def create_bcs(Lx, Ly, velocity_top, solutes, concentration_init,
surface_charge, surface_potential, enable_NS, enable_PF,
enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(top=[Top(Ly)], bottom=[Bottom()])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
u_top = Fixed((velocity_top, 0.))
noslip = Fixed((0., 0.))
if enable_NS:
bcs["top"]["u"] = u_top
bcs["bottom"]["u"] = noslip
bcs_pointwise["p"] = (
0., "x[0] < DOLFIN_EPS && x[1] > {Ly}-DOLFIN_EPS".format(Ly=Ly))
if enable_EC:
for solute in solutes:
bcs["top"][solute[0]] = Fixed(concentration_init / abs(solute[1]))
bcs["top"]["V"] = Fixed(0.)
if surface_potential:
bcs["bottom"]["V"] = Fixed(surface_charge)
else:
bcs["bottom"]["V"] = Charged(surface_charge)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, solutes, surface_charge, enable_NS, enable_PF,
enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(right=[Right(Lx)],
left=[Left(0)],
bottom=[Bottom(0)],
top=[Top(Ly)])
c0 = [1.0, 1.0]
noslip = Fixed((0., 0.))
V_ground = Fixed(0.0)
surfacecharge = Charged(surface_charge)
bcs = dict()
bcs_pointwise = dict()
bcs["right"] = dict()
bcs["left"] = dict()
bcs["top"] = dict()
bcs["bottom"] = dict()
if enable_NS:
bcs["right"]["u"] = noslip
bcs["left"]["u"] = noslip
bcs["top"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
if enable_EC:
bcs["top"]["V"] = surfacecharge
bcs["bottom"]["V"] = V_ground
for ci, solute in zip(c0, solutes):
bcs["bottom"][solute[0]] = Fixed(ci)
# Apply pointwise BCs e.g. to pin pressure.
return boundaries, bcs, bcs_pointwise
def create_bcs(Lz, V_top, V_btm,
enable_NS, enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(
wall=[Wall(Lz)],
top=[Top(Lz)],
bottom=[Bottom()]
)
bcs = dict()
bcs_pointwise = dict()
bcs["wall"] = dict()
bcs["top"] = dict()
bcs["bottom"] = dict()
noslip = Fixed((0., 0., 0.))
if enable_NS:
bcs["top"]["u"] = noslip
bcs["bottom"]["u"] = noslip
bcs["wall"]["u"] = noslip
bcs_pointwise["p"] = (0.,
"x[0] < DOLFIN_EPS && "
"x[1] < DOLFIN_EPS && "
"x[2] < DOLFIN_EPS")
if enable_EC:
bcs["top"]["V"] = Fixed(V_top)
bcs["bottom"]["V"] = Fixed(V_btm)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, concentration_top, concentration_bottom, V_top,
V_bottom, solutes, enable_NS, enable_PF, enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(top=[Top(Ly)], bottom=[Bottom()])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["top"]["u"] = noslip
bcs["bottom"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
if enable_EC:
for solute in solutes:
bcs["top"][solute[0]] = Fixed(concentration_top)
if solute[0] == "c_p":
bcs["bottom"][solute[0]] = Fixed(concentration_bottom)
bcs["top"]["V"] = Fixed(V_top)
bcs["bottom"]["V"] = Fixed(V_bottom)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, mesh, surface_charge, enable_NS, enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(right=[Right(Lx)],
left=[Left(Lx)],
bottom=[Bottom(Ly)],
top=[Top(Ly)])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["left"]["u"] = noslip
bcs["right"]["u"] = noslip
bcs["top"]["u"] = noslip
bcs["bottom"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS-{Lx}/2 && "
"x[1] < DOLFIN_EPS-{Ly}/2".format(Lx=Lx, Ly=Ly))
if enable_EC:
bcs["top"]["V"] = Fixed(0.)
bcs["bottom"]["V"] = Charged(surface_charge)
return boundaries, bcs, bcs_pointwise
def create_bcs(field_to_subspace, Lx, Ly, solutes, V_left, V_right, enable_NS,
enable_PF, enable_EC, **namespace):
""" The boundary conditions are defined in terms of field. """
boundaries = dict(wall=[Wall(Lx)], left=[Left()], right=[Right(Lx)])
noslip = Fixed((0., 0.))
