Dear all,
I am trying to solve the Navier Stokes equations for this problem: there is a 2d box with a circular inclusion. Within the circle there is a fluid (A), and between the circle boundary and the box boundary lives another fluid (B). For A, I impose boundary conditions for the traction, i.e. that on the disk
\sigma^A_{ij} n_j = \sigma^B_{ij} n_j
where \sigma^{A,B} are the stress tensors and n the unit normal to the circle. Here, I allow for the disk to deform and move with ALE. I can give you more details if needed.
I solve by using the IPCS splitting scheme with Crank Nicholson approximation for the convective term, for both fluids. It runs, but it is not quite stable.
I solved for similar problems, with the same scheme, where the disk was not filled with a fluid, but with a rigid or elastic body, for which this method is stable.
So I wonder: Is there a problem using this scheme for the inner fluid? Is there a more suited scheme that I can try here?