I'm still curious as to your opinions, if any, on the questions below.
In the Physalis method we use the the Stokes equations to transform
the no-slip boundary condition on the sphere to a surrounding
grid-conforming 'cage' of nodes. The presence of the sphere is then
communicated to the bulk flow via the extrapolated BC on the cage. So,
the task of getting Physalis to work in Gerris has two major
a) Determine the coefficients in Lamb's solution to Stokes equation on
a sphere and then evaluate the expansion on the cage. This has less to
do with Gerris and more with the Physalis idea.
b) Let Gerris know about the cage and the velocity of the points comprising it.
It seems I could define the cage as a solid and then do something like
"GfsSurfaceBc U/V/W Dirichlet VALUE_FROM_PHYSALIS". I have two
questions relating to this:
1) Are cells inside solids removed from the flow field? If so then the
cage will have to be inside the sphere (as opposed to
straddling/intersecting the spherical surface), increasing the error a
2) Gerris' discretization is 1st order near solid interfaces since
face gradients are not calculated at the center at partial faces. This
would mean the calculation near my cage is 1st order, partially
defeating the purpose of the exercise. However, it seems that 2nd
order accuracy will prevail if the cage is constructed as the union of
cell-interfaces, eliminating partial faces. Is this true?
Hope you're enjoying Paris!
Kristján Guđmundsson, Ph.D.
Physics of Fluids Group
Applied Physics Dept., Uni. of Twente