bcs = dict()
bcs_pointwise = dict()
bcs["wall"] = dict()
bcs["left"] = dict()
bcs["right"] = dict()
if enable_NS:
bcs["wall"]["u"] = noslip
bcs["left"]["u"] = noslip
bcs["right"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
if enable_EC:
bcs["left"]["V"] = Fixed(V_left)
bcs["right"]["V"] = Fixed(V_right)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly,inlet_velocity,
enable_NS, enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(
right=[Right(Lx)],
left=[Left(0)]
)
# Alocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
bcs["left"] = dict()
bcs["right"] = dict()
inletvelocity = Fixed((inlet_velocity, 0.))
pressurein_out = Fixed(0.0)
phi_inlet = Fixed(-1.0)
phi_outlet = Fixed(1.0)
if enable_NS:
bcs["left"]["u"] = inletvelocity
bcs["right"]["p"] = pressurein_out
bcs["left"]["p"] = pressurein_out
if enable_PF:
bcs["left"]["phi"] = phi_inlet
bcs["right"]["phi"] = phi_outlet
return boundaries, bcs, bcs_pointwise
def create_bcs(field_to_subspace, Lx, Ly,
solutes,
concentration_init_s,
V_top, V_bottom,
contact_angle,
enable_NS, enable_PF, enable_EC,
**namespace):
""" The boundary conditions are defined in terms of field. """
boundaries = dict(
top=[Top(Ly)],
bottom=[Bottom(Ly)],
left=[Left()],
right=[Right(Lx)]
)
noslip = NoSlip()
freeslip_y = FreeSlip(0., 0)
freeslip_x = FreeSlip(0., 1)
slip_x = Slip(0.005, 1)
bcs = dict()
bcs_pointwise = dict()
bcs["top"] = dict()
bcs["bottom"] = dict()
bcs["left"] = dict()
bcs["right"] = dict()
if enable_NS:
bcs["top"]["u"] = slip_x
bcs["bottom"]["u"] = noslip
bcs["left"]["u"] = freeslip_y
bcs["right"]["u"] = freeslip_y
bcs_pointwise["p"] = (
0.,
("x[0] > {Lx}- DOLFIN_EPS && "
"x[1] > {Ly} - DOLFIN_EPS").format(Lx=Lx, Ly=Ly))
if enable_EC:
for solute in solutes[:2]:
bcs["top"][solute[0]] = Fixed(concentration_init_s)
for solute in solutes[2:]:
bcs["top"][solute[0]] = Fixed(0.)
bcs["top"]["V"] = Fixed(V_top)
bcs["bottom"]["V"] = Fixed(V_bottom)
if enable_PF:
bcs["bottom"]["phi"] = ContactAngle(np.pi-contact_angle)
return boundaries, bcs, bcs_pointwise
def create_bcs(L, H, inlet_velocity, V_0, solutes, concentration_left,
interface_thickness, enable_NS, enable_PF, enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(wall=[Wall(L, H)],
cylinder=[Cylinder(L, H)],
right=[Right(L, H)],
left=[Left(H)])
# Alocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
for boundary in boundaries:
bcs[boundary] = dict()
velocity_expr = velocity_init(L, H, inlet_velocity)
velocity_in = Fixed(velocity_expr)
pressure_out = Pressure(0.0)
noslip = NoSlip()
V_left = Fixed(V_0)
V_right = Fixed(0.)
