Hi everybody

I am trying to model the propagation of a free surface based on an
Pseudo-concentration approach. In this way I need to solve the Stokes
equations in the whole domain for every time step, the properties of the
fluid are determined depending on the value of the
saturation/pseudo-concentration function. My first question deals with
the reinitialization of this function to avoid distortion of the
propagating front. I need to be able to get the value of the saturation
variable on a mesh node plus the value of the satuartion for the
surrounding nodes; namely the patch of elements centered (I am using a
grid aligned with the global axis) at the given node and the position of
these nodes so that I can compute the distance from the assumed contour
where the  free surface is located. So is there a functionality in
deal.II to do that?If not has anyone a suggestion of how I can do that?
The second question deals with the implementation of the boundary
conditions on solid boundaries. In general I need to be able to impose
full vanishing velocity vector only when the pseudo concentration at
this point indicates full saturation and apply free traction when the
saturation indicates the presence of pseudo-fluid. Does anyone have any
suggestion how can I do that?Obviously these boundary conditions need to
be adjusted with respect to time  somehow.
Thanks in advance and all the best
Alex

PS:It would have been good if I could solve only on the saturated domain
since this would save plenty of computation time can this be implemented
in deal.II?To start with, I am guessing that either a  global matrix
needs to be assembled at every time step which I am guessing that would
imply dynamically adapted global matrix or an ability to extract only
the relevant dofs from the once generated global matrix and solve only
for these dofs. But how these will constitute a well posed problem?

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