def corner_submesh(mesh):
"""create a submesh extending from the origin to the midpoint"""
#
# Because SubMesh only works sequentially, build the corner
# submesh in the rank 0 process, then distribute it.
#
submesh = None # needs to be initialized in all ranks
# if MPI.COMM_WORLD.rank == 0:
if True:
logPERIODIC('constructing submesh')
cf = MeshFunction("size_t", mesh, mesh.geometric_dimension())
logPERIODIC('CornerDomain')
corner = CornerDomain(mesh)
logPERIODIC('cf.set_all(0)')
cf.set_all(0)
logPERIODIC('corner.mark(cf, 1)')
corner.mark(cf, 1)
logPERIODIC('calling SubMesh')
logPERIODIC('mesh.mpi_comm().size', mesh.mpi_comm().size)
submesh = SubMesh(mesh, cf, 1)
logPERIODIC('submesh', submesh)
logPERIODIC('submesh.mpi_comm().size', submesh.mpi_comm().size)
logPERIODIC('distributing submesh')
dsubmesh = distribute_mesh(submesh)
return(dsubmesh)
def local_refine(mesh, center, r):
xc, yc = center
cell_markers = MeshFunction("bool", mesh, mesh.topology().dim())
for c in cells(mesh):
mp = c.midpoint()
cell_markers[c] = sqrt((mp[0] - xc) * (mp[0] - xc) + (mp[1] - yc) *
(mp[1] - yc)) < r
mesh = refine(mesh, cell_markers)
return mesh
def __init__(self, mesh, N=0):
# Define mesh parameters
self.mesh = mesh
self.cell_size = CellDiameter(mesh)
self.normal_vector = FacetNormal(mesh)
# Define measures
inner_boundary = Inner_boundary()
sub_domains = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
sub_domains.set_all(0)
inner_boundary.mark(sub_domains, 1)
self.dx = Measure("dx", domain=mesh)
self.ds = Measure("ds", domain=mesh, subdomain_data=sub_domains)
# Define function spaces
finite_element = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
self.function_space = FunctionSpace(mesh,
finite_element * finite_element)
self.function_space_split = [
self.function_space.sub(0).collapse(),
self.function_space.sub(1).collapse(),
]
def solve_wave_equation(u0, u1, u_boundary, f, domain, mesh, degree):
"""Solving the wave equation using CG-CG method.
Args:
u0: Initial data.
u1: Initial velocity.
u_boundary: Dirichlet boundary condition.
f: Right-hand side.
domain: Space-time domain.
mesh: Computational mesh.
degree: CG(degree) will be used as the finite element.
Outputs:
uh: Numerical solution.
"""
# Element
V = FunctionSpace(mesh, "CG", degree)
# Measures on the initial and terminal slice
mask = MeshFunction("size_t", mesh, mesh.topology().dim() - 1, 0)
domain.get_initial_slice().mark(mask, 1)
ends = ds(subdomain_data=mask)
# Form
g = Constant(((-1.0, 0.0), (0.0, 1.0)))
u = TrialFunction(V)
v = TestFunction(V)
a = dot(grad(v), dot(g, grad(u))) * dx
L = f * v * dx + u1 * v * ends(1)
# Assembled matrices
A = assemble(a, keep_diagonal=True)
b = assemble(L, keep_diagonal=True)
# Spatial boundary condition
bc = DirichletBC(V, u_boundary, domain.get_spatial_boundary())
bc.apply(A, b)
# Temporal boundary conditions (by hand)
(A, b) = apply_time_boundary_conditions(domain, V, u0, A, b)
# Solve
solver = LUSolver()
solver.set_operator(A)
uh = Function(V)
solver.solve(uh.vector(), b)
return uh
raise Exception("Boundary markers are not implemented yet")
# return dot(coupling_bc_expression, v) * dolfin.dss(boundary_marker)
a, L = lhs(F), rhs(F)
# Time-stepping
u_np1 = Function(V)
u_np1.rename("Temperature", "")
t = 0
# reference solution at t=0
u_ref = interpolate(u_D, V)
u_ref.rename("reference", " ")
# mark mesh w.r.t ranks
mesh_rank = MeshFunction("size_t", mesh, mesh.topology().dim())
if problem is ProblemType.NEUMANN:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 4)
else:
mesh_rank.set_all(MPI.rank(MPI.comm_world) + 0)
mesh_rank.rename("myRank", "")
# Generating output files
temperature_out = File("out/%s.pvd" % precice.get_participant_name())
ref_out = File("out/ref%s.pvd" % precice.get_participant_name())
error_out = File("out/error%s.pvd" % precice.get_participant_name())
ranks = File("out/ranks%s.pvd" % precice.get_participant_name())
# output solution and reference solution at t=0, n=0
n = 0
print('output u^%d and u_ref^%d' % (n, n))
def __init__(
self, eval_times, n=10, lx=1., ly=.1, lz=.1,
f=(0.0, 0.0, -50.), time=1., timestep=.1,
tol=1e-5, max_iter=30, rel_tol=1e-10, param_remapper=None):
"""Parameters
----------
eval_times: numpy.ndarray
Times at which evaluation (interpolation) of the solution is required.
