Hi, Dr. Guyer.
Thanks for the response. For the reasons you mention I have started trying
implement the two-dimensional case. I appreciate the comments and help.
As a brief comment on the issues I am working out, the two-dimensional
equation's for this problem are coupled. The two governing equations are
for (\partial w/\partial t) and (\partial \vec{u}/\partial t). The equation
for (\partial w/\partial t) involves a complicated convective term. The
coefficient inside the convective term is a 3x3 tensor (\sigma) and the
variable inside the convective term is grad(w). There is coupling that
enters in 3x3 tensor involves fairly complicated combinations of spatial
derivatives of w and the components of \vec{u}. I've written these out by
hand, but I can type these up and send them at a later time if it's
helpful.
The paper that I'm referencing use spectral methods to solve the problem. I
realize that for DiffusionTerms with a power greater than 3 the
documentation recommends spectral methods. I'm thinking this problem may be
one that needs to be solved through spectral methods.
All of this is to say, in your experience does this problem look feasible
for FiPy? I'll attach a snapshot of the equations for w and \vec{u}. A
smaller concern is actually figuring out how to write the tensor (\sigma)
in FiPy.
Looking forward to hearing more.
Cheers,
Kyle.
On Tue, Feb 10, 2015 at 1:48 PM, Guyer, Jonathan E. Dr. <
[email protected]> wrote:
> I understand what you mean about it being simpler, but I tend not to work
> in 1D, because it can be misleading. You've got combinations of even-order
> and odd-order terms that don't make much sense to me if you think about
> them in higher dimensions. Using \nabla instead of (\partial / \partial x)
> makes it a bit clearer whether you're working with vectors or scalars.
>
> If u and w are scalars, then (\partial u/partial x) is a vector and it
> doesn't make any sense to add (\partial^4 w\partial x^4), a scalar, to
> (\partial u/\partial x)(\partial^2 w / \partial x^2), a vector.
>
>
> On Feb 10, 2015, at 12:20 AM, Kyle Briton Lawlor <[email protected]>
> wrote:
>
> > Hello, FiPy.
> >
> > I am presently working with a set of coupled 1D pde’s.
> > Images with the equations are attached at the bottom of the email.
> > The first image shows the equations.
> > The second image shows the equations with a “sketch” of how I might
> write the terms in FiPy and some questions I have.
> >
> > Roughly, the equations are solving for displacements of a line subject
> to compressive stress.
> > Eventually I would like to model the two-dimensional problem.
> > However, I figure 1D is a good starting point as the 1D eq’s are quite
> complicated themselves.
> > Hopefully it is feasible to solve the 1D problem in FiPy.
> > In the paper I’m referencing for these evolution equations, they solve
> using a finite difference method.
> >
> > The two main variables in the problem as you can see in the pde’s are w
> and u.
> > w is the lateral displacement and u is the on-axis displacement.
> > As you can see in the equations, there are quite complicated
> coefficients on a few of the terms.
> > Also there are two terms in particular that I am not sure how to write.
> (See the second image; Term 1 and Term 2).
> >
> > I have not started coding up this problem, but I think some preliminary
> guidance could be useful.
> > This is a broad question but is solving these equations with FiPy
> feasible?
> >
> > Look forward to hearing responses.
> >
> > Thanks,
> > Kyle
> > <Screen Shot 2015-02-09 at 11.59.39 PM.png>
> > <Screen Shot 2015-02-09 at 11.59.58 PM.png>
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