if enable_NS:
bcs["left"]["u"] = velocity_in
bcs["right"]["p"] = pressure_out
bcs["wall"]["u"] = noslip
bcs["cylinder"]["u"] = noslip
if enable_PF:
phi_expr = df.Expression("tanh((abs(x[1]-H/2)-H/16)/(sqrt(2)*eps))",
H=H,
eps=interface_thickness,
degree=2)
phi_inlet = Fixed(phi_expr)
bcs["left"]["phi"] = phi_inlet
# bcs["right"]["phi"] = Fixed(df.Constant(1.))
if enable_EC:
bcs["left"]["V"] = V_left
bcs["right"]["V"] = V_right
for solute in solutes:
c_expr = df.Expression("c0*exp(-pow(x[1]-H/2, 2)/(2*0.01*0.01))",
H=H,
c0=concentration_left,
degree=2)
bcs["left"][solute[0]] = Fixed(c_expr)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, Lx_inner,
solutes,
concentration_init,
mesh,
surface_charge,
enable_NS, enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(
right=[Right(Lx, Ly, Lx_inner)],
left=[Left(Lx, Ly, Lx_inner)],
#inner_wall=[InnerWall(Lx, Ly, Lx_inner)],
#outer_wall=[OuterWall(Lx, Ly, Lx_inner)]
wall=[Wall(Lx, Ly, Lx_inner)]
)
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["left"]["p"] = Pressure(0.)
bcs["right"]["p"] = Pressure(0.)
#bcs["inner_wall"]["u"] = noslip
#bcs["outer_wall"]["u"] = noslip
bcs["wall"]["u"] = noslip
if enable_EC:
bcs["left"]["V"] = Fixed(0.)
bcs["right"]["V"] = Charged(0.)
#bcs["right"]["V"] = Fixed(0.)
#bcs["outer_wall"]["V"] = Charged(0.)
#bcs["inner_wall"]["V"] = Charged(surface_charge)
bcs["wall"]["V"] = Charged(df.Expression(
"0.5*sigma_e*(tanh((x[0]-0.5*(Lx-Lx_inner))/delta)-"
"tanh((x[0]-0.5*(Lx+Lx_inner))/delta))",
sigma_e=surface_charge, delta=2., Lx=Lx, Lx_inner=Lx_inner,
degree=1))
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_init)
bcs["right"][solute[0]] = Fixed(concentration_init)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly,
grid_spacing, rad, num_obstacles,
surface_charge, solutes, enable_NS, enable_EC,
p_lagrange, V_lagrange,
concentration_init, V_left,
**namespace):
""" The boundaries and boundary conditions are defined here. """
data = np.loadtxt(
"meshes/periodic_porous_Lx{}_Ly{}_rad{}_N{}_dx{}.dat".format(
Lx, Ly, rad, num_obstacles, grid_spacing))
centroids = data[:, :2]
rad = data[:, 2]
boundaries = dict(
left=[Left(Lx, Ly)],
right=[Right(Lx, Ly)],
obstacles=[Obstacles(Lx, centroids, rad, grid_spacing)]
)
# Allocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
for boundary in boundaries:
bcs[boundary] = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["left"]["p"] = Pressure(0.)
bcs["right"]["p"] = Pressure(0.)
bcs["obstacles"]["u"] = noslip
if enable_EC:
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_init)
bcs["right"][solute[0]] = Fixed(concentration_init)
bcs["left"]["V"] = Fixed(V_left)
bcs["right"]["V"] = Charged(0.)