n: int, default 10
Dimension of the grid along the smallest side of the beam
(the grid size along all other dimensions will be scaled proportionally.
lx: float, default 1.
Length of the beam along the x axis.
ly: float, default .1
Length of the beam along the y axis.
lz: float, default .1
Length of the beam along the z axis.
f: tuple or numpy.ndarray, default (0.0, 0.0, -50.)
Force per unit volume acting on the beam.
time: float, default 1.
Final time of the simulation.
timestep: float, default 1.
Time discretization step to solve the problem.
tol: float, default 1e-5
Tolerance parameter to ensure the last time step is included in the solution.
max_iter: int, default 30
Maximum iterations for the SNES solver.
rel_tol: int,
Relative tolerance for the convergence of the SNES solver.
param_remapper: object, default None
Either None (no remapping of the parameters), or a function remapping
the parameter of the problem (Young's modulus) to values suitable for the
definition of the solution.
"""
# solver parameters
self.solver = CountIt(solve)
self.solver_parameters = {
'nonlinear_solver': 'snes',
'snes_solver': {
'linear_solver': 'lu',
'line_search': 'basic',
'maximum_iterations': max_iter,
'relative_tolerance': rel_tol,
'report': False,
'error_on_nonconvergence': False}}
self.param_remapper = param_remapper
# mesh creation
self.n = n
self.lx = lx
self.ly = ly
self.lz = lz
min_len = min(lx, ly, lz)
mesh_dims = (int(n * lx / min_len), int(n * ly / min_len), int(n * lz / min_len))
self.mesh = BoxMesh(Point(0, 0, 0), Point(lx, ly, lz), *mesh_dims)
self.V = VectorFunctionSpace(self.mesh, 'Lagrange', 1)
# boundary conditions
self.left = CompiledSubDomain('near(x[0], side) && on_boundary', side=0.0)
self.right = CompiledSubDomain('near(x[0], side) && on_boundary', side=lx)
self.top = CompiledSubDomain('near(x[2], side) && on_boundary', side=lz)
self.boundaries = MeshFunction('size_t', self.mesh, self.mesh.topology().dim() - 1, 0)
self.boundaries.set_all(0)
self.left.mark(self.boundaries, 1)
self.right.mark(self.boundaries, 2)
self.top.mark(self.boundaries, 3)
self.bcs1 = DirichletBC(self.V, Constant([0.0, 0.0, 0.0]), self.boundaries, 1)
self.bcs2 = DirichletBC(self.V, Constant([0.0, 0.0, 0.0]), self.boundaries, 2)
self.bcs = [self.bcs1, self.bcs2]
# surface force
self.f = Constant(f)
self.ds = Measure('ds', domain=self.mesh, subdomain_data=self.boundaries)
# evaluation times
self.eval_times = eval_times
self.dt = timestep
self.T = time + tol
self.times = np.arange(self.dt, self.T, self.dt)
self.time = Expression('t', t=self.dt, degree=0)
class HyperelasticBeam:
"""Class implementing the solution to a hyperelastic problem on a deformable beam.
