# FiPy: Example mesh20x20
# This example solves a diffusion problem and demonstrates the use of
# applying boundary condition patches.
#
# .. index:: Grid2D
#
from fipy import *
#
nx = 20
ny = nx
dx = 1.
dy = dx
L = dx * nx
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
#
# We create a :class:`~fipy.variables.cellVariable.CellVariable` and initialize it to zero:
#
phi = CellVariable(name = "solution variable",
mesh = mesh,
value = 0.)
#
# and then create a diffusion equation. This is solved by default with an
# iterative conjugate gradient solver.
#
D = 1.
eq = TransientTerm() == DiffusionTerm(coeff=D)
#
# We apply Dirichlet boundary conditions
#
valueTopLeft = 0
valueBottomRight = 1
#
# to the top-left and bottom-right corners. Neumann boundary conditions
# are automatically applied to the top-right and bottom-left corners.
#
# .. index:: FixedValue
#
x, y = mesh.getFaceCenters()
facesTopLeft = ((mesh.getFacesLeft() & (y > L / 2))
| (mesh.getFacesTop() & (x < L / 2)))
facesBottomRight = ((mesh.getFacesRight() & (y < L / 2))
| (mesh.getFacesBottom() & (x > L / 2)))
#
BCs = (FixedValue(faces=facesTopLeft, value=valueTopLeft),
FixedValue(faces=facesBottomRight, value=valueBottomRight))
#
# We create a viewer to see the results
#
# .. index::
# module: fipy.viewers
#
viewer = Viewer(vars=phi, datamin=0., datamax=1.)
viewer.plot(filename="a.png")
#
# and solve the equation by repeatedly looping in time:
#
timeStepDuration = 10 * 0.9 * dx**2 / (2 * D)
steps = 10
for step in range(steps):
eq.solve(var=phi,
boundaryConditions=BCs,
dt=timeStepDuration)
viewer.plot(filename="b%02d.png" %step)
#
# .. image:: mesh20x20transient.*
# :width: 90%
# :align: center
#
# We can test the value of the bottom-right corner cell.
#
print numerix.allclose(phi(((L,), (0,))), valueBottomRight, atol = 1e-2)
# Expected:
## 1
#
#raw_input("Implicit transient diffusion. Press <return> to proceed...")
#
# -----
#
# We can also solve the steady-state problem directly
#
DiffusionTerm().solve(var=phi,
boundaryConditions = BCs)
viewer.plot(filename="c.png")
#
# .. image:: mesh20x20steadyState.*
# :width: 90%
# :align: center
#
# and test the value of the bottom-right corner cell.
#
print numerix.allclose(phi(((L,), (0,))), valueBottomRight, atol = 1e-2)
/home/ondrej/ext/femhub-0.9.9-debian32/local/lib/python2.6/site-pack\ ages/FiPy-2.1-py2.6.egg/fipy/solvers/pysparse/linearPCGSolver.py:70: DeprecationWarning: PyArray_FromDimsAndDataAndDescr: use PyArray_NewFromDescr. info, iter, relres = itsolvers.pcg(A, b, x, self.tolerance, self.iterations, Assor) True True            
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