Hi @nikrouz
I guess with artificial compressibility you refer to methods such as this one, correct?
Typically, the interface quasi-Newton methods in preCICE do an equally good job. You also find a comparison of IAC and IBQN-LS in this paper. The variants implemented in preCICE (e.g. IQN-ILS with QR filters) are an enhancement of IBQN-LS taking into account the experiences made by various people in the last 10 years.
The bigger challenge for your application will be the treatment of the moving boundary. But you already mentioned that your fluid solver has an Immersed Boundary Method implemented. So, sounds doable for me, but it remains a very challenging application depending on the original state of the balloon.
Benjamin