"""
def __init__(
self, eval_times, n=10, lx=1., ly=.1, lz=.1,
f=(0.0, 0.0, -50.), time=1., timestep=.1,
tol=1e-5, max_iter=30, rel_tol=1e-10, param_remapper=None):
"""Parameters
----------
eval_times: numpy.ndarray
Times at which evaluation (interpolation) of the solution is required.
n: int, default 10
Dimension of the grid along the smallest side of the beam
(the grid size along all other dimensions will be scaled proportionally.
lx: float, default 1.
Length of the beam along the x axis.
ly: float, default .1
Length of the beam along the y axis.
lz: float, default .1
Length of the beam along the z axis.
f: tuple or numpy.ndarray, default (0.0, 0.0, -50.)
Force per unit volume acting on the beam.
time: float, default 1.
Final time of the simulation.
timestep: float, default 1.
Time discretization step to solve the problem.
tol: float, default 1e-5
Tolerance parameter to ensure the last time step is included in the solution.
max_iter: int, default 30
Maximum iterations for the SNES solver.
rel_tol: int,
Relative tolerance for the convergence of the SNES solver.
param_remapper: object, default None
Either None (no remapping of the parameters), or a function remapping
the parameter of the problem (Young's modulus) to values suitable for the
definition of the solution.
"""
# solver parameters
self.solver = CountIt(solve)
self.solver_parameters = {
'nonlinear_solver': 'snes',
'snes_solver': {
'linear_solver': 'lu',
'line_search': 'basic',
'maximum_iterations': max_iter,
'relative_tolerance': rel_tol,
'report': False,
'error_on_nonconvergence': False}}
self.param_remapper = param_remapper
# mesh creation
self.n = n
self.lx = lx
self.ly = ly
self.lz = lz
min_len = min(lx, ly, lz)
mesh_dims = (int(n * lx / min_len), int(n * ly / min_len), int(n * lz / min_len))
self.mesh = BoxMesh(Point(0, 0, 0), Point(lx, ly, lz), *mesh_dims)
self.V = VectorFunctionSpace(self.mesh, 'Lagrange', 1)
# boundary conditions
self.left = CompiledSubDomain('near(x[0], side) && on_boundary', side=0.0)
self.right = CompiledSubDomain('near(x[0], side) && on_boundary', side=lx)
self.top = CompiledSubDomain('near(x[2], side) && on_boundary', side=lz)
self.boundaries = MeshFunction('size_t', self.mesh, self.mesh.topology().dim() - 1, 0)
self.boundaries.set_all(0)
self.left.mark(self.boundaries, 1)
self.right.mark(self.boundaries, 2)
self.top.mark(self.boundaries, 3)
self.bcs1 = DirichletBC(self.V, Constant([0.0, 0.0, 0.0]), self.boundaries, 1)
self.bcs2 = DirichletBC(self.V, Constant([0.0, 0.0, 0.0]), self.boundaries, 2)
self.bcs = [self.bcs1, self.bcs2]
# surface force
self.f = Constant(f)
self.ds = Measure('ds', domain=self.mesh, subdomain_data=self.boundaries)
# evaluation times
self.eval_times = eval_times
self.dt = timestep
self.T = time + tol
self.times = np.arange(self.dt, self.T, self.dt)
self.time = Expression('t', t=self.dt, degree=0)
def _solve(self, z, x=None):
# problem variables
du = TrialFunction(self.V) # incremental displacement
v = TestFunction(self.V) # test function
u = Function(self.V) # displacement from previous iteration
# kinematics
ii = Identity(3) # identity tensor dimension 3
f = ii + grad(u) # deformation gradient
c = f.T * f # right Cauchy-Green tensor
# invariants of deformation tensors
ic = tr(c)
j = det(f)
# elasticity parameters
if type(z) in [list, np.ndarray]:
param = self.param_remapper(z[0]) if self.param_remapper is not None else z[0]
else:
param = self.param_remapper(z) if self.param_remapper is not None else z
e_var = variable(Constant(param)) # Young's modulus
nu = Constant(.3) # Shear modulus (Lamè's second parameter)
mu, lmbda = e_var / (2 * (1 + nu)), e_var * nu / ((1 + nu) * (1 - 2 * nu))
# strain energy density, total potential energy
psi = (mu / 2) * (ic - 3) - mu * ln(j) + (lmbda / 2) * (ln(j)) ** 2
pi = psi * dx - self.time * dot(self.f, u) * self.ds(3)
ff = derivative(pi, u, v) # compute first variation of pi
jj = derivative(ff, u, du) # compute jacobian of f
# solving
if x is not None:
numeric_evals = np.zeros(shape=(x.shape[1], len(self.times)))
evals = np.zeros(shape=(x.shape[1], len(self.eval_times)))
else:
numeric_evals = None
evals = None
for it, t in enumerate(self.times):
self.time.t = t
self.solver(ff == 0, u, self.bcs, J=jj, bcs=self.bcs, solver_parameters=self.solver_parameters)
if x is not None:
numeric_evals[:, it] = np.log(np.array([-u(x_)[2] for x_ in x.T]).T)
# time-interpolation
if x is not None:
for i in range(evals.shape[0]):
evals[i, :] = np.interp(self.eval_times, self.times, numeric_evals[i, :])
return (evals, u) if x is not None else u
def __call__(self, z, x, reshape=True, retall=False):
"""Solves the equation for the provided parameter `z` and returns the evaluation
for each one of the nodes in `x` and each evaluation time instant (passed at creation).