# bcs["right"]["V"] = Fixed(V_right)
bcs["obstacles"]["V"] = Charged(surface_charge)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, mesh, grid_spacing, rad, num_obstacles, surface_charge,
solutes, enable_NS, enable_EC, p_lagrange, V_lagrange,
**namespace):
""" The boundaries and boundary conditions are defined here. """
data = np.loadtxt(
"meshes/periodic_porous_Lx{}_Ly{}_rad{}_N{}_dx{}.dat".format(
Lx, Ly, rad, num_obstacles, grid_spacing))
centroids = data[:, :2]
rad = data[:, 2]
# Find a single node to pin pressure to
x_loc = np.array(mesh.coordinates())
x_proc = np.zeros((size, 2))
ids_notboun = np.logical_and(
x_loc[:, 0] > x_loc[:, 0].min() + df.DOLFIN_EPS,
x_loc[:, 1] > x_loc[:, 1].min() + df.DOLFIN_EPS)
x_loc = x_loc[ids_notboun, :]
d2 = (x_loc[:, 0] + Lx / 2)**2 + (x_loc[:, 1] + Ly / 2)**2
x_bottomleft = x_loc[d2 == d2.min()][0]
x_proc[rank, :] = x_bottomleft
x_pin = np.zeros_like(x_proc)
comm.Allreduce(x_proc, x_pin, op=MPI.SUM)
x_pin = x_pin[x_pin[:, 0] == x_pin[:, 0].min(), :][0]
info("Pinning point: {}".format(x_pin))
pin_code = ("x[0] < {x}+{eps} && "
"x[0] > {x}-{eps} && "
"x[1] > {y}-{eps} && "
"x[1] < {y}+{eps}").format(x=x_pin[0], y=x_pin[1], eps=1e-3)
boundaries = dict(obstacles=[Obstacles(Lx, centroids, rad, grid_spacing)])
# Allocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
for boundary in boundaries:
bcs[boundary] = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["obstacles"]["u"] = noslip
if not p_lagrange:
bcs_pointwise["p"] = (0., pin_code)
if enable_EC:
bcs["obstacles"]["V"] = Charged(surface_charge)
if not V_lagrange:
bcs_pointwise["V"] = (0., pin_code)
return boundaries, bcs, bcs_pointwise
def create_bcs(field_to_subspace, Lx, Ly, solutes, V_boundary, enable_NS,
enable_PF, enable_EC, **namespace):
""" The boundary conditions are defined in terms of field. """
boundaries = dict(wall=[Wall()])
bcs = dict(wall=dict())
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
# Navier-Stokes
if enable_NS:
bcs["wall"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
# Electrochemistry
if enable_EC:
bcs["wall"]["V"] = Fixed(V_boundary)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, inlet_velocity, V_0, solutes, concentration_left,
enable_NS, enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(right=[Right(Lx)], left=[Left(0)])
# Alocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
bcs["left"] = dict()
bcs["right"] = dict()
inlet_velocity = Fixed((inlet_velocity, 0.))
#pressurein_out = Pressure(0.0)
phi_inlet = Fixed(-1.0)
phi_outlet = Fixed(1.0)
V_left = Fixed(V_0)
V_right = Fixed(0.)
if enable_NS:
bcs["left"]["u"] = inlet_velocity
bcs["right"]["u"] = inlet_velocity
# bcs["left"]["p"] = pressurein_out
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
if enable_PF:
bcs["left"]["phi"] = phi_inlet
bcs["right"]["phi"] = phi_outlet
if enable_EC:
bcs["left"]["V"] = V_left
bcs["right"]["V"] = V_right
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_left)
return boundaries, bcs, bcs_pointwise
def create_bcs(
Lx,
Ly,
grid_spacing, # inlet_velocity,
concentration_init,
solutes,
surface_charge,
V_left,
V_right,
pressure_left,
pressure_right,
enable_NS,
enable_PF,
enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
data = np.loadtxt("meshes/periodic_porous_dx" + str(grid_spacing) + ".dat")
centroids = data[:, :2]
rad = data[:, 2]
boundaries = dict(right=[Right(Lx)],
left=[Left(Lx)],
obstacles=[Obstacles(Lx, centroids, rad, grid_spacing)])
# Allocating the boundary dicts
bcs = dict()
bcs_pointwise = dict()
for boundary in boundaries:
bcs[boundary] = dict()
# u_inlet = Fixed((inlet_velocity, 0.))
noslip = Fixed((0., 0.))
p_inlet = Pressure(pressure_left)
p_outlet = Pressure(pressure_right)
phi_inlet = Fixed(-1.0)
phi_outlet = Fixed(1.0)
if enable_NS:
# bcs["left"]["u"] = u_inlet
bcs["obstacles"]["u"] = noslip
bcs["right"]["p"] = p_outlet
bcs["left"]["p"] = p_inlet
# bcs_pointwise["p"] = (0., "x[0] < -{Lx}/2+DOLFIN_EPS && x[1] > {Ly}/2-DOLFIN_EPS".format(Lx=Lx, Ly=Ly))
if enable_PF:
bcs["left"]["phi"] = phi_inlet
bcs["right"]["phi"] = phi_outlet
if enable_EC:
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_init)
