward + \
(pybamm.t > t_reverse) * Edc_backwards + \
deltaE * pybamm.sin(omega * pybamm.t)
# create PyBaMM model object
model = pybamm.BaseModel()
# Create state variables for model
theta = pybamm.Variable("ratio_A", domain="solution")
i = pybamm.Variable("Current")
# Effective potential
Eeff = Eapp - i * Ru
# Faradaic current
i_f = pybamm.BoundaryGradient(theta, "left")
# ODE equations
model.rhs = {
theta: pybamm.div(pybamm.grad(theta)),
i: 1 / (Cdl * Ru) * (-i_f + Cdl * Eapp.diff(pybamm.t) - i),
}
# algebraic equations (none)
model.algebraic = {}
# Butler-volmer boundary condition at electrode
theta_at_electrode = pybamm.BoundaryValue(theta, "left")
butler_volmer = k0 * (theta_at_electrode * pybamm.exp(-alpha *
(Eeff - E0)) -
(1 - theta_at_electrode) * pybamm.exp(
(1 - alpha) * (Eeff - E0)))
# Boundary and initial conditions
model.boundary_conditions = {
theta: {
"right": (pybamm.Scalar(1), "Dirichlet"),
"left": (butler_volmer, "Neumann"),
}
}
model.initial_conditions = {
theta: pybamm.Scalar(1),
i: Cdl * (-1.0 + deltaE * omega),
}
# set spatial variables and solution domain geometry
x = pybamm.SpatialVariable('x', domain="solution")
default_geometry = pybamm.Geometry({
"solution": {
x: {
"min": pybamm.Scalar(0),
"max": pybamm.Scalar(max_x)
}
}
})
default_var_pts = {x: n}
# Using Finite Volume discretisation on an expanding 1D grid for solution
default_submesh_types = {
"solution":
pybamm.MeshGenerator(pybamm.Exponential1DSubMesh, {'side': 'left'})
}
default_spatial_methods = {"solution": pybamm.FiniteVolume()}
# model variables
model.variables = {
"Current [non-dim]": i,
}
#--------------------------------
# Set model parameters
param.process_model(model)
geometry = default_geometry
param.process_geometry(geometry)
# Create mesh and discretise model
mesh = pybamm.Mesh(geometry, default_submesh_types, default_var_pts)
disc = pybamm.Discretisation(mesh, default_spatial_methods)
disc.process_model(model)
# Create solver
solver = pybamm.CasadiSolver(
mode="fast",
rtol=1e-9,
atol=1e-9,
extra_options_setup={'print_stats': False})
#model.convert_to_format = 'jax'
#solver = pybamm.JaxSolver(method='BDF')
#model.convert_to_format = 'python'
#solver = pybamm.ScipySolver(method='BDF')
# Store discretised model and solver
self._model = model
self._solver = solver
self._fast_solver = None
self._omega_d = param["Voltage frequency [rad s-1]"]
self._I_0 = param.process_symbol(I_0).evaluate()
self._T_0 = param.process_symbol(T_0).evaluate()
self._E_0 = param.process_symbol(E_0).evaluate()
self._L_0 = param.process_symbol(L_0).evaluate()
self._S = param.process_symbol(S).evaluate()
self._D = param.process_symbol(D).evaluate()
self._default_var_points = default_var_pts