Parameters
----------
z : float or numpy.ndarray
Value of the parameter (Young's modulus); if `z` is a vector, it has to have
only one cell (the rest will not be considered).
x : numpy.ndarray
Matrix containing the coordinates of the points at which the solution has to be evaluated
(one column per each point).
reshape : bool, default True
If `reshape` is set to True, then the results of the evaluations at different time points will
be concatenated into a single vector, otherwise they are returned as a matrix whose columns
correspond to values at different evaluation timesteps.
retall : bool, default False
If set to True, then also the solution at the last computed time step is returned.
Returns
-------
numpy.ndarray or (numpy.ndarray, object)
The vector or matrix of evaluation and additionally the FEniCS solution object
(if `retall` was set to true).
"""
evals, u = self._solve(z, x)
evals = evals.flatten() if reshape else evals
return (evals, u) if retall else evals
def plot(self, z):
"""Solves the problem and then plots the beam with a colormap corresponding to the displacement.
Parameters
----------
z : float or numpy.ndarray
Value of the parameter (Young's modulus); if `z` is a vector, it has to have
only one cell (the rest will not be considered).
"""
u = self._solve(z)
vplot(u)
E[0] = 1. # macroscopic value
E = Constant(E)
if dim == 2:
mesh = UnitSquareMesh(*N) # generation of mesh
inclusion = Inclusion_2d()
point0 = "near(x[0], 0) && near(x[1], 0)"
elif dim == 3:
mesh = UnitCubeMesh(*N) # generation of mesh
inclusion = Inclusion_3d()
point0 = "near(x[0], 0) && near(x[1], 0) && near(x[2], 0)"
V = FunctionSpace(mesh, "CG", order, constrained_domain=PeriodicBoundary(dim))
# setting the elements that lies in inclusion and in matrix phase
domains = MeshFunction("size_t", mesh, dim)
domains.set_all(0)
inclusion.mark(domains, 1)
dx = Measure('dx', subdomain_data=domains)
def bilf(up, vp): # bilinear form
return inner(mat * up, vp) * dx(0) + inner(inc * up, vp) * dx(1)
bc0 = DirichletBC(V, Constant(0.), point0, method='pointwise')
# SOLVER
u = TrialFunction(V)
v = TestFunction(V)
uE = Function(V)
def compute_potential_flow(self):
class Hole(SubDomain):
def inside(s, x, on_boundary):
return on_boundary and self.boundary_fnc(x)
#class ActiveArea(SubDomain):
# def inside(self, x, on_boundary):
# return between(x[0], (0., 0.1)) and between(x[1], (0, 0.2))
# Initialize sub-domain instances
hole = Hole()
# self.activate = ActiveArea()
# Initialize mesh function for interior domains
self.domains = MeshFunction("size_t", self.mesh, 2)
self.domains.set_all(0)
# self.activate.mark(self.domains, 1)
# Initialize mesh function for boundary domains
self.boundaries = MeshFunction("size_t", self.mesh, 1)
self.boundaries.set_all(0)
hole.mark(self.boundaries, 1)
# Define new measures associated with the interior domains and
# exterior boundaries
self.dx = Measure('dx', domain=self.mesh, subdomain_data=self.domains)
self.ds = Measure('ds', domain=self.mesh, subdomain_data=self.boundaries)
dx, ds = self.dx, self.ds
# Define function space and basis functions
V = FunctionSpace(self.mesh, "P", 1)
self.V_vel = V
phi = TrialFunction(V) # potential
v = TestFunction(V)
# Define Dirichlet boundary conditions at top and bottom boundaries
bcs = [fe.DirichletBC(V, 0.0, self.boundaries, 1)]
# Define input data
a0 = fe.Constant(1.0)
a1 = fe.Constant(0.01)
f_water = fe.Constant(self.water_in_flux)
# Define the reaction equation
# Define variational form
F_pot = inner(a0 * grad(phi), grad(v)) * dx - f_water * v * dx