# bcs["right"][solute[0]] = Fixed(0.)
bcs["left"]["V"] = Fixed(V_left)
bcs["right"]["V"] = Fixed(V_right)
bcs["obstacles"]["V"] = Charged(surface_charge)
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, solutes, concentration_init, surface_charge,
pressure_left, pressure_right, enable_NS, enable_PF, enable_EC,
**namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(
inner=[Inner(Lx, Ly)],
bottom=[Bottom()],
top=[Top(Ly)],
left=[Left()],
right=[Right(Lx)],
)
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
phi_inlet = Fixed(-1.0)
p_inlet = Pressure(pressure_left)
p_outlet = Pressure(pressure_right)
if enable_NS:
bcs["top"]["u"] = noslip
bcs["bottom"]["u"] = noslip
bcs["inner"]["u"] = noslip
bcs["left"]["p"] = p_inlet
bcs["right"]["p"] = p_outlet
#bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
# bcs["outer"]["p"] = Pressure(0.)
if enable_EC:
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_init)
bcs["right"][solute[0]] = Fixed(concentration_init)
bcs["top"]["V"] = Fixed(0.)
bcs["bottom"]["V"] = Fixed(0.)
bcs["left"]["V"] = Fixed(0.)
bcs["right"]["V"] = Fixed(0.)
bcs["inner"]["V"] = Charged(surface_charge)
if enable_PF:
bcs["left"]["phi"] = phi_inlet
#bcs["right"]["phi"] = phi_inlet
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, R, velocity_top, solutes, concentration_init,
surface_charge, enable_NS, enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(outer_narrowing=[Outer_Narrowing(Lx, R)],
inner_narrowing=[Inner_Narrowing(Lx, R)],
right=[Right(Lx)],
left=[Left(0)])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
ground = Fixed(0.)
noslip = Fixed((0., 0.))
phi_inlet = Fixed(-1.0)
phi_outlet = Fixed(1.0)
if enable_NS:
bcs["inner_narrowing"]["u"] = noslip
bcs["outer_narrowing"]["u"] = noslip
bcs_pointwise["p"] = (
0., "x[0] < DOLFIN_EPS && x[1] > {Ly}-DOLFIN_EPS".format(Ly=Ly))
if enable_EC:
for solute in solutes:
bcs["left"][solute[0]] = Fixed(concentration_init)
bcs["left"]["V"] = ground
bcs["outer_narrowing"]["V"] = Charged(0.0)
bcs["inner_narrowing"]["V"] = Charged(surface_charge)
if enable_PF:
bcs["left"]["phi"] = phi_inlet
bcs["right"]["phi"] = phi_outlet
return boundaries, bcs, bcs_pointwise
def create_bcs(t_0, Lx, Ly, concentration_init, concentration_init_dev,
surface_tension, interface_thickness, pf_init,
pf_mobility_coeff, solutes, density, permittivity, viscosity,
p_lagrange, enable_NS, enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(wall=[Wall()])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
exprs = reference(t=t_0, **vars())
for field, expr in exprs.items():
if field != "p":
bcs["wall"][field] = Fixed(expr)
if enable_NS and not p_lagrange:
bcs_pointwise["p"] = (0., ("x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS"))
return boundaries, bcs, bcs_pointwise
def create_bcs(Lx, Ly, surface_charge_top, surface_charge_bottom, enable_NS,
enable_PF, enable_EC, **namespace):
""" The boundaries and boundary conditions are defined here. """
boundaries = dict(top=[Top(Ly)], bottom=[Bottom()])
bcs = dict()
for boundary_name in boundaries.keys():
bcs[boundary_name] = dict()
# Apply pointwise BCs e.g. to pin pressure.
bcs_pointwise = dict()
noslip = Fixed((0., 0.))
if enable_NS:
bcs["top"]["u"] = noslip
bcs["bottom"]["u"] = noslip
bcs_pointwise["p"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
if enable_EC:
bcs["top"]["V"] = Charged(surface_charge_top)
bcs["bottom"]["V"] = Charged(surface_charge_bottom)
bcs_pointwise["V"] = (0., "x[0] < DOLFIN_EPS && x[1] < DOLFIN_EPS")
return boundaries, bcs, bcs_pointwise
