def __init__(self,
X=None,
T=None,
time_steps=5,
max_time=0.4,
num_cells=25,
L=1.):
"""Initialize the objet.
Keyword Arguments:
X --- The sensor locations.
T --- The sensor measurment times.
time_steps --- How many timesteps do you want to measure.
max_time --- The maximum solution time.
num_cells --- The number of cells per dimension.
L --- The size of the computational domain.
"""
assert isinstance(num_cells, int)
self._num_cells = num_cells
assert isinstance(L, float) and L > 0.
self._dx = L / self.num_cells
self._mesh = Grid2D(dx=self.dx,
dy=self.dx,
nx=self.num_cells,
ny=self.num_cells)
self._phi = CellVariable(name='solution variable', mesh=self.mesh)
self._source = CellVariable(name='source term',
mesh=self.mesh,
hasOld=True)
self._eqX = TransientTerm() == ExplicitDiffusionTerm(
coeff=1.) + self.source
self._eqI = TransientTerm() == DiffusionTerm(coeff=1.) + self.source
self._eq = self._eqX + self._eqI
assert isinstance(max_time, float) and max_time > 0.
self._max_time = max_time
#self.max_time / time_steps #.
if X is None:
idx = range(self.num_cells**2)
else:
idx = []
x1, x2 = self.mesh.cellCenters
for x in X:
dist = (x1 - x[0])**2 + (x2 - x[1])**2
idx.append(np.argmin(dist))
self._idx = idx
if T is None:
T = np.linspace(0, self.max_time, time_steps)[1:]
self._max_time = T[-1]
self._T = T
self._dt = self.T[0] / time_steps
super(Diffusion, self).__init__(5,
len(self.T) * len(self.idx),
name='Diffusion Solver')
alpha = 0.015
temperature = 1.
dx = L / nx
mesh = Grid1D(dx=dx, nx=nx)
phase = CellVariable(name='PhaseField', mesh=mesh, value=1.)
theta = ModularVariable(name='Theta', mesh=mesh, value=1.)
theta.setValue(0., where=mesh.cellCenters[0] > L / 2.)
mPhiVar = phase - 0.5 + temperature * phase * (1 - phase)
thetaMag = theta.old.grad.mag
implicitSource = mPhiVar * (phase - (mPhiVar < 0))
implicitSource += (2 * s + epsilon**2 * thetaMag) * thetaMag
phaseEq = TransientTerm(phaseTransientCoeff) == \
ExplicitDiffusionTerm(alpha**2) \
- ImplicitSourceTerm(implicitSource) \
+ (mPhiVar > 0) * mPhiVar * phase
if __name__ == '__main__':
phaseViewer = Viewer(vars=phase)
phaseViewer.plot()
for step in range(steps):
phaseEq.solve(phase, dt=timeStepDuration)
phaseViewer.plot()
input('finished')
from fipy import CellVariable, Tri2D, TransientTerm, ExplicitDiffusionTerm, DefaultSolver, Viewer
from fipy.tools import numerix
dx = 1.
dy = 1.
nx = 10
ny = 1
valueLeft = 0.
valueRight = 1.
timeStepDuration = 0.02
mesh = Tri2D(dx, dy, nx, ny)
var = CellVariable(name="concentration", mesh=mesh, value=valueLeft)
eq = TransientTerm() == ExplicitDiffusionTerm()
solver = DefaultSolver(tolerance=1e-6, iterations=1000)
var.constrain(valueLeft, mesh.facesLeft)
var.constrain(valueRight, mesh.facesRight)
answer = numerix.array([
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 1.58508452e-07, 6.84325019e-04,
7.05111362e-02, 7.81376523e-01, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 4.99169535e-05, 1.49682805e-02, 3.82262622e-01,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 4.06838361e-06,
3.67632029e-03, 1.82227062e-01, 0.00000000e+00, 0.00000000e+00,
# Provide value for diffusion coefficient D = 1.0 # Setting boundary conditions valueLeft = 1.0 valueRight = 0.0 c.constrain(valueLeft, mesh.facesLeft) c.constrain(valueRight, mesh.facesRight) # Specifying our alpha value alpha = 0 # Defining the equation with alpha which gives us the flexibility to choose the time-stepping scheme eq = (TransientTerm() == DiffusionTerm(coeff= alpha* D) + ExplicitDiffusionTerm(coeff = (1.0 - alpha)*D)) # dt = 0.00018 should be stable for forward Euler with the default simulation conditions dt = 0.00018 # We might not want to see the output from every single timestep, so we define a stride parameter time_stride = 1 timestep = 0 run_time = 1 # We need to implement the analytical solution. We can do two solutions: 1) Full solution, 2) S.S. solution pi = numerix.pi x = mesh.cellCenters[0] t = Variable(0.0)
try:
print("\n done") #Intermediate Print Statement
viewer = VTKViewer(vars=phi,datamin=0., datamax=1.) #Changed Statement
print("\n Daemon file") #Intermediate Print Statement
except (NameError,ImportError,SystemError,TypeError):
viewer = VTKViewer(vars=phi,datamin=0., datamax=1.) #Changed Statement
viewer.plot(filename="trial.vtk") #It will only save the final vtk file. You can change the name
eqI = (TransientTerm()
== DiffusionTerm(coeff=D)
- ExponentialConvectionTerm(coeff=Teff)) # doctest: +GMSH
eqX = (TransientTerm()
== ExplicitDiffusionTerm(coeff=D)
- ExponentialConvectionTerm(coeff=Teff)) # doctest: +GMSH
steps = 1000
timeStepDuration = 1e-6
time = 0
for step in range(steps):
if step < 0 :
eqX.solve(var=phi,
dt=timeStepDuration)
else:
eqI.solve(var=phi,
dt=timeStepDuration)
time = time + timeStepDuration
if __name__ == "__main__":#Parameters to be changed are in the seciton below.
viewer.plot(filename="trial.vtk") #It will only save the final vtk file. You can change the name