# Separate left and right hand sides of equation
a, L = fe.lhs(F_pot), fe.rhs(F_pot)
# Solve problem
phi = fe.Function(V)
fe.solve(a == L, phi, bcs)
# Evaluate integral of normal gradient over top boundary
n = fe.FacetNormal(self.mesh)
result_flux = fe.assemble(dot(grad(phi), n) * ds(1))
# test conservation of water
expected_flux = -self.water_in_flux * fe.assemble(1 * dx)
print("relative error of conservation of water %f" % ((result_flux - expected_flux) / expected_flux))
self.phi = phi
self.flow = -grad(phi)
# Save result
output = fe.File("/tmp/potential.pvd")
output << self.phi
class DuctState:
def __init__(self):
self.mesh = None
self.vid = None
# parameters
self.water_in_flux = 0.1
self.boundary_fnc = lambda x: near(x[0], 1) and 0.3 < x[1] < 0.6
def load_mesh(self, fn):
self.mesh = Mesh(fn)
def load_video_mesh(self, nx = 30, ny = 30):
self.mesh = UnitSquareMesh(nx, ny)
def load_video(self, fn):
self.video_filename = fn
def compute_potential_flow(self):
class Hole(SubDomain):
def inside(s, x, on_boundary):
return on_boundary and self.boundary_fnc(x)
#class ActiveArea(SubDomain):
# def inside(self, x, on_boundary):
# return between(x[0], (0., 0.1)) and between(x[1], (0, 0.2))
# Initialize sub-domain instances
hole = Hole()
# self.activate = ActiveArea()
# Initialize mesh function for interior domains
self.domains = MeshFunction("size_t", self.mesh, 2)
self.domains.set_all(0)
# self.activate.mark(self.domains, 1)
# Initialize mesh function for boundary domains
self.boundaries = MeshFunction("size_t", self.mesh, 1)
self.boundaries.set_all(0)
hole.mark(self.boundaries, 1)
# Define new measures associated with the interior domains and
# exterior boundaries
self.dx = Measure('dx', domain=self.mesh, subdomain_data=self.domains)
self.ds = Measure('ds', domain=self.mesh, subdomain_data=self.boundaries)
dx, ds = self.dx, self.ds
# Define function space and basis functions
V = FunctionSpace(self.mesh, "P", 1)
self.V_vel = V
phi = TrialFunction(V) # potential
v = TestFunction(V)
# Define Dirichlet boundary conditions at top and bottom boundaries
bcs = [fe.DirichletBC(V, 0.0, self.boundaries, 1)]
# Define input data
a0 = fe.Constant(1.0)
a1 = fe.Constant(0.01)
f_water = fe.Constant(self.water_in_flux)
# Define the reaction equation
# Define variational form
F_pot = inner(a0 * grad(phi), grad(v)) * dx - f_water * v * dx
# Separate left and right hand sides of equation
a, L = fe.lhs(F_pot), fe.rhs(F_pot)
# Solve problem
phi = fe.Function(V)
fe.solve(a == L, phi, bcs)
# Evaluate integral of normal gradient over top boundary
n = fe.FacetNormal(self.mesh)
result_flux = fe.assemble(dot(grad(phi), n) * ds(1))
# test conservation of water
expected_flux = -self.water_in_flux * fe.assemble(1 * dx)
print("relative error of conservation of water %f" % ((result_flux - expected_flux) / expected_flux))
self.phi = phi
self.flow = -grad(phi)
# Save result
output = fe.File("/tmp/potential.pvd")
output << self.phi
def F_diff_conv(self, u, v, n, flow, D, s, source):
dx, ds = self.dx, self.ds
return D * inner(grad(u), grad(v)) * dx \
+ s * inner(flow, grad(u)) * v * dx \
- source * v * dx
def compute_steady_state(self):
names = {'Cl', 'Na', 'K'}
P1 = FiniteElement('P', fe.triangle, 1)
element = MixedElement([P1, P1, P1])
V = FunctionSpace(self.mesh, element)
self.V_conc = V
(u_cl, u_na, u_k) = TrialFunction(V)
(v_cl, v_na, v_k) = TestFunction(V)
assert (self.flow is not None)
n = fe.FacetNormal(self.mesh)
