Re: CylindricalGrid1D mesh volumes

[Daniel Wheeler]

On Wed, Jan 15, 2020 at 4:21 AM Pavel Aleynikov
 wrote:
>
> Hi,
>
> How are "mesh.cellVolumes" defined in fp.CylindricalGrid1D case?
> The surface of a circle grid is not equal pi*r^2.
>
> import fipy as fp
> L= 1.; nx   = 1000
> mesh = fp.CylindricalGrid1D(dx=L/nx, nx=nx)
> print(mesh.cellVolumes.sum())
> >> 0.5
>
> Why not pi?

I'm not sure. It's an arbitrary choice though. The angle was chosen as
"1" rather than "2 * pi". The volume of an element is "theta * r * dr"
where "theta" is the
angle, "r" are the cell centers and "dr" is the cell spacing. It's
possible that by choosing "theta=1", then the "theta" can be omitted
saving an extra operation.

> How should I integrate Variables on such a grid? 
> (2*pi*Var*mesh.cellVolumes).sum()?

Makes sense. Argulably, these quantities should be calculated in some
sort of ratio so the absolute value of the volume won't matter.

-- 
Daniel Wheeler
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CylindricalGrid1D mesh volumes

[Pavel Aleynikov]

Hi, 

How are "mesh.cellVolumes" defined in fp.CylindricalGrid1D case? 
The surface of a circle grid is not equal pi*r^2. 

import fipy as fp
L= 1.; nx   = 1000 
mesh = fp.CylindricalGrid1D(dx=L/nx, nx=nx)
print(mesh.cellVolumes.sum())
>> 0.5  

Why not pi?
How should I integrate Variables on such a grid? 
(2*pi*Var*mesh.cellVolumes).sum()?

Thank you,
Pavel

PS. The solution of a diffusion equation on the CylindricalGrid1D seems fine, 
i.e. it converges to Bessel J_0 eigenvalue fairly well.

PPS. I've accidentally sent this message from an unregistered email first and 
the cancelation link in the autoreply does not work. So, sorry if this is the 
duplicate. 
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