# Re: how to compute interface velocity in examples.phase.anisotropy?

Hi Drew,

The velocity vector is the velocity magnitude multiplied by the
normal. The normal is the gradient over the gradient magnitude so,

\vec{v} = \frac{\nabla \phi}{\nabla \phi \cdot \nabla \phi}
\frac{\partial \phi}{\partial t}

In Fipy you can get the gradient and gradient magnitude with the
example,
https://www.ctcms.nist.gov/fipy/examples/phase/generated/examples.phase.impingement.mesh40x1.html,

Cheers,

Daniel

On Tue, Apr 3, 2018 at 4:55 PM, Drew Davidson <davidson...@gmail.com> wrote:
> Hello,
>
> I was just looking at:
>
> Boettinger, W. J., J. A. Warren, C. Beckermann, and A. Karma. “Phase-Field
> Simulation of Solidification.” Annual Review of Materials Research 32, no. 1
> (August 1, 2002): 163–94.
> https://doi.org/10.1146/annurev.matsci.32.101901.155803.
>
> and maybe Equation 27 is the way to compute interface velocity in
> examples.phase.anisotropy:
>
> v = -\frac{1}{\| \nabla \phi \|}\frac{\partial \phi}{\partial t}
>
> Then it remains to express the right hand side of that equation in the FiPy
> language.  It does look like this only gives the velocity magnitude rather
> than the velocity vector.
>
>
> On Tue, Apr 3, 2018 at 12:27 PM, Drew Davidson <davidson...@gmail.com>
> wrote:
>>
>> Hello,
>>
>> In FiPy, how would one calculate the interface velocity at a given time
>> step in examples.phase.anisotropy?
>>
>> At this time, I was mostly interested in the max and min of the magnitude
>> of the interface velocity.
>>
>> Thanks
>
>
>
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--
Daniel Wheeler

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