On Tue, Jun 11, 2013 at 9:52 AM, Kundar <[email protected]> wrote:
> ** > Dear fipy users, > > I cooks my fourth order diffusion term as: > DiffusionTerm(coeff=(Gamma1, Gamma2)) > where Gamma1 and Gamma2 are tensors, or Gamma1 is a tensor and Gamma2 is > a scalar. > When I throw it into fipy, it runs. As the manual says that it does not > support the anisotropic high order terms, I'm wondering whether the result > is reliable or fake. > Thanks for your email. I wrote this part of the code and I am only sure that the anisotropic terms are correct for regular diffusion (not higher order diffusion). I have never tried running a problem with the higher order (biharmonic terms) and anisotropy. When I wrote this I had the feeling that something was being overlooked, but I can't remember now. I think the only sensible way forward it to devise a few test cases and check the solution carefully (if you come up with some tests and FiPy doesn't work then I will try and fix it if possible). > How to check the accuracy? > If the above representation is incorrect, please show me an > alterantive method in fipy, or help me to put this fourth order diffusion > term into a right form. Thank you very much. > An alternative way is to just use coupled equations in FiPy with anisotropy, but I can't be sure that anisotropy and coupled equations works either, it is untried. If you are unsure about coupling equations, see http://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.polyxtalCoupled.htmland and http://www.ctcms.nist.gov/fipy/examples/cahnHilliard/generated/examples.cahnHilliard.mesh2DCoupled.html The coupled code and the higher order code should give the same results though if FiPy is internally consistent. You (me or someone) needs to come up with some nice test cases. Do you know of any papers with test cases for this? -- Daniel Wheeler
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