examples.phase.missOrientation package¶

Submodules¶

examples.phase.missOrientation.circle module¶

In this example, a phase equation is solved in one dimension with a misorientation between two solid domains. The phase equation is given by:

$\tau_{\phi} \frac{\partial \phi}{\partial t} = \alpha^2 \nabla^2 \phi + \phi ( 1 - \phi ) m_1 ( \phi , T) - 2 s \phi | \nabla \theta | - \epsilon^2 \phi | \nabla \theta |^2$

where

$m_1(\phi, T) = \phi - \frac{1}{2} - T \phi ( 1 - \phi )$

The initial conditions are:

$\phi &= 1 \qquad \forall x \\ \theta &= \begin{cases} 1 & \text{for $(x - L / 2)^2 + (y - L / 2)^2 > (L / 4)^2$} \\ 0 & \text{for $(x - L / 2)^2 + (y - L / 2)^2 \le (L / 4)^2$} \end{cases} \\ T &= 1 \qquad \forall x$

and boundary conditions $\phi = 1$ for $x = 0$ and $x = L$ .

Here the phase equation is solved with an explicit technique.

The solution is allowed to evolve for steps = 100 time steps.

>>> from builtins import range
>>> for step in range(steps):
...     phaseEq.solve(phase, dt = timeStepDuration)

The solution is compared with test data. The test data was created with a FORTRAN code written by Ryo Kobayashi for phase field modeling. The following code opens the file circle.gz extracts the data and compares it with the phase variable.

>>> import os
>>> from future.utils import text_to_native_str
>>> testData = numerix.loadtxt(os.path.splitext(__file__)[0] + text_to_native_str('.gz'))
>>> print(phase.allclose(testData))
1

examples.phase.missOrientation.mesh1D module¶

In this example a phase equation is solved in 1 dimension with a misorientation present. The phase equation is given by:

$\tau_{\phi} \frac{\partial \phi}{\partial t} = \alpha^2 \nabla^2 \phi + \phi ( 1 - \phi ) m_1 ( \phi , T) - 2 s \phi | \nabla \theta | - \epsilon^2 \phi | \nabla \theta |^2$

where

$m_1(\phi, T) = \phi - \frac{1}{2} - T \phi ( 1 - \phi )$

The initial conditions are:

$\phi &= 1 \qquad \text{for $0 \le x \le L$} \\ \theta &= \begin{cases} 1 & \text{for $0 \le x \le L/2$} \\ 0 & \text{for $L/2 < x \le L$} \end{cases} \\ T &= 1 \qquad \text{for $0 \le x \le L$}$

and boundary conditions $\phi = 1$ for $x = 0$ and $x = L$ .

Here the phase equation is solved with an explicit technique.

The solution is allowed to evolve for steps = 100 time steps.

>>> from builtins import range
>>> for step in range(steps):
...     phaseEq.solve(phase, dt = timeStepDuration)

The solution is compared with test data. The test data was created with a FORTRAN code written by Ryo Kobayashi for phase field modeling. The following code opens the file mesh1D.gz extracts the data and compares it with the theta variable.

>>> import os
>>> from future.utils import text_to_native_str
>>> testData = numerix.loadtxt(os.path.splitext(__file__)[0] + text_to_native_str('.gz'))
>>> print(phase.allclose(testData))
1

examples.phase.missOrientation.modCircle module¶

In this example a phase equation is solved in one dimension with a misorientation present. The phase equation is given by:

$\tau_{\phi} \frac{\partial \phi}{\partial t} = \alpha^2 \nabla^2 \phi + \phi ( 1 - \phi ) m_1 ( \phi , T) - 2 s \phi | \nabla \theta | - \epsilon^2 \phi | \nabla \theta |^2$

where

$m_1(\phi, T) = \phi - \frac{1}{2} - T \phi ( 1 - \phi )$

The initial conditions are:

$\phi &= 1 \qquad \forall x \\ \theta &= \begin{cases} 2 \pi / 3 & \text{for $(x - L / 2)^2 + (y - L / 2)^2 > (L / 4)^2$} \\ -2 \pi / 3 & \text{for $(x - L / 2)^2 + (y - L / 2)^2 \le (L / 4)^2$} \end{cases} \\ T &= 1 \qquad \forall x$

and boundary conditions $\phi = 1$ for $x = 0$ and $x = L$ .

Here the phase equation is solved with an explicit technique.

The solution is allowed to evolve for steps = 100 time steps.

>>> from builtins import range
>>> for step in range(steps):
...     phaseEq.solve(phase, dt = timeStepDuration)

The solution is compared with test data. The test data was created with a FORTRAN code written by Ryo Kobayashi for phase field modeling. The following code opens the file modCircle.gz extracts the data and compares it with the phase variable.

>>> import os
>>> from future.utils import text_to_native_str
>>> testData = numerix.loadtxt(os.path.splitext(__file__)[0] + text_to_native_str('.gz'))
>>> print(phase.allclose(testData))
1

examples.phase.missOrientation.test module¶

Last updated on Jun 27, 2023. Created using Sphinx 6.2.1.