# F = ( self.F_diff_conv(u_cl, v_cl, n, grad(self.phi), 1. ,1., 0.)
# + self.F_diff_conv(u_na, v_na, n, grad(self.phi), 1. ,1., 0.)
# + self.F_diff_conv(u_k , v_k , n, grad(self.phi), 1. ,1., 0.) )
dx, ds = self.dx, self.ds
flow = self.flow
F = inner(grad(u_cl), grad(v_cl)) * dx \
+ inner(flow, grad(u_cl)) * v_cl * dx \
+ inner(grad(u_na), grad(v_na)) * dx \
+ inner(flow, grad(u_na)) * v_na * dx \
+ inner(grad(u_k), grad(v_k)) * dx \
+ inner(flow, grad(u_k)) * v_k * dx
a, L = fe.lhs(F), fe.rhs(F)
a_mat = fe.assemble(a)
L_vec = fe.assemble(L)
# solve
u = Function(V)
fe.solve(a_mat, u.vector(), L_vec)
u_cl, u_na, u_k = u.split()
output1 = fe.File('/tmp/steady_state_cl.pvd')
output1 << u_cl
output2 = fe.File('/tmp/steady_state_na.pvd')
output2 << u_na
output3 = fe.File('/tmp/steady_state_k.pvd')
output3 << u_k
self.u_cl = u_cl
self.u_na = u_na
self.u_k = u_k
def compute_conv_diff_reac(self, initial_condition=None):
names = {'Cl', 'Na', 'K'}
dt = 0.1
t = 0.
t_end = 1.
P1 = FiniteElement('P', fe.triangle, 3)
element = MixedElement([P1, P1, P1])
V = FunctionSpace(self.mesh, element)
self.V_conc = V
u_init = Function(V)
(u_cl, u_na, u_k) = TrialFunction(V)
(v_cl, v_na, v_k) = TestFunction(V)
if initial_condition is None:
initial_condition = Expression(("exp(-((x[0]-0.1)*(x[0]-0.1)+x[1]*x[1])/0.01)",
"exp(-((x[0]-0.12)*(x[0]-0.12)+x[1]*x[1])/0.01)",
"0."), element=element)
u_init = fe.interpolate(initial_condition, V)
u_init_cl = u_init[0]
u_init_na = u_init[1]
u_init_k = u_init[2]
assert (self.flow is not None)
n = fe.FacetNormal(self.mesh)
dx, ds = self.dx, self.ds
flow = 10 * self.flow
f_in = fe.Constant(0.00)
D = fe.Constant(0.01)
k1 = fe.Constant(0.1)
k_1 = fe.Constant(0.001)
F = (
(u_cl - u_init_cl) * v_cl * dx
+ dt * D * inner(grad(u_cl), grad(v_cl)) * dx
+ dt * inner(flow, grad(u_cl)) * v_cl * dx
+ (u_na - u_init_na) * v_na * dx
+ dt * D * inner(grad(u_na), grad(v_na)) * dx
+ dt * inner(flow, grad(u_na)) * v_na * dx
+ (u_k - u_init_k) * v_k * dx
+ dt * D * inner(grad(u_k), grad(v_k)) * dx
+ dt * inner(flow, grad(u_k)) * v_k * dx
+ f_in * v_cl * dx
+ f_in * v_na * dx
+ f_in * v_k * dx
+ dt * k1 * u_init_cl * u_init_na * v_cl * dx
+ dt * k1 * u_init_cl * u_init_na * v_na * dx
- dt * k1 * u_init_cl * u_init_na * v_k * dx
- dt * k_1 * u_init_k * v_cl * dx
- dt * k_1 * u_init_k * v_na * dx
+ dt * k_1 * u_init_k * v_k * dx
)
self.F = F
a, L = fe.lhs(F), fe.rhs(F)
a_mat = fe.assemble(a)
L_vec = fe.assemble(L)
output1 = fe.File('/tmp/cl_dyn.pvd')
