Hello, following the manual, at the first example with the 1D diffusion, I have
tried to make the python script for this (python2.7) and I get a missing name,
which is not defined in the example at all.
This is the name "cell", which appears on p 58 in the manual.
Please see this code which describes this example:
Thanks!
#Python script for solving a Partial Differential Equation in a diffusion case
from fipy import *
nx = 50
dx = 1
mesh = Grid1D(nx=nx, dx=dx)
phi = CellVariable(name="Solution variable",
mesh=mesh,
value=0.)
#We'll use the coefficient set to D=1
D=1
# We give then 2000 time-steps for the computation, which is defined by 90
percent of the maximum stable timestep, which is given
timeStepDuration = 0.9 * dx**2 / (2 * D)
steps = 2000
#Then we define the boundary conditions
valueLeft = 1
valueRight = 0
#The boundary conditions are represented as faces around the exterior of the
mesh, so we define the constraint by the given values on the left and right
side of the boundary using the phi.constrain() command
phi.constrain(valueLeft, mesh.facesRight)
phi.constrain(valueRight, mesh.facesLeft)
# We can also omit giving boundary conditions, then the default bc is
equivalent to a zero gradient.
#At this stage we define the partial differential equation as a numerical
problem to be solved
for step in range(steps):
for j in range(cells):
phi_new[j] = phi_old[j] \
+ (D * dt / dx**2) * (phi_old[j+1] - 2 * phi_old[j] + phi_old[j-1])
time += dt
#and additional code for the boundary conditions
eqX = TransientTerm() == ExplicitDiffusionTerm(coeff=D)
#We then want to view the results of the calculation and use the command
Viewer() for this
phiAnalytical = CellVariable(name="analytical value",
mesh=mesh)
if __name__ == '__main__':
viewer = Viewer(vars=(phi, phiAnalytical),
datamin=0., datamax=1.)
viewer.plot()
#If we have a semi-infinite domain, then the solution for this PDE is
phi=1-erf(x/2(Dt)^(0.5)). This requires to import SciPy library, so we import
that.
x = mesh.cellCenters[0]
t = timeStepDuration * steps
try:
from scipy.special import erf
phiAnalytical.setValue(1-erf(x / (2 * numerix.sqrt(D * t))))
except ImportError:
print ("The Scipy Library is not avaliable to test the solution to the given
trasient diffusion equation")
# The equation is then solved by repeatedly looping
for step in range(steps):
eqX.solve(var=phi,
dt=timeStepDuration)
if __name__ == '__main__':
viewer.plot()
print (phi.allclose(phiAnalytical, atol = 7e-4))
1
if __name__ == '__main__':
raw_input("Explicit transient diffusion. Press <return> to proceed...")
_______________________________________________
fipy mailing list
[email protected]
http://www.ctcms.nist.gov/fipy
[ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
