def _plot(self):
var = self.vars[0]
mesh = var.mesh
U, V = var.numericValue
U = numerix.take(U, self.indices)
V = numerix.take(V, self.indices)
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag, ),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, datamax, mag)
mag = numerix.ma.masked_array(mag, mag < datamin)
if self.log:
mag = numerix.log10(mag)
mag = numerix.ma.masked_array(mag, numerix.isnan(mag))
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
self._quiver.set_UVC(U, V)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def _plot(self):
var = self.vars[0]
mesh = var.mesh
U, V = var.numericValue
U = numerix.take(U, self.indices)
V = numerix.take(V, self.indices)
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag,),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, datamax, mag)
mag = numerix.ma.masked_array(mag, mag < datamin)
if self.log:
mag = numerix.log10(mag)
mag = numerix.ma.masked_array(mag, numerix.isnan(mag))
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
self._quiver.set_UVC(U, V)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def _plot(self):
from scipy.interpolate import griddata
var = self.vars[0]
mesh = var.mesh
xmin, ymin = mesh.extents['min']
xmax, ymax = mesh.extents['max']
N = 100
X = numerix.linspace(xmin, xmax, N)
Y = numerix.linspace(ymin, ymax, N)
grid_x, grid_y = numerix.mgrid[xmin:xmax:N * 1j, ymin:ymax:N * 1j]
if isinstance(var, FaceVariable):
C = mesh.faceCenters
elif isinstance(var, CellVariable):
C = mesh.cellCenters
U = griddata(C.value.T, var.value[0], (grid_x, grid_y), method='cubic')
V = griddata(C.value.T, var.value[1], (grid_x, grid_y), method='cubic')
lw = self.linewidth
if isinstance(lw, (FaceVariable, CellVariable)):
lw = griddata(C.value.T,
lw.value, (grid_x, grid_y),
method='cubic')
color = self.color
if isinstance(color, (FaceVariable, CellVariable)):
color = griddata(C.value.T,
color.value, (grid_x, grid_y),
method='cubic',
fill_value=color.min())
U = U.T
V = V.T
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag, ),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, numerix.nan, mag)
mag = numerix.where(mag < datamin, numerix.nan, mag)
if self.log:
mag = numerix.log10(mag)
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
# if self._stream is not None:
# # the following doesn't work, nor does it help to `add_collection` first
# # self._stream.arrows.remove()
# self._stream.lines.remove()
self.axes.cla()
self._stream = self.axes.streamplot(X,
Y,
U,
V,
linewidth=lw,
color=color,
**self.kwargs)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
mesh=mesh,
value=initialTemperature,
hasOld=1
)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1.+ c * beta) * betaPsi
D = alpha**2 * (1.+ c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis = 1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
phaseEq = TransientTerm(tau) == ExplicitDiffusionTerm(D) + \
ImplicitSourceTerm(mVar * ((mVar < 0) - phase)) + \
((mVar > 0.) * mVar * phase + anisotropySource)
def arctan2(self, other):
return self._BinaryOperatorVariable(lambda a,b: numerix.arctan2(a,b), other)
temperature = CellVariable(name='temperature',
mesh=mesh,
value=initialTemperature,
hasOld=1)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1. + c * beta) * betaPsi
D = alpha**2 * (1. + c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis=1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
phaseEq = TransientTerm(tau) == ExplicitDiffusionTerm(D) + \
ImplicitSourceTerm(mVar * ((mVar < 0) - phase)) + \
((mVar > 0.) * mVar * phase + anisotropySource)
def make_tau(phase_):
theta_cell = numerix.arctan2(phase_.grad[1], phase_.grad[0])
a_cell = 1 + epsilon_m * numerix.cos(mm * theta_cell + theta_0)
return tau_0 * a_cell**2
initialize()
def make_tau(phase_):
theta_cell = numerix.arctan2(phase_.grad[1], phase_.grad[0])
a_cell = 1 + epsilon_m * numerix.cos(mm * theta_cell + theta_0)
return tau_0 * a_cell**2
tau = make_tau(phase)
tau_old = make_tau(phase.old)
source = (phase - lamda * uu * (1 - phase**2)) * (1 - phase**2)
theta = numerix.arctan2(phase.faceGrad[1], phase.faceGrad[0])
W = W_0 * (1 + epsilon_m * numerix.cos(mm * theta - theta_0))
W_theta = - W_0 * mm * epsilon_m * numerix.sin(mm * theta - theta_0)
# Build up the diffusivity matrix
I0 = Variable(value=((1,0), (0,1)))
I1 = Variable(value=((0,-1), (1,0)))
Dphase = W**2 * I0 + W * W_theta * I1
heat_eqn = TransientTerm() == DiffusionTerm(DD) + (phase - phase.old) / dt / 2.
phase_eqn = TransientTerm(tau) == DiffusionTerm(Dphase) + source
initialize()