output2 = fe.File('/tmp/na_dyn.pvd')
output3 = fe.File('/tmp/k_dyn.pvd')
output4 = fe.File('/tmp/all_dyn.pvd')
# solve
self.sol = []
while t < t_end:
t = t + dt
print(t)
u = Function(V)
a_mat = fe.assemble(a)
L_vec = fe.assemble(L)
fe.solve(a_mat, u.vector(), L_vec)
# NonlinearVariationalProblem(F,u)
u_init.assign(u)
u_cl, u_na, u_k = u.split()
# u_init_cl.assign(u_cl)
# u_init_na.assign(u_na)
# u_init_k.assign(u_k)
u_cl.rename("cl", "cl")
u_na.rename("na", "na")
u_k.rename("k", "k")
output1 << u_cl, t
output2 << u_na, t
output3 << u_k, t
self.sol.append((u_cl, u_na, u_k))
self.u_cl = u_cl
self.u_na = u_na
self.u_k = u_k
def compute_conv_diff_reac_video(self, initial_condition=None, video_ref=None, video_size=None):
names = {'Cl', 'K'}
P1 = FiniteElement('P', fe.triangle, 1)
element = fe.MixedElement([P1, P1])
V_single = FunctionSpace(self.mesh, P1)
V = FunctionSpace(self.mesh, element)
self.V_conc = V
# load video
video = VideoData(element=P1)
video.load_video(self.video_filename)
if( video_ref is not None and video_size is not None):
video.set_reference_frame(video_ref, video_size)
print(video)
dt = 0.05
t = 0.
t_end = 20.
u_init = Function(V)
(u_cl, u_k) = TrialFunction(V)
(v_cl, v_k) = TestFunction(V)
#u_na = video
if initial_condition is None:
#initial_condition = Expression(("f*exp(-0.5*((x[0]-a)*(x[0]-a)+(x[1]-b)*(x[1]-b))/var)/(sqrt(2*pi)*var)",
# "0."), a = 80, b= 55, var=10, f=10, pi=fe.pi, element=element)
initial_condition = Expression(("f",
"0."), a=80, b=55, var=0.1, f=0.1, pi=fe.pi, element=element)
u_init = fe.interpolate(initial_condition, V)
u_init_cl = u_init[0]
u_init_k = u_init[1]
u_init_na : VideoData= video
assert (self.flow is not None)
n = fe.FacetNormal(self.mesh)
dx, ds = self.dx, self.ds
flow = 5. * self.flow
f_in = fe.Constant(0.00)
f_in_cl = fe.Constant(-0.05)
D = fe.Constant(0.1)
C_na = fe.Constant(0.1)
k1 = fe.Constant(0.2)
k_1 = fe.Constant(0.00001)
# explicit
F = (
(u_cl - u_init_cl) * v_cl * dx
+ dt * D * inner(grad(u_cl), grad(v_cl)) * dx
+ dt * inner(flow, grad(u_cl)) * v_cl * dx
#+ (u_na - u_init_na) * v_na * dx
#+ dt * D * inner(grad(u_na), grad(v_na)) * dx
#+ dt * inner(flow, grad(u_na)) * v_na * dx
+ (u_k - u_init_k) * v_k * dx
+ dt * D * inner(grad(u_k), grad(v_k)) * dx
+ dt * inner(flow, grad(u_k)) * v_k * dx
+ f_in_cl * v_cl * dx
#+ f_in * v_na * dx
+ f_in * v_k * dx
+ dt * k1 * u_init_cl * C_na * u_init_na * v_cl * dx
#+ dt * k1 * u_init_cl * u_init_na * v_na * dx
- dt * k1 * u_init_cl * C_na * u_init_na * v_k * dx
