On Apr 7, 2006, at 12:46 PM, Zhiheng Huang wrote:
Could anyone of you answer my questions in the attached
QFiPy060407.pdf?
(1) What is \theta in the equation \Phi = \tan(\theta/2 + (N/2)
arctan\psi)?
\theta is the grain orientation. Taken to be zero in this single-
grain problem. For any questions of mathematical notation, please see
the paper cited at the beginning of the chapter:
James A. Warren, Ryo Kobayashi, Alexander E. Lobkovsky, and W. Craig
Carter, “Extending Phase
Field Models of Solidification to Polycrystalline Materials”. Acta
Materialia, 51(20), (2003) 6035–6058,
URL http://dx.doi.org/10.1016/S1359-6454(03)00388-4 31, 59
(2) ... dbdpsi=-N*2*Phi/(1+PhiSq), I do not know whether dbdpsi is
equal to \Phi_\psi?
dbdpsi = d \beta / d \psi = \beta_\psi
(3) On page 34, it is clearly stated that "ExplicitDiffusionTerm is
provided only for
illustrative purposes", but why on page 67, the diffusion term in
phaseEq is
constructed using the "ExplicitDiffusionTerm"?
In order to have a reliable benchmark, Daniel wrote this example to
give exact numerical correspondence with Ryo Kobayashi's FORTRAN
code. We don't know why Ryo made this particular term explicit. This
choice on our part isn't ideal for exactly the reason you raise; we
recommend the one, but then use the other. I guess I can only offer
my parents' response to me as a child: "Do as we say, not as we do".
Would the result be the same if using
the "ImplictDiffusionTerm" instead?
Not exactly the same, but it should be consistent. In general, we
certainly recommend the ImplicitDiffusionTerm.
(4) On page 34, when constructing the implicit source term, why is
it necessary to test
whether mVar is greater than zero or less than zero? In the case
of mVar < 0, how the
ImplicitSourceTerm in the program could match \nabla A \nabla \zeta
+ \phi(1-\phi)m ?
Have you worked through Example 9.1 examples.phase.simple.input ? The
rationale for exactly how to linearize a source is discussed there.
Let us know if we can further clear things up.
(5) I wish to see the dendritic growth and therefore, I have
changed the parameters as
requested on page 65, i.e. numberOfCells=500, steps=10000,
radius=dx*5.,
seedCenter=(0.,0,), initialTemperature=-0.5. The program is
attached. The program
runs slowly as expected but why I could not see any structure even
after 155 steps?
I don't recall how many steps it takes, but quite a few. There is no
explicit noise in this problem, only the noise resulting from the
discreteness of the mesh, so it takes a while for branching to be
observable.
--
Jonathan E. Guyer, PhD
Metallurgy Division
National Institute of Standards and Technology
<http://www.metallurgy.nist.gov/>
