[yt-users] Flux Across Surfaces

[Matthew Turk]

On Wed, Jul 30, 2014 at 4:59 PM, Matthew Turk <matthewturk at gmail.com> wrote:
> Hi Melinda,
>
> (As a quick note, we have test coverage for a few cases like this, but
> non-spherical.  The rest of my email assumes that the flux calculation
> is working as desired, but I can also attempt to set up a simple
> problem to demonstrate this from first principles, which I will put on
> my todo list.)
>
> I can think of a few things that might be going on.  The first is that
> the flux is typically computed using tri-linear interpolation, as well
> as a dot product.  This will interpolate to the barycenter of the
> triangles found through the marching cubes algorithm the velocity and
> density.  Increasing the refinement will increase this value, but
> we're still both approximating the sphere surface as a set of
> triangles, as well as taking the interpolated velocities and
> multiplying them by the area.  So the weak points:
>
>  * Interpolation
>  * Dot product of interpolated values
>  * Approximating surface
>
> One possible thing to try would be to examine the flux of "ones"
> across the surface, where the fluxing field is defined radially
> outward.  This would then give the total surface area.  So, we'd
> create three new derived fields:
>
> @derived_field(name="rad_x_vec")
> def rad_x_vec(field, data):
>     center = data.get_field_parameter("center")
>     return data["x"] - center[0]
>
> @derived_field(name="rad_y_vec")
> def rad_y_vec(field, data):
>     center = data.get_field_parameter("center")
>     return data["y"] - center[1]
>
> @derived_field(name="rad_z_vec")
> def rad_z_vec(field, data):
>     center = data.get_field_parameter("center")
>     return data["z"] - center[2]
>
> Then you can use "rad_x_vec", "rad_y_vec", "rad_z_vec" as the vector
> fields, which should point radially outward, and the "ones" field as
> the fluxing field.  This should return to you the total surface area,
> which you can then compare against 4/3 pi r**3, and see the total
> difference between the two.  That will at least indicate how different
> they are, and provide a semblance of a normalization?

Immediately, I received a message from someone else off-list, kindly
pointing out to me that I don't know how to compute the surface area
of a sphere.  I'd make a joke about aspiring to live in a
higher-dimensional space, but I'm too embarrassed.

>
> -Matt
>
> On Mon, Jul 28, 2014 at 5:13 PM, Melinda Soares-Furtado
> <msoares.physics at gmail.com> wrote:
>> I have used yt to determine the flux calculation for a region surrounding a
>> single star with a given mass loss rate. This region is right outside the
>> stellar radius (see attached). Comparing the flux calculation to the known
>> mass loss rate, I see that not all of the mass is accounted for and, what's
>> more, improved refinement of the simulation enhances this percentage,
>> however it is still below 70%. I need to calculate the flux for a region
>> surrounding a large group of stars, so simply increasing the refinement is
>> really not an option. Any suggestions as to how I can use yt for my flux
>> diagnostics in a manner that is more accurate?
>>
>> Best,
>> Melinda
>>
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