espresso
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espressomd
Replace Stokes sphere test
The force on the sphere should be determined by a surface integral involving the surface normal and the stress around the sphere. The consistency of that would be sufficient to show the correctnes of the boundary force
to me it's not clear how to do this. the stress is not known at the "surface" of the sphere, since this surface is not located at a LB node in general. Therefore we would have to extrapolate the stress which is not implemented. Am I missing something here? maybe @mkuron knows?
I think you should be able to calculate fluid stress times normal on all surfaces between fluid and boundary cells, sum that up, and divide by 1.5 to account for the different surface areas of spheres in the L2 and L1 metric. That will give you a slightly larger effective sphere though because you can't interpolate stress between fluid and boundary cells.
I think you should be able to calculate fluid stress times normal on all surfaces between fluid and boundary cells
How exactly can I calculate this fluid stress? I only know it on the nodes that are closest to the boundary node.
divide by 1.5 to account for the different surface areas of spheres in the L2 and L1 metric
What do you mean by that?
That will give you a slightly larger effective sphere though because you can't interpolate stress between fluid and boundary cells
Is it possible to estimate the error we would have with this calculation? If not, we can't use it for a test.
I only know it on the nodes that are closest to the boundary node.
That will have to suffice.
Is it possible to estimate the error we would have with this calculation?
It's probably a factor of (R+0.5)/R as Stokes friction is linear in R.
What do you mean by that?
An infinitely large discrete sphere has 1.5 times the surface area of an actual sphere. That may need to be accounted for when you perform the surface integral for the discrete sphere.