- dt * k_1 * u_init_k * v_cl * dx
#- dt * k_1 * u_init_k * v_na * dx
+ dt * k_1 * u_init_k * v_k * dx
)
# implicit
F = (
(u_cl - u_init_cl) * v_cl * dx
+ dt * D * inner(grad(u_cl), grad(v_cl)) * dx
+ dt * inner(flow, grad(u_cl)) * v_cl * dx
# + (u_na - u_init_na) * v_na * dx
# + dt * D * inner(grad(u_na), grad(v_na)) * dx
# + dt * inner(flow, grad(u_na)) * v_na * dx
+ (u_k - u_init_k) * v_k * dx
+ dt * D * inner(grad(u_k), grad(v_k)) * dx
+ dt * inner(flow, grad(u_k)) * v_k * dx
+ f_in_cl * v_cl * dx
# + f_in * v_na * dx
+ f_in * v_k * dx
+ dt * k1 * u_cl * C_na * u_init_na * v_cl * dx
# + dt * k1 * u_init_cl * u_init_na * v_na * dx
- dt * k1 * u_cl * C_na * u_init_na * v_k * dx
- dt * k_1 * u_k * v_cl * dx
# - dt * k_1 * u_init_k * v_na * dx
+ dt * k_1 * u_k * v_k * dx
)
self.F = F
a, L = fe.lhs(F), fe.rhs(F)
a_mat = fe.assemble(a)
L_vec = fe.assemble(L)
output1 = fe.File('/tmp/cl_dyn.pvd')
output2 = fe.File('/tmp/na_dyn.pvd')
output3 = fe.File('/tmp/k_dyn.pvd')
output4 = fe.File('/tmp/all_dyn.pvd')
# solve
self.sol = []
u_na = Function(V_single)
u_na = fe.interpolate(u_init_na,V_single)
na_inflow = 0
t_plot = 0.5
t_last_plot = 0
while t < t_end:
t = t + dt
t_last_plot += dt
print(t)
u = Function(V)
u_init_na.set_time(5*t)
a_mat = fe.assemble(a)
L_vec = fe.assemble(L)
fe.solve(a_mat, u.vector(), L_vec)
# NonlinearVariationalProblem(F,u)
u_init.assign(u)
u_cl, u_k = u.split()
# u_init_cl.assign(u_cl)
# u_init_na.assign(u_na)
# u_init_k.assign(u_k)
u_na = fe.interpolate(u_init_na, V_single)
u_cl.rename("cl", "cl")
u_na.rename("na", "na")
u_k.rename("k", "k")
output1 << u_cl, t
output2 << u_na, t
output3 << u_k, t
self.sol.append((u_cl, u_na, u_k))
print( fe.assemble(u_cl*self.dx))
if t_last_plot > t_plot:
t_last_plot = 0
plt.figure(figsize=(8,16))
plt.subplot(211)
fe.plot(u_cl)
plt.subplot(212)
fe.plot(u_k)
plt.show()
self.u_cl = u_cl
#self.u_na = u_na
self.u_k = u_k
def check_conservation_law(self, sol):
dx = self.dx
ds = self.ds
total = []
out = []
for s in sol:
cl = s[0]
na = s[1]
k = s[2]
# integrate interior concentration
mass_cl = fe.assemble(cl * dx)
mass_na = fe.assemble(na * dx)
mass_k = fe.assemble(k * dx)
# integrate outflux
n = fe.FacetNormal(self.mesh)
flow = self.flow
outflux_cl = fe.assemble(cl * inner(flow, n) * ds)
outflux_na = fe.assemble(na * inner(flow, n) * ds)
outflux_k = fe.assemble(k * inner(flow, n) * ds)
total.append(mass_cl + mass_na + 2 * mass_k)
out.append(outflux_cl + outflux_na + 2 * outflux_k)
self.total_mass = total
self.outflux = out