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import pybamm | ||
import numpy as np | ||
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R = 1e-5 | ||
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def time_create_expression(): | ||
global model | ||
model = pybamm.BaseModel() | ||
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R = pybamm.Parameter("Particle radius [m]") | ||
D = pybamm.Parameter("Diffusion coefficient [m2.s-1]") | ||
j = pybamm.Parameter("Interfacial current density [A.m-2]") | ||
F = pybamm.Parameter("Faraday constant [C.mol-1]") | ||
c0 = pybamm.Parameter("Initial concentration [mol.m-3]") | ||
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c = pybamm.Variable("Concentration [mol.m-3]", domain="negative particle") | ||
N = -D * pybamm.grad(c) | ||
dcdt = -pybamm.div(N) | ||
model.rhs = {c: dcdt} | ||
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lbc = pybamm.Scalar(0) | ||
rbc = -j / F / D | ||
model.boundary_conditions = { | ||
c: {"left": (lbc, "Neumann"), "right": (rbc, "Neumann")} | ||
} | ||
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model.initial_conditions = {c: c0} | ||
model.variables = { | ||
"Concentration [mol.m-3]": c, | ||
"Surface concentration [mol.m-3]": pybamm.surf(c), | ||
"Flux [mol.m-2.s-1]": N, | ||
} | ||
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def setup_parameterise(): | ||
time_create_expression() | ||
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def time_parameterise(): | ||
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global param | ||
param = pybamm.ParameterValues( | ||
{ | ||
"Particle radius [m]": 10e-6, | ||
"Diffusion coefficient [m2.s-1]": 3.9e-14, | ||
"Interfacial current density [A.m-2]": 1.4, | ||
"Faraday constant [C.mol-1]": 96485, | ||
"Initial concentration [mol.m-3]": 2.5e4, | ||
} | ||
) | ||
global r | ||
r = pybamm.SpatialVariable( | ||
"r", domain=["negative particle"], coord_sys="spherical polar" | ||
) | ||
global geometry | ||
geometry = {"negative particle": {r: {"min": pybamm.Scalar(0), "max": R}}} | ||
param.process_model(model) | ||
param.process_geometry(geometry) | ||
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time_parameterise.setup = setup_parameterise | ||
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def setup_discretise(): | ||
time_create_expression() | ||
time_parameterise() | ||
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def time_discretise(): | ||
time_create_expression() | ||
time_parameterise() | ||
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submesh_types = {"negative particle": pybamm.Uniform1DSubMesh} | ||
var_pts = {r: 20} | ||
mesh = pybamm.Mesh(geometry, submesh_types, var_pts) | ||
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spatial_methods = {"negative particle": pybamm.FiniteVolume()} | ||
disc = pybamm.Discretisation(mesh, spatial_methods) | ||
disc.process_model(model) | ||
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time_discretise.setup = setup_discretise | ||
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def setup_solve(): | ||
time_create_expression() | ||
time_parameterise() | ||
time_discretise() | ||
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def time_solve(): | ||
solver = pybamm.ScipySolver() | ||
t = np.linspace(0, 3600, 600) | ||
solver.solve(model, t) | ||
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time_solve.setup = setup_solve |