[Dune] gridcheck.cc : Integral over outer normals is not always zero.

[Aleksejs Fomins]

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Dear Martin,

Thank you for your reply. I am using a volume grid. I misunderstood the warning. The confusion came from the fact that I use curvilinear elements, not a curvilinear 2D world, so I was puzzled as of how the curvature of the elements can affect the divergence theorem, and of course it can't.

So far my normals seemed fine, I was able to calculate the integral in Gauss theorem.

I will replicate this exact normal integral test, and if it passes, I will report a bug.

Thanks,
Aleksejs


On 18/03/15 20:26, Martin Nolte wrote:
> Hi Aleksejs,
> 
> the divergence theorem only holds for volumes, not for surfaces. On a surface, the surface integral over all normals equals the integral over the mean curvature. And this is exactly what the message states: In case of a surface grid, the integral might be non-zero if the mean curvature of is nonzero.
> 
> If you encounter this message for a volume grid (i.e., a grid with dimgrid = dimworld), then something went wrong. In this case, the divergence theorem holds and, as you stated, the surface integral over all normals should be zero. Apart from a bug in your normal implementation, this might also result from an insufficient quadrature order. Would you consider filing a bug report in the latter case?
> 
> Best,
> 
> Martin
> 
> PS: I am merely the author of the warning, not of the test. Originally, the test simply failed for surface grids with element geometries of nonzero mean curvature (which is plain wrong).
> 
> On 03/18/2015 04:23 PM, Aleksejs Fomins wrote:
> Dear Dune,
> 
> When running the gridcheck.cc I notice I encounter the following warning:
> 
> -- Checking Intersection Iterator
> Warning: Integral over outer normals is not always zero.
>           This behaviour may be correct for entities with nonzero curvature.
> Warning: Integral over outer normals is not always zero.
>           This behaviour may be correct for entities with nonzero curvature.
> 
> Could the person who wrote this test please explain what this means.
> 
> I assume that this refers to the integral Int(vec{n} dS) over the surface of an element.
> If this is indeed the case, then this integral should be zero by divergence theorem.
> In particular, could you explain the case in which the integral would not be zero
> 
> Greetings,
> Aleksejs
>>
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