Dear Daniel, I am wondering if you can clarify a small. thing.
In the given script, phi is set as e^ix, and the numerical simulation treats
the given PDE. Is phi tested for wether it is a result of the given PDE in this
script ? Or does the script do something else?
#!/usr/bin/env python
# testing a non-complex variant of the NLSE
import numpy
import cmath as math
from fipy import *
from fipy import numerix
nx = 50
dx = 1. / float(nx)
mesh = Grid1D(nx=nx,dx=dx)
X = mesh.cellCenters[0]
phi = CellVariable(mesh=mesh, name="Solution")
phi.setValue(0.5-0.5*numerix.exp((1j*X)))
vi = Viewer(vars=phi,datamin=0.0, datamax=1.0)
vi.plot()
raw_input("Initialization ...")
phi.constrain(1., mesh.facesLeft)
phi.constrain(0., mesh.facesRight)
phi_sq = CellVariable(mesh=mesh)
phi_sq.setValue( phi*phi )
#We now represent the equation, where u = phi, du/dt + d^2u/dx^2 + u^2 = 0 in
fipy commands. du/dx : is a convection term with a unit scalar coefficient,
i.e. <SpecificConvectionTerm>(coeff=(1.,), var=u) ,
# du/dt : is a transient term that one can treat as before, i.e.
TransientTerm(var=u). one can add a second order derivative as
ExplicitDiffusionTerm(coeff=D)
eq = TransientTerm(coeff=1., var=phi) + ExponentialConvectionTerm(coeff=(1.,),
var=phi) + abs((phi_sq))*(phi) == 0.0
dt = 0.01
steps = 100
for step in range(steps):
eq.sweep(dt=dt)
#
phi_sq.setValue( phi * phi )
#
vi.plot()
phiAnalytical = CellVariable(name="Analytical value",
mesh=mesh)
vi = Viewer(vars=(phi, phiAnalytical))
vi.plot()
raw_input("Press <return> ...")
Thanks!
Sergio Manzetti
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From: "Daniel Wheeler" <[email protected]>
To: "fipy" <[email protected]>
Sent: Friday, May 19, 2017 5:41:56 PM
Subject: Re: Complex conjugates in FiPY
On Thu, May 18, 2017 at 9:23 AM, Sergio Manzetti
<[email protected]> wrote:
>
> Hello, in the manual on p 318 it gives an example of including the complex
> conjugate in a fipy script, however this does not seem to work when including
> the complex conjugate in the actual PDE given.
Can you link to the example on the webpage?
http://www.ctcms.nist.gov/fipy/documentation/manual.html
> Can fiPy include complex conjugate in a PDE, such as
>
> u_x + i*u_y = 0
>
> ?
No, it can't. Sorry about that. It would be great functionality, but
never implemented.
--
Daniel Wheeler
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