examples.phase.missOrientation.modCircle

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

$${\tau }_{\varphi }\frac{\partial \varphi }{\partial t}={\alpha }^2{\mathrm{\nabla }}^2\varphi +\varphi (1-\varphi )m_1(\varphi ,T)-2s\varphi |\mathrm{\nabla }\theta |-{ϵ}^2\varphi |\mathrm{\nabla }\theta {|}^2$$

where

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

The initial conditions are:

$$\begin{array}{rl}\varphi & =1\mathrm{\forall }x\\ \theta & =\{\begin{array}{ll}2\pi /3& \text{for }(x-L/2{)}^2+(y-L/2{)}^2>(L/4{)}^2\\ -2\pi /3& \text{for }(x-L/2{)}^2+(y-L/2{)}^2\le (L/4{)}^2\end{array}\\ T& =1\mathrm{\forall }x\end{array}$$

and boundary conditions $\varphi =1$ 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))
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Last updated on Feb 06, 2025. Created using Sphinx 7.1.2.