def test_discretise_spatial_variable(self):
# create discretisation
mesh = get_mesh_for_testing()
spatial_method = pybamm.SpatialMethod()
spatial_method.build(mesh)
# centre
x1 = pybamm.SpatialVariable("x", ["negative electrode"])
x2 = pybamm.SpatialVariable("x", ["negative electrode", "separator"])
r = pybamm.SpatialVariable("r", ["negative particle"])
for var in [x1, x2, r]:
var_disc = spatial_method.spatial_variable(var)
self.assertIsInstance(var_disc, pybamm.Vector)
np.testing.assert_array_equal(
var_disc.evaluate()[:, 0], mesh.combine_submeshes(*var.domain)[0].nodes
)
# edges
x1_edge = pybamm.SpatialVariableEdge("x", ["negative electrode"])
x2_edge = pybamm.SpatialVariableEdge("x", ["negative electrode", "separator"])
r_edge = pybamm.SpatialVariableEdge("r", ["negative particle"])
for var in [x1_edge, x2_edge, r_edge]:
var_disc = spatial_method.spatial_variable(var)
self.assertIsInstance(var_disc, pybamm.Vector)
np.testing.assert_array_equal(
var_disc.evaluate()[:, 0], mesh.combine_submeshes(*var.domain)[0].edges
)
def get_error(n):
# create mesh and discretisation (single particle)
mesh = get_mesh_for_testing(rpts=n)
disc = pybamm.Discretisation(mesh, spatial_methods)
submesh = mesh["negative particle"]
r = submesh.nodes
r_edge = pybamm.SpatialVariableEdge("r_n", domain=["negative particle"])
# Define flux and bcs
N = r_edge * pybamm.sin(r_edge)
div_eqn = pybamm.div(N)
# Define exact solutions
# N = r*sin(r) --> div(N) = 3*sin(r) + r*cos(r)
div_exact = 3 * np.sin(r) + r * np.cos(r)
# Discretise and evaluate
div_eqn_disc = disc.process_symbol(div_eqn)
div_approx = div_eqn_disc.evaluate()
# Return difference between approx and exact
return div_approx[:, 0] - div_exact
coord_sys="spherical polar",
)
r_p = pybamm.SpatialVariable(
"r_p",
domain=["positive particle"],
auxiliary_domains={
"secondary": "positive electrode",
"tertiary": "current collector",
},
coord_sys="spherical polar",
)
# Domains at cell edges
x_n_edge = pybamm.SpatialVariableEdge(
"x_n",
domain=["negative electrode"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_s_edge = pybamm.SpatialVariableEdge(
"x_s",
domain=["separator"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_p_edge = pybamm.SpatialVariableEdge(
"x_p",
domain=["positive electrode"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_edge = pybamm.SpatialVariableEdge(
coord_sys="cartesian")
r_w = pybamm.SpatialVariable(
"r_w",
domain=["working particle"],
auxiliary_domains={
"secondary": "working electrode",
"tertiary": "current collector",
},
coord_sys="spherical polar",
)
# Domains at cell edges
x_Li_edge = pybamm.SpatialVariableEdge(
"x_Li",
domain=["lithium counter electrode"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_s_edge = pybamm.SpatialVariableEdge(
"x_s",
domain=["separator"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_w_edge = pybamm.SpatialVariableEdge(
"x_w",
domain=["working electrode"],
auxiliary_domains={"secondary": "current collector"},
coord_sys="cartesian",
)
x_edge = pybamm.SpatialVariableEdge(
def test_spatial_variable_edge(self):
x = pybamm.SpatialVariableEdge("x", "negative electrode")
self.assertEqual(x.name, "x")
self.assertTrue(x.evaluates_on_edges("primary"))